Session Q2: Invited Session: Manipulating Spin Waves

Magnons, Spin Current and Spin Seebeck Effect

When metals and semiconductors are placed in a temperature gradient, the electric voltage is generated. This mechanism to convert heat into electricity, the so-called Seebeck effect, has attracted much attention recently as the mechanism for utilizing wasted heat energy. [1]. Ferromagnetic insulators are good conductors of spin current, i.e., the flow of electron spins [2]. When they are placed in a temperature gradient, generated are magnons, spin current and the spin voltage [3], i.e., spin accumulation. Once the spin voltage is converted into the electric voltage by inverse spin Hall effect in attached metal films such as Pt, the electric voltage is obtained from heat energy [4-5]. This is called the spin Seebeck effect. Here, we present the linear-response theory of spin Seebeck effect based on the fluctuation-dissipation theorem [6-8] and discuss a variety of the devices. \\[4pt] [1] S. Maekawa et al, \textit{Physics of Transition Metal Oxides} (Springer, 2004). \\[0pt] [2] S. Maekawa: Nature Materials \textbf{\textit{8}}, 777 (2009). \\[0pt] [3] \textit{Concept in Spin Electronics}, eds. S. Maekawa (Oxford University Press, 2006). \\[0pt] [4] K. Uchida et al., Nature \textbf{\textit{455}}, 778 (2008). \\[0pt] [5] K. Uchida et al., Nature Materials \textbf{\textit{9}}, 894 (2010) \\[0pt] [6] H. Adachi et al., APL \textbf{\textit{97}}, 252506 (2010) and Phys. Rev. B \textbf{\textit{83}}, 094410 (2011). \\[0pt] [7] J. Ohe et al., Phys. Rev. B (2011) \\[0pt] [8] K. Uchida et al., Appl. Phys. Lett. \textbf{\textit{97}}, 104419 (2010).   

Spin Wave Transport in Microscopic Magnetic Structures

The coherent transport of spin information is one of the great challenges in condensed matter physics and is of fundamental importance for the development of spintronic devices. Spin waves carry angular momentum and can be utilized to transport spin information over distances much larger than the spin diffusion length in metals. Recent experiments showing that spin waves can be manipulated via spin currents and vice versa due to spin torque, spin pumping, spin Hall and spin Seebeck effects have drawn great attention to the transport properties of spin waves. Fundamental topics are spin-wave propagation characteristics in microstructures with reduced dimensionality\footnote{H. Schultheiss, S. Sch\"afer, P. Candeloro, B. Leven, B. Hillebrands, and A. N. Slavin, Phys. Rev. Lett. \textbf{100}, 047204 (2008).}$^{,}$\footnote{K. Vogt, H. Schultheiss, S. J. Hermsdoerfer, P. Pirro, A. A. Serga, and B. Hillebrands, Appl. Phys. Lett. \textbf{95} 182508 (2009)}, realization of spin-wave transport in two-dimensional waveguides, including directional changes along the spin-wave propagation path\footnote{P. Clausen, K. Vogt, H. Schultheiss, S. Sch\"afer, B. Obry, G. Wolf, P. Pirro, B. Leven, and B. Hillebrands, Appl. Phys. Lett. \textbf{99}, 162505 (2011)}, and the effect of nonlinear damping mechanisms when spin waves are spatially confined in microstructures. We use phase- and time-resolved Brillouin light scattering microscopy to address these topics in micron-sized spin-wave conduits made from permalloy. These experiments allow us to develop a simple model for calculating dispersion relations in spin-wave conduits. This model can be applied to understand how spin waves are transported in conduits with broken translation symmetry and how nonlinear damping via four-magnon-scattering is enhanced due to spatial confinement.   

Using magnons to probe spintronic materials properties

For many spin-based electronic devices, from the read sensors in modern hard disk drives to future spintronic logic concepts, the device physics originates in spin polarized currents in ferromagnetic metals. In this talk, I will describe a novel ``Spin Wave Doppler'' method that uses the interaction of spin waves with spin-polarized currents to determine the spin drift velocity and the spin current polarization [1]. Owing to differences between the band structures of majority-spin and minority-spin electrons, the electrical current also carries an angular momentum current and magnetic moment current. Passing these coupled currents though a magnetic wire changes the linear excitations of the magnetization, i.e spin waves. Interestingly, the excitations can be described as drifting ``downstream'' with the electron flow. We measure this drift velocity by monitoring the spin-wave-mediated transmission between pairs of periodically patterned antennas on magnetic wires as a function of current density in the wire. The transmission frequency resonance shifts by 2$\pi \Delta $f = \textbf{v\textbullet k} where the drift velocity $v$ is proportional to both the current density and the current polarization $P$. I will discuss measurements of the spin polarization of the current in Ni$_{80}$Fe$_{20}$ [2], and novel alloys (CoFe)$_{1-x}$Ga$_{x}$ [3] and (Ni$_{80}$Fe$_{20})_{1-x}$Gd$_{x}$ [4]. \\[4pt] [1] V. Vlaminck and M. Bailleul, Science, \textbf{322}, 410 (2008) \\[0pt] [2] M. Zhu, C. L. Dennis, and R. D. McMichael, Phys. Rev. B, \textbf{81}, 140407 (2010). \\[0pt] [3] M. Zhu, B. D. Soe, R. D. McMichael, M. J. Carey, S. Maat, and J. R. Childress, Appl. Phys. Lett., \textbf{98}, 072510 (2011). \\[0pt] [4] R. L. Thomas, M. Zhu, C. L. Dennis, V. Misra and R. D. McMichael, J. Appl. Phys., \textbf{110}, 033902 (2011).   

Interaction between spin-wave excitations and pure spin currents in magnetic structures

The generation of pure spin current (PSC) in magnetic structures has attracted much attention not only for its fundamental importance in spintronics, but also because it opens up potential applications. One of the most exciting aspects of this area is the interplay between spin-waves (SW) and PSC. Here we report experimental results in which the PSC, generated by both spin pumping (SPE) [1] and spin Seebeck (SSE) [2] effects, can exert a spin-transfer torque sufficient to compensate the SW relaxation in yttrium iron garnet (YIG)/non-magnetic structures. By measuring the propagation of SW packets in single-crystal YIG films we were able to observe the amplification of volume and magnetostatic modes (MSW) by both SSE and SHE [3,4]. The excitation and detection of the SW packets is carried out by using a MSW delay line device. In both cases the amplification is attributed to the spin-transfer torque due to PSC generated by SSE as well as SHE. It will also be presented new results in which PSC are simultaneously excited by SSE and SPE effects in YIG films. While the spin current generated by SPE is obtained by exciting the ferromagnetic resonance (FMR) of the YIG film, the spin current due to SSE is created by applying a temperature gradient along the film plane. The effect of the superposition of both spin currents is characterized by measuring the spin Hall voltage (V$_{H})$ along thin strips of Pt deposited on top of the YIG films. Whereas V$_{H}$ corresponding to the uniform FMR is amplified due the SSE the voltages corresponding to the other magnetostatic spin-wave modes are attenuated [5]. \\[4pt] [1] Y. Tserkovnyak, et al., Rev. Mod. Phys. 77, 1375 (2005).\\[0pt] [2] K. Uchida, et al., Nature 455, 778 (2008).\\[0pt] [3] E. Padr\'{o}n-Hern\'{a}ndez, A. Azevedo, and S. M. Rezende, Phys. Rev. Letts., \textbf{107}, 197203 (2011).\\[0pt] [4] E. Padr\'{o}n-Hern\'{a}ndez, A. Azevedo, and S. M. Rezende, Appl. Phys. Letts., \textbf{99} (2011) in press.\\[0pt] [5] G.L. da Silva, L.H. Vilela-Le\~{a}o, S. M. Rezende and A. Azevedo, (in preparation).   

Manipulation of Spin Waves in Yttrium Iron Garnet Thin Films through Interfacial Spin Scattering

Spin waves in magnetic films have many properties that can be utilized for microwave signal processing and logic operations. These applications, however, are bottlenecked by the damping of spin waves. This presentation reports on a new method for the amplification of spin waves. Specifically, the presentation reports the electric manipulation of spin waves in yttrium iron garnet (YIG) thin films via interfacial spin scattering (ISS). Experiments used a 4.6 $\mu$m-thick YIG film strip with a 20 nm-thick Pt capping layer. A dc pulse was applied to the Pt film that produced a spin current along the Pt thickness direction via the spin-Hall effect. As the spin current scatters off the surface of the YIG film, it exerts a torque on the YIG surface spins. Due to the dipolar and exchange interactions, the effect of this torque is extended to other spins across the YIG thickness and thereby to spin-wave pulses traveling in the YIG film. The net effect of the ISS process depends critically on the relative orientation of (1) the magnetic moments of the electrons in the Pt layer that scatter off the YIG surface and (2) the precession axis of the magnetic moments on the YIG surface. When they are anti-parallel, the spin-wave damping is reduced and the amplitude of a traveling spin-wave pulse is increased. In a parallel configuration, the pulse experiences an enhanced attenuation.   

Session Q3: Invited Session: Recent Advances in Pnictide Superconductors

Study of the Multiorbital Hubbard Model for the Fe-Superconductors Beyond Weak Coupling

A variety of experimental and theoretical investigations indicate that the pnictides and chalcogenides are materials with on-site Hubbard repulsion intermediate between weak coupling, where simple nesting ideas apply, and strong coupling where the spins are localized. For this reason, it is desirable to broaden the range of couplings theoretically studied as well as the many-body models and techniques employed. In this talk, an extensive analysis of model Hamiltonians for the Fe-based superconductors is presented. The multiorbital Hubbard models with two, three, and five orbitals are studied, via the Hartree-Fock approximation and exact diagonalization techniques. The main topics to be discussed are: magnetic ordering tendencies [1], range of realistic Hubbard repulsion and Hund couplings [2], orbital-weight redistribution at the Fermi surface and comparison with photoemission data [3], low-temperature transport properties [4], and competing pairing channels [5]. The possible magnetic states of the $\sqrt{5}\times \sqrt{5}$ Fe-vacancy arrangement will also be presented [6]. The experimental reports of local moments at room temperature leads to our most recent efforts employing a three-orbital spin-fermion model, analyzed via Monte Carlo simulations, to study the temperature dependence of the (anisotropic) conductance [7]. It is concluded that considerable progress has been made in the understanding of these materials in spite of their difficult range of intermediate couplings. However, the existence of several open problems will also be discussed.\\[4pt] [1] R. Yu {\it et al.}, Phys. Rev. B {\bf 79}, 104510 (2009); A. Moreo {\it et al.}, Phys. Rev. B {\bf 79}, 134502 (2009).\\[0pt] [2] Q. Luo {\it et al.}, Phys. Rev. B {\bf 82}, 104508 (2010); A. Nicholson {\it et al.}, Phys. Rev. B {\bf 84}, 094519 (2011).\\[0pt] [3] M. Daghofer {\it et al.}, Phys. Rev. B {\bf 81}, 180514(R) (2010).\\[0pt] [4] X. Zhang and E. Dagotto, Phys. Rev. B {\bf 84}, 132505 (2011). See also Q. Luo {\it et al.}, Phys. Rev. B {\bf 83}, 174513 (2011).\\[0pt] [5] A. Nicholson {\it et al.}, Phys. Rev. Lett. {\bf 106}, 217002 (2011); M. Daghofer {\it et al.}, Phys. Rev. Lett. {\bf 101}, 237004 (2008).\\[0pt] [6] Q. Luo {\it et al.}, Phys. Rev. B {\bf 84}, 140506(R) (2011).\\[0pt] [7] S. Liang {\it et al.}, submitted.   

Doping - dependent anisotropy of the superconducting gap in underdoped pnictide superconductors

The in-plane London penetration depth, $\Delta\lambda(T)$, was studied in single crystals of Ba$_{1-x}$K$_x$Fe$_2$As$_2$ (``Ba122") and Ca$_{10}$(Pt$_3$As$_8$)[(Fe$_{1-x}$Pt$_{x}$)$_2$As$_2$]$_5$ (``10-3-8"). Whereas in Ba122 magnetism and superconductivity coexist in the underdoped regime, the 10-3-8 compound exhibits a clear separation of two order parameters. By comparing the results obtained in these two systems, we could study general features of the superconducting gap structure as function of doping in the underdoped regime. Similar to all other pnictides, the low-temperature variation of London penetration depth exhibits a power-law behavior, $\Delta\lambda(T)= AT^n$, in both systems. Moving towards the underdoped edge of the superconducting dome, the exponent $n$ decreases well below scattering - limited value of $n=2$ and, at the same time, the pre-factor $A$ increases. Both trends indicate an increasing anisotropy of the superconducting gap in more underdoped compounds. These and previous results suggest that the development of the superconducting gap anisotropy towards the underdoped edge of the superconducting dome is an intrinsic property of iron pnictides, similar to the known tendency on the overdoped side where magnetism and superconductivity do not interfere.\\[4pt] In collboration with M.A. Tanatar, H. Kim, The Ames Laboratory; Bing Shen, Hai-Hu Wen, Nanjing University; and N. Ni, R.J. Cava, Princeton University.   

Nematic susceptibility and quantum criticality in Fe-pnictide superconductors

The concept of broken symmetry is ubiquitous in condensed matter physics because it allows us to write the proper Hamiltonian description of an electron in a solid. Determining which symmetry is broken and how it is broken is therefore crucial. I will present results from transport and magnetization experiments on both underdoped and overdoped pnictide superconductors of the ``122'' structural motif that help reveal the intrinsic symmetry of the electronic ground state. We reveal the nature of the nematic susceptibility as optimal doping is approached on the underdoped side, and the breakdown of Fermi liquid like quasiparticles from the overdoped side. We discuss the universality of these properties to other pnictides.   

Controlling vortex pinning and vortex phase diagrams of FeAs-based superconductors through particle irradiation and substitution

The prominent vortex pinning features of the Ba-122 and Sm-1111 family of pnictide superconductors are presented. For isovalently doped BaFe$_2$(As$_{1-x}$P$_x$)$_2$ we observe the systematic evolution of vortex pinning with increasing P-doping from fishtail behavior to a distinct peak effect near the irreversibility field to a reversible magnetization and Bean Livingston surface barriers. The enhancement of vortex pinning resulting from heavy ion and proton irradiation is shown to arise from delta-Tc-type pinning. These results will be compared to those on optimal doped BaKFe$_2$As$_2$ and SmFeAs(O$_{1-x}$F$_x$). High-energy heavy-ion irradiation induced defects lead to a decrease in the superconducting anisotropy, an increase in the slope of the temperature dependence of the irreversibility line and only small suppression of Tc. In all cases, we see a large enhancement of the critical current following particle irradiation. In particular, on BaKFe$_2$As$_2$ irradiated to a dose matching field of 21 T with 1.3-GeV Pb-ions, Jc $\sim$ 4 MA/cm$^2$ at 5 K and in 7 T $||$ c is achieved, comparable to results for YBCO coated conductors at the same temperature and field.\\[4pt] In collaboration with L. Fang, Y. Jia, J. A. Schlueter, H. Claus, C. Chaparro, G. Sheet, A. E. Koshelev, G. W. Crabtree, W. K. Kwok, Materials Science Division, Argonne National Laboratory, Argonne, Illinois, USA; S. F. Xu, Physics Division, Argonne National Laboratory, Argonne, Illinois, USA; H. F. Hu, J. M. Zuo, Department of Materials Science and Engineering, University of Illinois, Urbana, Illinois, USA; A. Kayani, Physics Department, Western Michigan University, Kalamazoo, Michigan, USA; H.-H. Wen, University of Nanjing, Nanjing, China; and N. D. Zhigadlo, J. Karpinski, Solid State Physics Laboratory, ETH Zurich, Switzerland.\\[4pt] This work was supported by the Center for Emergent Superconductivity, an Energy Frontier Research Center funded by the DoE, Office of Basic Energy Sciences (LF, YJ, HC, AEK, CC, GS, GWC, HFH, JMZ), by the DoE, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357 (UW, JAS, WKK) and by the ATLAS accelerator at Argonne (SFZ).   

Unusual electronic structure and pairing in the K$_{x}$Fe$_{2-y}$Se$_{2}$ and BaFe$_{2}$(As$_{1-x}$P$_{x})_{2}$ superconductors

In this talk, we present the angle resolved photoemission study of the unusual electronic structure and pairing behavior in two rather unique iron based superconductors: K$_{x}$Fe$_{2-y}$Se$_{2}$ and BaFe$_{2}$(As$_{1-x}$P$_{x})_{2}$ For K$_{x}$Fe$_{2-y}$Se$_{2}$, large electron Fermi surfaces are observed around the zone corners with an almost isotropic superconducting gap of 10.3 meV, while there is no hole Fermi surface near the zone center, which demonstrate the inter-band scattering or Fermi surface nesting is not a necessary ingredient for the unconventional superconductivity in iron-based superconductors. Moreover, two insulating and one semiconducting parental phases of K$_{x}$Fe$_{2-y}$Se$_{2}$ were identified. The two insulating phases exhibit Mott-insulator-like signatures, and one of the insulating phases is mesoscopically phase-separated from the superconducting/semiconducting phase in the superconductor/semiconductor [2]. For BaFe$_{2}$(As$_{1-x}$P$_{x})_{2}$, which is a prototypical iron-based superconductor with nodal gap behaviors, we have determined the systematic change of its low energy electronic structures as a function of the Phosphor concentration. We found the so-called iso-valent doping actually introduce significant amount of holes into the system. The chemical pressure effect is largely a doping effect in addition to the non-rigid band behavior [3]. Moreover, we report the direct observation of a circular line node on the largest hole Fermi surface around the Z point at the Brillouin zone boundary. We found that the nodes are due to the strong three dimensional character of this Fermi surface (large kz dispersion, strong mixing of d$_{3z2-r2}$ orbitals), instead of d-wave pairing or other scenarios involving the electron pockets [4]. \\[4pt] [1] Y. Zhang et al. Nature. Materials 10, 273 (2011).\\[0pt] [2] F. Chen et al. arXiv:1106.3026v1[cond-mat.supr-con] (2011).\\[0pt] [3] Z. R. Ye et al. arXiv:1105.5242v1[cond-mat.supr-con] (2011).\\[0pt] [4] Y. Zhang et al. arXiv:1109.0229v1[cond-mat.supr-con] (2011).   

Session Q4: Focus Session: Many-body Quantum Phases in Cold Atom Systems

Orbital ice: an exact Coulomb phase on the diamond optical lattice

The rapid advances in loading and controlling alkali atoms on the excited bands of optical lattices have made it possible to investigate orbital-related many-body physics in new settings. Here we demonstrate the existence of orbital Coulomb phase as the exact ground state of $p$-orbital exchange Hamiltonian on the diamond lattice. The Coulomb phase is an emergent state characterized by algebraic dipolar correlations and a gauge structure resulting from local constraints (ice~rules) of the underlying lattice models. For most ice models on the pyrochlore lattice, these local constraints are a direct consequence of minimizing the energy of each individual tetrahedron. On the contrary, the orbital ice rules are emergent phenomena resulting from the quantum orbital dynamics. We show that the orbital ice model exhibits an emergent geometrical frustration by mapping the degenerate quantum orbital ground states to the spin-ice states obeying the 2-in-2-out constraints on the pyrochlore lattice. We also discuss possible realization of the orbital ice model in optical lattices with $p$-band fermionic cold atoms. [1] Gia-Wei~Chern and Congjun Wu, arXiv:1104.1614 (2011).   

Time reversal symmetry breaking of $p$-orbital bosons in a one-dimensional optical lattice

We study bosons loaded in a one-dimensional optical lattice of two-fold $p$-orbital degeneracy at each site. Our numerical simulations find an anti-ferro-orbital p$_x$+ip$_y$, a homogeneous p$_x$ Mott insulator phase and two kinds of superfluid phases distinguished by the orbital order (anti-ferro-orbital and para-orbital). The anti-ferro-orbital order breaks time reversal symmetry. Experimentally observable evidence is predicted for the phase transition between the two different superfluid phases. We also discover that the quantum noise measurement is able to provide a concrete evidence of time reversal symmetry breaking in the first Mott phase.   

Correlated phases of bosons in tilted, frustrated lattices

We study the ``tilting'' of Mott insulators of bosons into metastable states. These are described by Hamiltonians acting on resonant subspaces, and have rich possibilities for correlated phases with non-trivial entanglement of pseudospin degrees of freedom measuring the boson density. We extend a previous study (Phys. Rev. B {\bf 66}, 075128 (2002)) of cubic lattices to a variety of lattices and tilt directions in 2 dimensions: square, triangular, decorated square, and kagome, while noting the significance of three-body interactions. We find quantum phases with Ising density wave order, with superfluidity transverse to the tilt direction, a sliding Luttinger liquid phase, and quantum liquid states with no broken symmetry. Some cases map onto effective quantum dimer models.   

Quantum simulations with ultracold atoms

Precise understanding of strongly interacting systems, from electrons in materials and frustrated magnets to nuclear matter, is a major challenge for modern physics. Often, theoretical description of key models is severely plagued by the intricate quantum mechanics at play. This prompted a challenging effort of using ultra-cold atoms to realize Feynman's emulators of fundamental microscopic models. I will discuss some of the current efforts in realizing quantum simulators for cold bosonic and fermionic systems and how the theory tries to caught up with the experiment in making reliable predictions for strongly interacting quantum matter.   

A Mott Glass to Superfluid Transition for Random Bosons in Two Dimensions

We study the zero temperature superfluid-insulator transition for a two-dimensional model of interacting, lattice bosons in the presence of quenched disorder and particle-hole symmetry. We follow the approach of a recent series of papers by Altman, Kafri, Polkovnikov, and Refael, in which the strong disorder renormalization group is used to study disordered bosons in one dimension. Adapting this method to two dimensions, we study several different species of disorder and uncover universal features of the superfluid-insulator transition. In particular, we locate an unstable finite disorder fixed point that governs the transition between the superfluid and a gapless, glassy insulator. We present numerical evidence that this glassy phase is the incompressible Mott glass and that the transition from this phase to the superfluid is driven by percolation-type process. Finally, we provide estimates of the critical exponents governing this transition.   

Disordered Supersolids in the Extended Bose-Hubbard Model

Studies of the extended Bose-Hubbard model seek to capture the essential properties of a wide variety of physical systems including helium, Josephson junction arrays, certain narrow-band superconductors, and bosons in optical lattices. We theoretically study the stability of lattice supersolid states in the extended Bose-Hubbard model with bounded spatial disorder. We construct a disorder mean field theory and compare with quantum Monte Carlo calculations. We find that the supersolid survives weak disorder on the simple cubic lattice. We also find that increasing disorder strength can transform a lattice solid into a supersolid as it tends to percolate through the disorder landscape.   

Density instabilities in a two-dimensional dipolar Fermi gas

We investigate the inhomogeneous phases of fermionic polar molecules confined in a single two-dimensional (2D) layer, where the molecule dipole moments are all aligned by an external electric field. We show that the Random Phase Approximation (RPA) for the density-density response function is never accurate for the 2D dipolar Fermi gas. To incorporate correlations beyond RPA, we use an improved version of the Singwi-Tosi-Land-Sjolander scheme, which has been successful for electron systems. In addition to density-wave instabilities, our formalism captures the collapse instability that is expected from Hartree-Fock calculations but is absent from RPA. Crucially, we find that when the dipoles are oriented perpendicular to the layer, the system spontaneously breaks rotational symmetry and forms a stripe phase, in defiance of conventional wisdom.   

Scaling of noise correlations of hard-core bosons in incommensurate lattices

We study the scaling of the momentum distribution function and the noise correlations in the Mott insulator, Bose glass, and superfluid quantum phases of hard-core bosons subjected to quasi-periodic disorder. The exponents of the correlation functions at the superfluid to Bose-glass transition are found to be approximately one half of the ones that characterize the superfluid phase. We also find a divergence in the derivative of the noise correlation peaks with respect to the strength of disorder at the superfluid to Bose-glass critical point. This behavior is found not to occur in the corresponding free fermion system, where an Anderson-like transition takes place at the same critical point.   

Quantum Orders and Space-Time Vortices for Spin 2 Atomic Chains

Laser cooled atoms with spin can become magnetically ordered, like electrons in solids, but a greater variety of orders is possible in this setting. Spin one atoms can form nematic states with the symmetry of an undirected line segment while spin two atoms can form states with the symmetry of a tetrahedron. Such atoms could be confined to a one-dimensional optical lattice. In one dimension, quantum fluctuations become much more significant, and lead to a few interesting phases. In particular, the nematic state spontaneously breaks translational symmetry. If a state has a Berry's phase of a certain order under rotations, the fluctuations will often be modulated with a period of the same order. I will argue that this connection can be broken for a non-abelian symmetry group--both uniform and periodic phases can be stabilized. As an example, computer calculations (with DMRG) on a tetrahedral state find both a uniform and a period 3 phase.   

Thermal versus quantum fluctuations of optical lattice fermions

We show that, for fermionic atoms in a one-dimensional optical lattice, the fraction of atoms in doubly occupied sites is a highly non-monotonic function of temperature. We demonstrate that this property persists even in the presence of realistic harmonic confinement, and that it leads to a suppression of entropy at intermediate temperatures that offers a clear route to adiabatic cooling. Our interpretation of the suppression is that such intermediate temperatures are simultaneously too high for quantum coherence and too low for significant thermal excitation of double occupancy thus offering a clear indicator of the onset of quantum fluctuations.   

Tunable quantum glasses and phase transitions of atoms and photons: firstpredictions for glassy physics with many-body cavity QED

Recent studies of strongly interacting atoms and photons in opticalhave rekindled interest in the Dicke model of atomic qubitsto discrete photon cavity modes. In this talk, we argue thatof the Dicke model with variable atom-photon couplings canrise to a ground state phase diagram exhibiting quantum phasebetween paramagnetic, ferromagnetic, and a spin glass phase. These quantum optics realizations of quantum glasses are distinctive to condensed matter systems and provide new opportunities for glassy physics with many-bodyQED. The photon-mediated random couplings between the atomic qubitsIsing spins) are truly long-ranged and the theory for these systemsanalytically tractable. We compute atomic and photon spectralfunctions across this phase diagram, and outline how ourcan be observed in experiments.   

The boson-Hubbard model on a kagome lattice with a sextic ring-exchange term

We present exact quantum Monte Carlo simulations of hard-core bosons in a two-dimensional Kagome lattice with a sextic ring-exchange term. We study how the superfluid density evolves as the ring-exchange interactions are increased. We show that the system becomes unstable in the limit of large interactions at all fillings and undergoes a phase separation, except at $\frac13$ and $\frac23$ fillings for which the superfluid density vanishes and a solid state forms.   

Session Q5: Nonequilibrium and Gauge/Gravity Duality

Solution to the d=2 Hertz-Millis problem from a hairy electron star

We use holography to study the spontaneous condensation of a neutral order parameter in a (2+1)-dimensional field theory at zero-temperature and finite density, dual to the electron star background of Hartnoll and Tavanfar. An appealing feature of this field theory is the emergence of an IR Lifshitz fixed-point with a finite dynamical critical exponent $z$, which is due to the strong interaction between critical bosonic degrees of freedom and a finite density of fermions (metallic quantum criticality). We show that under some circumstances the electron star background develops a neutral scalar hair whose holographic interpretation is that the boundary field theory undergoes a quantum phase transition, with a Berezinski-Kosterlitz-Thouless character, to a phase with a neutral order parameter. Including the backreaction of the bulk neutral scalar on the background, we argue that the two phases across the quantum critical point have different $z$, a novelty that exists in certain quantum phase transitions in condensed matter systems. We also analyze the system at finite temperature and find that the phase transition becomes, as expected, second-order. Embedding the neutral scalar into a higher form, a variety of interesting phases could potentially be realized for the boundary field   

Non-Relativistic Holographic Quantum Liquids

We explore the phase structure of a holographic toy model of superfluid states in non-relativistic conformal field theories. At low background mass density, we find a familiar second-order transition to a superfluid phase at finite temperature. Increasing the chemical potential for the probe charge density drives this transition strongly first order as the low-temperature superfluid phase merges with a thermodynamically disfavored high-temperature condensed phase. At high background mass density, the system reenters the normal phase as the temperature is lowered further, hinting at a zero-temperature quantum phase transition as the background density is varied. Given the unusual thermodynamics of the background black hole, however, it seems likely that the true ground state is another configuration altogether.   

Striped Superconductor and Holography

Using gauge/gravity duality, we analytically study the properties of a strongly coupled striped superconductor, with the charge density wave sourced by a modulated chemical potential. The calculation is done in the large modulation wavenumber $Q$ regime and comparing the results with numerical calculations, we find good agreement for $Q \geq 3 T_c$. In the absence of a homogeneous term in the chemical potential, we show that the critical temperature scales as a negative power of $Q$ for scaling dimensions $\Delta < \frac{3}{2}$, whereas for $\Delta > \frac{3}{2}$, there is no phase transition above a certain critical value of $Q$. The order parameter or the condensate is found to scale as a positive power of $Q$ such that the gap is proportional to $Q$. We discuss how these results change if a homogeneous term is added to the chemical potential. We also calculate the conductivity with its spatial dependence.   

Holographic noise near quantum critical points

The dynamical scaling present in equilibrium correlations near to a quantum critical point suggests the possibility of universal, out-of-equilibrium steady states. This has been demonstrated in analyses of the response of the bosonic Hubbard model to a strong electric field. The universal out-of-equilibrium behaviour is particularly apparent in the current noise; at high field, a current noise power ${\cal S}_j \propto \sqrt{E}$ was found which was interpreted as Johnson-like with an effective temperature $\propto \sqrt{E}$ [Phys. Rev. Lett. 97, 227003 (2006)]. We revisit this problem using the holographic mapping to a classical gravitational system. We recover a current noise that extends the previously known equilibrium and strongly out-of-equilibrium results with a full interpolation between the two: ${\cal S}_j \propto T_{eff}$ with $T_{eff}=(T^4+E^2/\pi^4)^{1/4}$.   

Out-of-equilibrium conductivity and current noise at quantum critical points

Quantum critical points display universal behaviour across a wide range of physical systems. These effects appear in both thermodynamics and transport. Such behaviour should also be present out-of-equilibrium where, for example, the current and current noise should follow scaling laws as a function of applied field. These expectations have been borne out in calculations for out-of-equilibrium transport at the Superfluid-Mott Insulator quantum critical point of the Bose-Hubbard model \cite{Green_2005,Green_2006}. These analyses extend the quantum Boltzmann description \cite{Damle_1997} of equilibrium transport using a trick of the 1/N expansion. Here we use an epsilon expansion to obtain similar results. This approach has the advantage of making the physical constraints of the results more transparent. We also present preliminary analysis of the evolution to the non-equilibrium steady state after the electric field is applied. \begin{thebibliography}{3} \bibitem{Green_2005}A.G. Green and S.L. Sondhi, PRL 95, 267001 (2005) \bibitem{Green_2006}A.G. Green, J.E. Moore, S.L. Sondhi and A. Vishwanath, PRL 97, 227003 (2006) \bibitem{Damle_1997}K. Damle and S. Sachdev, PRB 56, 14 (1997) \end{thebibliography}   

Wigner-Mott scaling of transport near the two-dimensional metal-insulator transition

Thermal destructions of heavy quasiparticles often dominates the transport behavior of many strongly correlated materials. It typically leads to pronounced resistivity maxima in the incoherent regime around the coherence temperature $T^{*}$, reflecting the tendency of carriers to undergo Mott localization following the demise of the Fermi liquid. This behavior is best pronounced in the vicinity of interaction-driven (Mott-like) metal-insulator transitions, where the $T^{*}$ decreases, while the resistivity maximum $\rho_{max}$ increases. Here we show that, in this regime, the entire family of resistivity curves display a characteristic scaling behavior $\rho(T)/\rho_{max}\approx F(T/T_{max}),$ while the $\rho_{max}$ and $T_{max}\sim T^{*}$ assume a powerlaw dependence on the quasi-particle effective mass $m^{*}$. Remarkably, precisely such trends are found from an appropriate scaling analysis of experimental data obtained from diluted two-dimensional electron gases in zero magnetic fields. Our analysis provides strong evidence that inelastic electron-electron scattering -- and not disorder effects -- dominates finite temperature transport in these systems, validating the Wigner-Mott picture of the two-dimensional metal-insulator transition.   

Finite-size effects in transport data from Quantum Monte Carlo simulations

We have examined the behavior of the compressibility, of the dc-conductivity, and of the Drude weight as probes of the density-driven metal-insulator transition in the Hubbard model on a square lattice. These quantities have been obtained through determinantal quantum Monte Carlo simulations at finite temperatures on lattices up to $16\times 16$ sites. While the compressibility and the dc-conductivity are known to suffer from `closed-shell' effects due to the presence of artificial gaps in the spectrum (caused by the finiteness of the lattices), we have established that the former tracks the average sign of the fermionic determinant, and that a shortcut often used to calculate the conductivity may neglect important corrections. We have also performed systematic studies of the dependence of our data with the imaginary-time interval. Our analyses also show that, by contrast, the Drude weight is not too sensitive to finite-size effects, being much more reliable as a probe to the insulating state.   

Universal transport near a continuous Mott transition in two dimensions

We discuss the universal transport signatures near a zero-temperature continuous Mott transition between a Fermi liquid and a spin liquid in 2 spatial dimensions. This transition can be described using a slave-rotor field theory, where the electron is decomposed into a fermionic spinon and charge-carrying rotor, both interacting with an emergent U(1) gauge field. The universal part of the non-zero temperature charge transport is determined by the dynamics of the charged rotors and is affected by the gauge fluctuations. Explicit predictions for the behavior of the electrical conductivity are made via the solution of a quantum kinetic equation using controlled approximations.   

Dissipation-Induced Quantum Phase Transition in a Resonant Level

We measure conductance through a resonant level coupled to a dissipative environment, which suppresses tunneling rate at low energies. Our sample consists of a single-walled carbon nanotube quantum dot contacted by resistive metal leads that serve as the dissipative environment. We study the shape of the resonant conductance peak, with the expectation that its width and height, both dependent on the tunneling rate, will be suppressed at low temperatures. However, we observe distinct regimes, including a case where the resonant tunneling conductance reaches the unitary limit, despite the presence of dissipation. We discuss the implication of these findings for a dissipation-induced quantum phase transition and extract the scaling exponents.   

Collective excitations and low temperature transport properties of bismuth

We examine the influence of collective excitations on the transport properties (resistivity and magneto-optical conductivity) for semimetals, focusing on the case of bismuth. We show, using a random-phase approximation (RPA), that the properties of the system are drastically affected by the presence of an acoustic-plasmon mode, which is a consequence of the presence of two types of carriers (electrons and holes) in this system. We find a crossover temperature $T^*$ separating two different regimes of transport. At high temperatures where $T > T^*$, the Baber scattering explains quantitatively the dc resistivity experiments, while at low temperatures where $T < T^*$, the interactions of the carriers with this collective mode lead to a $T^5$ behavior of the resistivity. We examine other consequences of the presence of this mode. In particular a two-plasmon edge feature in the magneto-optical conductivity is predicted. We compare our results with the experimental findings on bismuth. We discuss the limitations and extensions of our results beyond the RPA, and examine the case of other semimetals such as $1T-TiSe_2$.   

Photo-excitation and relaxation dynamics in junction of double-exchange systems

The photo-induced insulator-metal (I-M) transition is studied by the numerical simulation of real-time quantum dynamics of a double-exchange model. We find a characteristic multiplication of particle-hole (p-h) pairs by a p-h pair of high energy during the I-M transition. To examine the conversion from the p-h pairs into electric energy, we perform the numerical study on the junction systems combined by the double exchange models. The numerical results have been revealed including (i) the threshold behavior with respect to the intensity and energy of light, (ii) p-h pairs are well separated and pair annihilation is suppressed, (iii) enhancement of collected carrier by meta-stability of I-M transition.   

Photo excited state in spin-charge coupled correlated electron system

Recent ultrafast optical techniques open up a new frontier for research of the phase transition. Photo-induced phase is transient and highly nonequilibrium. photo-induced phenomena in correlated electron systems offer large possibility of new hidden phases which do not realize in the thermal equilibrium state, and prompt several theoretical challenges. In this talk, I will talk about recent our theoretical results for the photo-induced phase transition in correlated electron systems. We study the photo-induced spin state change in itinerant correlated electron system, motivated from the experiments in perovskite cobaltites [1]. The effective models before and after photon-pumping are derived from the two-orbital Hubbard model and are analyzed by the exact diagonalization method. When a photon is introduced in the low-spin band insulator, we found a spin-polarized bound state of photo-excited hole and the high-spin state. This bound state directly reflects the optical pump-probe spectra. These results well explain the recent femtosecond spectroscopy experiments in perovskite cobaltites We also show the unusual double-exchange interaction in photo excited state. \\[4pt] [1] Y. Kanamori, H. Matsueda and S. Ishihara, Phys. Rev. Lett. 107, 167403-1-5 (2011)   

Non-equilibrium steady state of field-driven strongly correlated electrons

We theoretically study the nature of non-equilibrium steady state of strongly correlated electrons on lattices under the influence of a static electric field. We describe the dynamics of steady state by the Floquet theory, and the electron correlation by the dynamical mean-field theory, respectively. We find that the steady-state current in a closed system is characterized by the Bloch oscillation in the metallic regime, while it vanishes in the Mott-insulating regime. Importantly, the coherent contribution to the current can be captured by measuring the quasiparticle weight in the local spectral density as in equilibrium. Based on these criteria, we draw the non-equilibrium phase diagram as a function of the strength of electric field and the on-site interaction at zero temperature. *References: [1] A. V. Joura, J. K. Freericks, and Th. Pruschke, Phys. Rev. Lett. 101, 196401 (2008); [2] N. Tsuji, T. Oka, and H. Aoki, Phys. Rev. B 78, 235124 (2008).   

Dynamical DMRG study of non-linear optical response in one-dimensional dimerized Hubbard model with nearest neighbor Coulomb interaction and alternating on-site potential

The optical response of organic compounds has been attracting much attention. The one of the reasons is the huge non-linear and ultrafast optical response [K. Yamamoto \textit{et}. \textit{al}., J. Phys. Soc. Jpn. \textbf{77}, 074709(2008)]. In order to investigate such optical properties, we carry out dynamical DMRG calculations to obtain optical responses in the 1/4-filled one-dimensional Hubbard model including the nearest neighbor Coulomb interaction and the alternating electron hopping. The charge gap [S. Nishimoto, M. Takahashi, and Y. Ohta, J. Phys. Soc. Jpn. \textbf{69}, 1594(2000)] and the bound state [H. Benthien and E. Jeckelmann, Eur. Phys. J. B \textbf{44}, 287(2005)] in this model have been discussed based on DMRG calculations. In the present study, we introduce an alternating on-site potential giving the polarization in the system into the dimerized Hubbard model, which breaks the reflection symmetry of the system. In this talk, we discuss the obtained linear and the 2nd order non-linear optical susceptibility in order to make a prediction for non-linear optical experiments in the future.   

Non-Kondo mechanism of resistivity upturn in a spin-ice Kondo lattice model

Ice rule is a configurational constraint observed in a broad range of systems in which two-state variables are defined at the vertices of a pyrochlore lattice. The constraint enforces the so-called `two-in two-out' configuration; two out of four neighboring sites within each tetrahedron are in the opposite state to the other two. Under this peculiar local constraint, the system remains disordered, whereas the ground state is characterized by macroscopic degeneracy with a hidden gauge structure. Recent experiments on pyrochlore metallic oxides have promoted interest in itinerant electrons coupled with such ice-rule type localized moments. Here we investigate how electronic and transport properties are affected by the coupling to the spin ice by applying a cellular dynamical mean-field theory to a spin-ice type Kondo lattice model. We found that a spin-ice liquid state emerges in a wide temperature range at low electron density, in which two-in two-out local correlation well develops in the absence of long-range ordering. In this spin liquid state, the resistivity shows an upturn because of an anomalous scattering of electrons by the local spin-ice type correlation. The details of this non-Kondo resistivity upturn will be discussed in relation with experiments in pyrochlore oxides.   

Session Q6: Carbon Nanotubes: Electronic and Thermal Properties

Ultra-short single-wall carbon nanotube NEMS transistors

We study electron transport in clean suspended single-wall carbon nanotube (SWCNT) transistors hosting a single quantum dot (QD) ranging in length from a few tens of nm down to $\approx$ 3 nm. To fabricate these ultra-short QD transistors, we align narrow gold bow-tie junctions on top of individual SWCNTs and suspend the devices. We then use a feedback-controlled electromigration to break the gold junctions and expose nm-sized sections of the SWCNTs. We measure electron transport in these devices at low temperature and show that they form clean and tunable quantum dot transistors. We observe QD excited states which correspond to both the stretching and flexural vibronic modes. The out-of-plane vibron resonances approach the THz range, and show that these ultra-short suspended transistors are promising candidates to develop highly sensitive NEMS and explore the strong electron-vibron coupling regime.   

Measurement of intrinsic resistivity of individual single walled carbon nanotubes with known-chirality

We report the electrical resistivity measured on individual single walled nanotubes (SWNTs) whose atomic structures are characterized by Rayleigh and Raman spectroscopy. Since electrical transport of SWNTs on substrates is predominantly limited by surface polar phonon from substrate at elevated temperatures, intrinsic transport properties of SWNTs limited by nanotube phonons remained to be probed experimentally. Here we present electrical transport measurement of long suspended individual SWNTs with exactly assigned atomic structures. SWNTs are grown by the chemical vapor deposition method on pre-patterned electrodes and their exact chiral indices are obtained using Rayleigh and Raman spectroscopy. We investigate temperature dependent resistivity of metallic SWNTs in the diffusive regime. We will discuss the chirality dependence of the electron-acoustic phonon interaction inferred from the temperature dependent intrinsic resistivity of SWNTs.   

Probing Magnetic Susceptibility Anisotropy of Large-Diameter Armchair Carbon Nanotubes via Magnetic Linear Dichroism Spectroscopy

We studied magnetic susceptibility anisotropy, via magnetic linear dichroism spectroscopy, of aqueous suspensions of single-walled carbon nanotubes in high magnetic fields up to 22T using a unique magnet system (Split-Florida Helix magnet). Specifically, we measured magnetic susceptibility anisotropies, $\Delta \chi$, of several armchair species ranging from (5,5)-(13,13) at room temperature over an excitation wavelength range of 400-900 nm. For large diameter armchairs such as (12,12) and (13,13), we have observed some of the strongest alignment in a static magnetic field due to their large diameters. Results will be discussed in comparison with detailed calculations involving the Aharonov-Bohm effect.   

Helical modes and Majorana fermions in carbon nanotubes

We derive an effective low-energy theory for metallic (armchair and nonarmchair) single-wall nanotubes in the presence of an electric field perpendicular to the nanotube axis, and in the presence of magnetic fields, taking into account spin-orbit interactions and screening effects on the basis of a microscopic tight-binding model [1,2]. The interplay between electric field and spin-orbit interaction allows us to tune armchair nanotubes into a helical conductor in both Dirac valleys. Metallic nonarmchair nanotubes are gapped by the surface curvature, yet helical conduction modes can be restored in one of the valleys by a magnetic field along the nanotube axis. If in proximity with a superconductor, helical modes give rise to Majorana bound states. Furthermore, we discuss electric dipole spin resonance in carbon nanotubes, and find that the Rabi frequency shows a pronounced dependence on the momentum along the nanotube. \\[4pt] [1] J. Klinovaja, M. Schmidt, B. Braunecker, and D. Loss, Phys. Rev. Lett. 106, 156809 (2011).\\[0pt] [2] J. Klinovaja, M. Schmidt, B. Braunecker, and D. Loss, Phys. Rev. B 84, 085452 (2011).   

Extracting Diameter and Chirality Dependences of Optical and Electronic Properties of Semiconducting Single-Wall Carbon Nanotubes from First-Principles Calculations

First-principles methods based on the combination of density-functional theory (DFT) for ground-state properties, GW approximation for quasiparticle properties and Bethe-Salpeter equation (BSE) for optical properties represent the state-of-art for accurate and reliable calculations of optical and electronic properties of solids and molecules. For semiconducting carbon nanotubes (CNTs), they have been applied successfully to selected small-diameter tubes. In this work, we systematically calculate such properties for all zig-zag semiconducting single-wall carbon nanotubes with diameters ranging from (10,0) to (20,0) CNTs, allowing us to extract in a reliable way the diameter and chirality dependence of many properties, such as: (i) optical transition energies; (ii) quasiparticle band gaps; (iii) exciton binding energies; (iv) bright-dark exciton splittings; (v) excited exciton states properties; (vi) transverse-polarized exciton states properties; (vii) electron and hole effective masses (and therefore excitonic reduced masses). All properties are described with good accuracy by diameter- and chirality-dependent analytical formulas, with parameters extracted from the first-principles calculations.   

Modeling the Thermal Conductivity of Nanocomposites Using Monte-Carlo Methods and Realistic Nanotube Configurations

The effective thermal conductivity (K$_{eff})$ of carbon nanotube (CNT) composites is affected by the thermal boundary resistance (TBR) and by the dispersion pattern and geometry of the CNTs. We have previously modeled CNTs as straight cylinders and found that the TBR between CNTs (TBR$_{CNT-CNT})$ can suppress K$_{eff}$ at high volume fractions of CNTs [1]. Effective medium theory results assume that the CNTs are in a perfect dispersion state and exclude the TBR$_{CNT-CNT }$[2]. In this work, we report on the development of an algorithm for generating CNTs with worm-like geometry in 3D, and with different persistence lengths. These worm-like CNTs are then randomly placed in a periodic box representing a realistic state, since the persistence length of a CNT can be obtained from microscopic images. The use of these CNT geometries in conjunction with off-lattice Monte Carlo simulations [1] in order to study the effective thermal properties of nanocomposites will be discussed, as well as the effects of the persistence length on K$_{eff}$ and comparisons to straight cylinder models. \textbf{References} [1] K. Bui, B.P. Grady, D.V. Papavassiliou, Chem. Phys. Let., 508(4-6), 248-251, 2011 [2] C.W. Nan, G. Liu, Y. Lin, M. Li, App. Phys. Let., 85(16), 3549-3551, 2006   

Computational study of the thermal conductivity of defective carbon nanostructures

We use molecular dynamics simulations to study the role of defects on the thermal conductivity in low-dimensional graphitic nanostructures such as schwarzites (3D), graphene (2D), carbon nanotubes and graphene nanoribbons (1D). Since the simulations are very demanding due to the very long phonon mean free path, we describe forces acting on carbon atoms by a parameterized valence force field. Our calculations make use of the non-equilibrium molecular dynamics technique, which incorporates the constant-temperature Nose-Hoover thermostat and non-equilibrium driving forces, which mimic the effect of the heat flow. We study different types of defects, including vacancies and isotope impurities, and show that their importance changes with changing dimension of the system.   

Near-field heat transfer between an array of SWNTs and a quartz substrate

The near-field heat transfer between a quartz substrate and a sparse array of SWNTs oriented normal to the substrate was studied theoretically. The heat power transferred from the hot quartz substrate to the cold SWNTs was expressed through the electric field Green tensor of the system using the fluctuation-dissipation theorem . The integral equation for the Green tensor was obtained and solved numerically. The spectra of the transferred power were calculated and the pronounced resonance lines in the spectra were demonstrated at the frequencies of the polariton resonances in the quartz and antenna resonances of the surface plasmons in the SWNTs. The dependence of the transferred power on separation between the SWNTs and the substrate and on the SWNTs lengths in the array was also studied.   

Ab initio studies of mechanical, electric, and magnetic properties of functionalized carbon nanotubes

We present results of extensive theoretical studies of mechanical, electric, and magnetic properties of functionalized carbon nanotubes (CNTs). Our studies are based on the ab initio calculations in the framework of the density functional theory. We have performed calculations for various metallic and semiconductor single wall CNTs, functionalized with simple organic molecules such as OH, COOH, NH$_{n}$, CH$_{n}$ and metals, Al, Fe, Ni, Cu, Zn, and Pd. We have determined the stability of the functionalized CNTs, their elastic moduli, conductance, and magnetic moments (in the case of CNTs decorated with magnetic ions). These studies shed light on physical mechanisms governing the binding of the adsorbed molecules and also provide valuable quantitative predictions that are of importance for design of novel composite materials and functional devices. In particular, we find out that the Young's modulus of functionalized CNTs is smaller than in the case of bare CNTs, however it is large enough to provide a strong enforcement of composites. The functionalization with molecules leads also to the metallization of semiconducting CNTs, being relevant in the context of CNT interconnects, whereas the functionalization with metals might be used to cut CNTs into ribbons.   

Nanotube based engine

We discuss a mechanism for converting electrical energy into translational motion using a variable-shape bistable carbon nanotube. Clamping one tube end open and the other one closed, we use an applied voltage to switch the tube between mostly collapsed and mostly inflated shapes. Devices based on such a double-pinned tube geometry can operate as a voltage-controlled constant-force spring, a charge-controlled harmonic spring, or an electromechanical engine performing work by coupling to a propagating collapsed/inflated transition region. Making an analogy to ideal-gas thermodynamics, constant-voltage, constant-charge, and constant-geometry operational regimes correspond to isothermal, adiabatic and isochoric processes. Constant-voltage, constant-charge, and constant-geometry processes coupled can be combined into cycles analogous to those of a heat engine. Unlike a heat engine, the tube bistability enables it to collect useful work on both inflation and collapse motions, thus eliminating the need for external forces to restore the system to its initial state during the operational cycle.   

Influence of temperature and adsorbates on a carbon nanotube resonator by molecular dynamics simulations

The bending modes of carbon nanotube have been studied for ultralow mass and force sensing and its tunable resonance frequency. On the other hand, the nonlinear damping of flexural mode has been shown to be vulnerable to temperature and adsorbates. For this reason, we have studied the interaction between mechanical and thermal characteristics in a carbon nanotube cantilever resonator observing the phase space trajectories, strain-stress distributions, and lattice vibrational spectra for various temperatures and adsorbate conditions. The calculation was based on molecular dynamics simulations using the REBO potential, where a carbon nanotube was excited by sinusoidal mechanical forcing at a tube end with constant-temperature boundary condition. The result confirms that the localized strain distribution is in agreement with previous high-resolution transmission electron microscopy result. Based on the simulations, the dynamic Young's modulus and the damping coefficient will be extracted in the frequency domain for different nanotube length and chirality, and will be compared with the continuum theories. In addition, the interaction between the first resonance mode and the background phonons will be discussed based on the obtained dissipated thermal energy and the phonon energy spectra.   

Electron Spin Resonance as a route to Spin-Gap detection in Carbon Nanotubes

The recent observation of a charge-neutral excitation gap in ultraclean carbon nanotubes\footnote[1]{V. V. Deshpande {\it{et al.}}, Science {\bf 323}, 106 (2009)} raises the intriguing possibility of a phase with gapless charge spectrum and gapped spin spectrum: the Luther-Emery liquid. We note that ESR would be an ideal probe to directly test whether the observed gap is a spin-gap, as it probes the non-local correlations of conduction electron spins. We focus on the Luther-Emery point ($K_s=1/2$, also known as free fermion point) where an explicit calculation of relevant spin-spin correlation function is possible, to calculate the ESR signal in a Luther-Emery liquid. At high frequencies of $\omega>2 \Delta_s$ where $\Delta_s$ is the spin-gap, the ESR signal of the Luther-Emery liquid will exhibits a second peak at magnetic fields away from the resonance condition of $B=\omega/\mu_B g K_s$. We discuss how to measure the spin-gap from the location of this additional peak as a function of applied field strength.   

Coherent non-local transport in quantum wires with strongly coupled electrodes

We report a one-dimensional non-local experiment, where the conductance of a section of carbon nanotube shows regular oscillations due to coherent and ballistic transport in an adjacent section. This occurs in spite of wide strongly coupled contact electrodes, which are expected to divide the nanotube into independent sections. Our simulations show that the electrodes form shallow and wide barriers, which maintain quantum coherence between the adjacent sections.   

Nanofissure formation during selective breakdown of m-SWNT in an aligned array

Selective removal of metallic single walled carbon nanotubes (m-SWNT) in an aligned array is needed for restoring semiconducting properties and better device performance. The selective removal is done via electrical breakdown of m-SWNT while applying a large gate voltage to preserve semiconducting SWNT. In this work, we show using electrical measurements and scanning electron microscopy imaging that in a sufficiently dense array, not only the m-SWNT breaks down but also s-SWNT breaks down in a correlated fashion giving rise to a nano fissure pattern. This is in contrast to the established understanding that SWNTs are broken in a random fashion. The origin of the correlated breakdown is due to the electrostatic field of the broken nanotubes that produces locally inhomogeneous current and Joule heating distributions in the neighboring intact nanotubes triggering their breakdowns in the vicinity of the broken nanotubes   

An optically pumped InGaAsP/InP quantum dot rolled-up microtube laser

Rolled-up quantum dot microtubes are a promising candidate for light sources in integrated photonics. We have fabricated InGaAsP/InAs quantum dot rolled-up microtubes from InGaAsP strained bilayers with embedded InAs quantum dots (grown by chemical beam epitaxy). In room-temperature photoluminescence experiments we have observed resonant-mode emission with wavelengths in the telecom range. This resonant emission is consistent with whispering gallery modes. At a temperature of 82 K, we have demonstrated multi-mode lasing under continuous wave optical pumping. We estimate an ultra-low lasing threshold near 1.25 $\mu$Ws of absorbed optical power.   

Session Q7: Focus Session: Computational Design of Materials: Graphene - Strain, defect and interface engineering

Formation of hydrogenated graphene nanoripples by strain engineering and directed surface self-assembly

We propose a class of semiconducting graphene-based nanostructures: hydrogenated graphene nanoripples (HGNRs), based on continuum-mechanics analysis and first-principles calculations. They are formed via a two-step combinatorial approach: first by strain-engineered pattern formation of graphene nanoripples, followed by a curvature-directed self-assembly of H adsorption. It offers a high level of control of the structure and morphology of the HGNRs, and hence of their band gaps, which share common features with graphene nanoribbons. A cycle of H adsorption (desorption) at (from) the same surface locations completes a reversible metal-semiconductor-metal transition with the same band gap.   

Engineering electronic properties of armchair graphene nanoribbons using strain and functional species

First principles density-functional theory calculations were performed to study effects of strain, edge passivation, and surface functional species on structural and electronic properties. Particularly band gap and work function, of armchair graphene nanoribbons (AGNRs), are addressed. It was found that the band gap of the O-passivated AGNRs experiences a direct-to-indirect transition with sufficient tensile strain. The indirect band gap reduces to zero with further increased strain. The work function was found to increase with uniaxial tensile strain while decreasing with compression. The variation of the work function under strain is primarily due to the shift of the Fermi energy with strain. For AGNRs with edge carbon atoms passivated by oxygen, the work function is higher than that of nanoribbons with edge passivated by hydrogen under a moderate strain. The difference between work functions in these two edge passivations is enlarged (reduced) under a sufficient tensile (compressive) strain. Furthermore, the effect of surface species decoration, such as H, F, or OH with different covering density, was investigated. It was found the work function varies with the type and coverage of surface functional species. F and OH decoration increase the work function while H decreases it. The surface functional species were decorated on either one side or both sides of AGNRs. The difference in the work functions between one-side and two-side decorations was found to be relatively small, which may suggest the introduced surface dipole plays a minor role.   

Electronic Band Engineering of Epitaxial Graphene by Atomic Intercalation

Using calculations from first principles, we have investigated possible ways of engineering the electronic band structure of epitaxial graphene on SiC. In particular, intercalation of different atomic species, such as Hydrogen, Fluorine, Sodium, Germanium, Carbon and Silicon is shown to modify and tune the interface electronic properties and band alignments. Our results suggest that intercalation in graphene is quite different from that in graphite, and could provide a fundamentally new way to achieve electronic control in graphene electronics.   

Interplay of Defects, Magnetism, Ripples and Strain in Graphene

We present a comprehensive study based on first-principles calculations about the interplay of four important ingredients on the electronic structure of graphene: defects + magnetism + ripples + strain. So far they have not been taken into account simultaneously in a set of ab initio calculations. Furthermore, we focus on the strain dependence of the properties of carbon monovacancies, with special attention to magnetic spin moments. We demonstrated that such defects show a very rich structural and spin phase-diagram with many spin solutions as function of strain. At zero strain the vacancy shows a spin moment of 1.5 Bohrs that increases up to 2 Bohrs with stretching. Changes are more dramatic under compression: the vacancy becomes non-magnetic under a compression larger than 2{\%}. This transition is linked to the structural modifications associated with the formation of ripples in the graphene layer. Our results suggest that such interplay could have important implications for the design of future spintronics devices based on graphene derivatives, as for example a spin-strain switch based on vacancies.   

Spin switching in organic molecules by strain engineering in graphene

One of the primary objectives in molecular nano-spintronics is to manipulate the spin states of organic molecules with a d-electron center, by suitable external means. Here, we demonstrate by first principles density functional calculations, as well as second order perturbation thoery, that a strain induced change of the spin state, from S=1 $\to$ S=2, takes place for an iron porphyrin (FeP) molecule deposited at a divacancy site in a graphene lattice. The process is reversible in a sense that the application of tensile or compressive strains in the graphene lattice can stabilize FeP in different spin states, each with a unique saturation moment and easy axis orientation. The effect is brought about by a change in Fe-N bond length in FeP, which influences the molecular level diagram as well as the interaction between the C atoms of the graphene layer and the molecular orbitals of FeP. We propose that the spin switching should be detected by x-ray magnetic circular dichroism experiments through the contributions from spin dipole and magnetic anisotropy.   

The magnetism in graphene under strain

We theoretically study the magnetic features in graphene dot under mechanical deformation using the mean field Hubbard model. The edge local magnetic moment (ELMM) is considerably modified in accordance with an effective quantum well originating from a strain-induced gauge field. Applying a uniaxial strain along the zigzag or armchair directions enhances or dampens the ELMM due to the development of the edge quantum wells. Whereas a circular arc bending deformation is applied, the inner and outer edge display ELMM caused by nonuniform gauge field, a direct consequence of the presence of the bulk localized states. These states suggest that an effective single well potential is introduced by a nonuniform pseudo-magnetic field.   

Vacancy-induced order-to-disorder transition in single-layer graphene

Defect engineering provides a potential route for tuning the mechanical, electronic, and chemical properties of graphene. While individual defects in single-layer graphene have been investigated in much detail, the outcomes of collective interactions of multiple defects remain elusive. In this work, we address the collective interaction of populations of vacancies in single-layer graphene using classical molecular-dynamics simulations based on reliable bond-order potentials; we examine random vacancy distributions with the vacancy concentration and temperature being the key parameters in the analysis. We demonstrate that a crystalline-to-amorphous structural transition occurs as the vacancy concentration in single-layer graphene increases beyond a critical level; the transition leads to complete loss of long-range order in the graphene layer. The onset of this order-to-disorder transition typically occurs over the vacancy concentration range from 10 to 20\% and is independent of the details of the interatomic interactions in the classical potentials employed. We present a systematic parametric study of the phenomenon and discuss the implications of our findings for the mechanical and electronic properties of single-layer graphene.   

Two magnetic impurities in graphene

We theoretically investigate two magnetic impurities in graphene. We mainly study the indirect interaction between the two magnetic impurities mediated by conducting electrons, which is so called RKKY interaction. The spin-spin and charge-charge correlation functions are calculated by quantum Monte Carlo simulations when the Fermi energy of the system is changed by gate voltage. The spectral density of the two impurities is also studied by maximum entropy methods.   

Power-Law Correlated Disorder in Graphene and Square Nanoribbons

Two dimensional metal-insulator transitions have remained an active topic in condensed matter physics do to the lack of a general model that can predict when an MIT occurs. With the creation of truly 2D crystals and nanostructures, the question has become increasingly relevant. Though initially predicted to not contain a MIT transition, the inclusion of electron-electron interactions and/or spatial disorder can drive a MIT in some 2D systems. In the case of graphene, correlated ripples are present even when the nanoribbons are freestanding and can have an effect on the transport properties while electron-electron interactions are normally considered negligible. To explore the effect of ripples, we model graphene with a long-range power-law spatial correlation of the form $\langle \epsilon_i^2 \rangle = 1/(1 + |\vec{r_i}/a|)^\alpha$ where $\epsilon_i$, $\vec{r}$, $a$, and $\alpha$ are the on-site energy, position, lattice constant, and strength of the correlation respectively. It should be noted that much work has been completed on short-range correlations but little on truly long-range correlations. We also present our finding for the square lattice for comparison.\\[4pt] [1] Abrahams E. Phys. Rev. Lett. 42, 673-676 (1979)\\[0pt] [2] Abrahams E. Ann. Phys. 8 (1999) 7-9, 539-548   

Thermally-driven Isotope Separation Across Nanoporous Graphene

Experiment and theory indicate that a single graphene sheet is impermeable to gases even as small as helium; pores are required for transmission of atoms and molecules. Nanoporous forms of graphene, such as two-dimensional polyphenylene (2D-PP), consist of a regular array of sub-nanometer pores which can be used for separating atoms and molecules by size. Because the nanoporous graphene barrier is only an atom-thick, quantum tunneling plays a role in the the transmission of atoms through the nanoporous barrier, even at room temperature. This talk describes how the mass-dependence of the tunneling, combined with a temperature gradient, can be used to separate isotope mixtures under conditions where classical transmission cannot. Using transition state theory, we show that the zero-point and tunneling contributions lead to isotopic separations in opposite directions with respect to the temperature gradient. We examine the separation of $^{3}$He/$^{4}$He across a 2D-PP membrane under modest temperature and pressure conditions. We will also describe 2D-PP bilayer structures that yield resonant tunneling of helium atoms, and new nanoporous graphene structures suitable for separating heavier noble-gas isotopes.   

Phonon instabilities in graphene

We study the thermal distribution of phonons in graphene and compare in-plane and out-of-plane contributions with a focus on two in-plane modes that represent intervalley scattering. Due to the two electronic bands there are also two out-of-plane phonon modes with respect to the two sublattices. The electron-phonon interaction softens the phonon modes with a tendency to create instabilities for a sufficiently large electron-phonon coupling. The instabilities are characterized by phase transitions, where one of the out-of-plane mode undergoes an Ising transition by spontaneously breaking the sublattice symmetry. The in-plane modes undergo a Berezinskii-Kosterlitz-Thouless transition. We calculate the critical points of the instabilities, the renormalization of the phonon frequencies and the phonon frequency splitting for in-plane modes. The possibility to observe these instabilities in doped graphene and their consequences for transport are discussed.   

Electronic Properties of Epitaxial Graphene on Si(111)-7$\times$7 and 3CS-SiC(100) Substrates

The synthesis of epitaxial graphene is an attractive method for industrial-scale fabrication and mass production of graphene-based electronic devices. Recently, efforts of epitaxial growth of graphitic carbon films on Si(111)-7$\times$7 and 3CS-SiC(100) substrates have been undertaken in order to explore new potential substrates compatible with conventional Si technology. In this talk, we will discuss the electronic properties of epitaxial graphene on Si (111)-7$\times$7 and 3CS-SiC(100) substrates using calculations from first principles based on Density Functional Theory. In particular, we found that a single graphene layer on Si(111)-7$\times$7 displays ripples of about 0.5 {\AA} and shows an n type electronic behavior. We also calculated the band structures for a graphene bilayer on 3CS-SiC(100) surface with different staking sequences. While AA stacking on Si face and turbostratic stacking on C face show n type behavior, turbostratic stacking on Si face and AA stacking on C face show p type behavior. On both faces, the first carbon plane is covalently bonded to the substrate and serves as a buffer layer similarly to the graphene/6H-SiC(0001) system previously studied.   

Graphene-nickel interface: hybridization and magnetization

The unique properties of graphene have opened up a new avenue for fundamental research as well as technological applications. Whereas the in-plane $sp^{2}$ bonding is primarily responsible for the overall structural stability and mechanical strength of graphene, the out-of-plane pp-$\pi$ states control its transport and interfacing properties. In this talk, we present a first principles study of the of single layer graphene/Ni(111) interface. We discuss how hybridization between the carbon pp-$\pi$ and nickel d orbitals modifies the electronic and magnetic properties of the interface. \\ \\ We acknowledge the computational support provided by the Center for Computational Research at the University at Buffalo, SUNY. This work is supported by the Department of Energy under Grant No. DE-SC0002623 and by the National Science Foundation under Grant No. DMR-0946404.   

Correlated magnetic states in domain and grain boundaries in graphene

Ab initio calculations indicate that while the electronic states introduced by grain boundaries in graphene are only partially confined to the defect core, a domain boundary introduces states near the Fermi level that are very strongly confined to the core of the defect, and that display a ferromagnetic ground state. The domain boundary is fully immersed within the graphene matrix, hence this magnetic state is protected from reconstruction effects that have hampered experimental detection in the case of ribbon edge states. Furthermore, our calculations suggest that charge transfer between one-dimensional extended defects and the bulk in graphene is short ranged for both grain and domain boundaries. http://arxiv.org/abs/1109.6923   

A Nanocluster Based Study of Silicon Carbide Nanocones: Existence and Stability

A systematic study of silicon carbide nanocones of different disclination angles and different tip geometries using the finite cluster approximation is presented. The geometries of the nanocones have been spin optimized using the hybrid functional B3LYP (Becke's three-parameter exchange functional and the Lee-Yang-Parr correlation functional) and the all electron 3-21G* basis set. The study indicates that the binding energy per atom or the cohesive energy of the nanocones depends not only on the size of the nanocones but also on the disclination angle of the nanocones. The electronic properties of nanocones depend on disclination angles, size of the nanocone clusters and the edge structure of the nanocones. Given similar cluster size, silicon carbide appears to favor tubular structures over two dimensional graphene-like structures. For relatively smaller clusters the B.E./atom oscillates in all cases except in nanocones of disclination angle 300$^{\circ}$. This indicates the greater stability of nanocones of some particular size as compared with its neighboring sizes. A study of binding energies, NBO charge, density of states and HOMO-LUMO gaps has been performed for all nanocones from disclination angles of 60$^{\circ}$ to 300$^{\circ}$.   

Session Q8: Focus Session: Spin Liquids II

Absence of magnetic order and unusual spin dynamics in the spin liquid candidate Na$_4$Ir$_3$O$_8$

Na$_4$Ir$_3$O$_8$ has spin-1/2 iridium ions on a hyperkagome lattice of corner sharing triangles and is a candidate three-dimensional spin liquid [1], which has led to active theoretical study [2,3,4]. Previously reported measurements have shown no evidence for magnetic ordering down to temperatures around three orders of magnitude below the Curie-Weiss constant of $\sim 650$K [1]. We have carried out muon-spin relaxation measurements which exclude magnetic ordering above 55mK. The field dependence of the muon spin relaxation rate provides further information on the spin dynamics with a temperature-dependent crossover between power laws at intermediate fields suggesting that more than one energy scale is relevant to the fluctuations in this system. $[1]$ Y.\ Okamoto {\em et al.}, Phys.\ Rev.\ Lett. {\bf 99}, 137207 (2007). $[2]$ M.\ J.\ Lawler {\em et al.}, Phys.\ Rev.\ Lett. {\bf 100}, 227201 (2008). $[3]$ Yi Zhou {\em et al.}, Phys.\ Rev.\ Lett. {\bf 101}, 197201 (2008). $[4]$ E.\ J.\ Bergholtz {\em et al.}, Phys.\ Rev.\ Lett. {\bf 105}, 237202 (2010).   

Short range magnetic correlations and the possible role of frustration in the heavy-fermion CeCu$_{4}$Ga

Neutron scattering, longitudinal and transverse resistivity, heat capacity, ac susceptibility, and magnetization measurements on single and polycrystalline samples of the heavy-fermion compound CeCu$_{4}$Ga suggest that its hexagonal lattice and disorder due to Ga substitution may frustrate formation of the long-range magnetic order found in its parent CeCu$_{5}$. The absence of magnetic Bragg peaks in neutron diffraction data, field-dependent specific heat data, a Weiss temperature of $\sim $ 10 K, and diffuse scattering below\textit{ $\sim $}1 K which can be fit to an isotropic model describing spin-spin correlations between third through fifth nearest neighbors support this suggestion. Kondo behavior also plays a role in determining the physical properties of CeCu$_{4}$Ga.   

Mean field phase digram of the layered perovskite $\mathrm{(Li,Na)_2IrO_3}$ in the strong interaction limit: possible realization of spin liquid phases

We study the phase diagram of layered perovskite $\mathrm{(Li,Na)_2IrO_3}$ with an underlying honeycomb lattice structure in the strongly interacting limit. Because of the strong spin-orbit coupling of iridium, the effective spin exchange model is highly anisotropic and frustrated. We use the Schwinger fermion approach to map out the phase diagram of the model. At the mean field level several spin liquid phases are found: a gapless spin liquid , a chiral spin liquid, and a helical spin liquid phase. Moreover, in the strong exchange coupling limit we obtain a dimerized phase. The gapless spin liquid phase is characterized by Dirac nodes. In the chiral phase the Dirac nodes are gapped in the bulk, and the system possess a nonzero Chern number signifying existence of chiral modes along the boundary of the system. The helical phase preserves time reversal symmetry, has a bulk gap, and features helical gapless edge modes along boundary analogous to those in topological insulators with a nontrivial invariant. We further investigate the nature of the spin liquid phase by considering the gauge fluctuations above the mean field solution. The chiral spin liquid phase is stable as it breaks time reversal symmetry and acquires a nonzero Chern-Simon term in the effective low energy theory.   

Magnetic torque measurement in a gapless spin-liquid state of EtMe$_3$Sb[Pd(dmit)$_2$]$_2$

The organic Mott insulator EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ with nearly identical 2D triangular lattice of $S = 1/2$ is the most promising candidate material of a quantum spin liquid, in which gapless spin excitations have been reported by the thermal transport measurements [1]. However, it remains unsettled whether the observed gapless excitations are magnetic ($S \geq 1/2$) or nonmagnetic ($S=0$). The magnetic torque measurement is a powerful tool to probe the magnetic properties down to very low temperature, because it is not affected by isotropic impurities. We report the magnetic torque measurements of EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ down to 30 mK up to 32 T. A finite magnetic susceptibility is observed at the lowest temperature. Magnetization increases linearly with the magnetic field up to 32 T without exhibiting any anomarly. These results indicate that the gapless excitations reported by the thermal conductivity measurements are magnetic and that the present system is in an algebraic spin liquid phase. \\[4pt] [1] M. Yamashita \textit{et al.}, Science \textbf{328}, 1246 (2010).   

Field-Dependent Instability of the Candidate Quantum Spin Liquid in EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ as Revealed by NMR

In recent years, the two-dimensional spin-$1/2$ triangular lattice of the organic salt EtMe$_3$Sb[Pd(dmit)$_2$]$_2$ has emerged as a candidate for the realization of a quantum spin liquid. Furthermore, thermal conductivity and nuclear magnetic resonance (NMR) experiments unveiled the presence of a low-temperature instability in the spin liquid state, the opening of a spin gap. We performed a detailed $^{13}$C NMR study on this material at low temperatures \mbox{($30$mK$\leq T\leq 1.5$ K)} and for a wide range of external magnetic field values \mbox{($B_0=0.6-9$T)}. In finite fields, a clear break in the temperature derivative of the spin-lattice relaxation is observed at a temperature $T_m(B_0)$, with $T_m$ following the empirical form $T_m(B_0)\sim \left| B_0-B_c\right| ^{1/2}$. Moreover, a uniform broadening of the NMR line for finite fields suggests the presence of a small field-induced staggered magnetization. We discuss these results in the context of possible instabilities, and existing thermodynamic data.   

Low temperature magnetodielectric coupling in the spin-liquid candidate $\kappa $-(BEDT-TTF)$_{2}$Cu$_{2}$(CN)$_{3}$

In the context of geometrical frustration of exchange coupling between spins on dimer orbitals, the possibility of a quantum spin-liquid state has been inferred for the quasi-2D organic Mott insulator $\kappa $-(BEDT-TTF)$_{2}$ Cu$_{2}$ (CN)$_{3}$. However, because the geometrical frustration effect is not strong, it has been proposed that the suppression of magnetic order could result from fluctuating quantum electric dipoles. Indeed, non-trivial charge degrees of freedom survive in this dimer Mott insulator as observed in dielectric measurements. Here, we report in-plane microwave dielectric measurements that reveal a coupling of the electric dipoles to the spins at low temperatures. Anomalies in the complex dielectric permittivity are observed at 6 K and around 3-4 K. The one at 6 K is in clear correlation with the thermal expansion measurements for which a second-order phase transition was inferred. The second dielectric anomaly is frequency dependent and cannot be associated to a phase transition; however, it is rapidly modified and ultimately suppressed by a magnetic field which effects are highly anisotropic. These results could be consistent with the scenario of a dipolar-spin liquid phase where spins couple to the dipoles through the interdimer charge fluctuation. Such a phase appears inhomogeneous since the dielectric anomalies are sensitive to thermal cycling and small pressures.   

Coulombic Quantum Liquids in Spin-1/2 Pyrochlores

We develop a non-perturbative ``gauge Mean Field Theory'' (gMFT) method to study a general effective spin-$1/2$ model for magnetism in rare earth pyrochlores. gMFT is based on a novel exact slave-particle formulation, and matches both the perturbative regime near the classical spin ice limit and the semiclassical approximation far from it. We show that the full phase diagram contains two exotic phases: a quantum spin liquid and a coulombic ferromagnet, both of which support deconfined spinon excitations and emergent quantum electrodynamics. Phenomenological properties of these phases are discussed.   

Spin Liquid Ground State of Spin-1/2 Square J$_{1}$-J$_{2}$ Heisenberg Model

We perform highly accurate density matrix renormalization group (DMRG) simulations to investigate the ground state properties of the spin-1/2 antiferromagnetic (AFM) square lattice Heisenberg J$_{1}$-J$_{2}$ model on numerous long cylinders with circumference up to 10 lattice spacings. Besides finding the conventional Neel AFM phase at small J$_{2}$/J$_{1}<$0.41 and the stripe AFM phase at large J$_{2}$/J$_{1}>$0.62, we establish an intriguing gapped quantum spin liquid phase within the parameter space 0.41$<$ J$_{2}$/J$_{1}<$0.62 by showing the absence of various conventional broken symmetries as well as by identifying topological features such as finite topological entanglement entropy and topological ``even-odd'' effect.   

Projected wave function study of Z$_2$ spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet

Within the class of Gutzwiller projected fermionic wave functions, by using quantum variational Monte Carlo simulations, we investigated the energetics of all possible $Z_2$ spin liquids that can potentially occur as ground states of the nearest-neighbor S=1/2 quantum Heisenberg model on the Kagome lattice [1]. We conclusively show that all gapped and gapless $Z_2$ spin liquids are higher in energy compared to the U(1) gapless states in whose neighborhoods they lie. In particular, the most promising gapped $Z_2$ spin liquid (the so-called $Z_2[0,\pi]\beta$ state), conjectured to describe the ground state [2], is always higher in energy compared to the U(1) Dirac spin liquid. We also extended the U(1) Dirac state and the uniform RVB spin liquid to include next-nearest-neighbor hopping terms, and studied its local and global stability towards various valence bond crystal patterns. We found that a non-trivial 36-site VBC is stabilized upon addition of a small ferromagnetic exchange coupling [3]. \\[4pt] [1] Y. Iqbal, F. Becca, and D. Poilblanc, Phys. Rev. B 84, 020407(R) (2011)\\[0pt] [2] Y.-M. Lu, Y. Ran, and P.A. Lee. Phys. Rev. B 83, 224413 (2011)\\[0pt] [3] Y. Iqbal, F. Becca, and D. Poilblanc, Phys. Rev. B 83, 100404(R) (2011)   

Edge states of $(2+1)D$ $BF$ theory as the effective field theory of translational invariant ${\bf Z}_{2}$ spin liquids

We classify (2+1)-dimensional $BF$ field theory as the effective field theory for the achiral and translation invariant ${\bf Z}_{2}$ spin liquids on the square lattice. We use the pattern of the crystal momenta of $BF$ field theory to find the corresponding ${\bf Z}_{2}$ spin liquid. Then, we show that some classes of ${\bf Z}_{2}$ spin liquids can support gapless helical edge states depending on the projective symmetry group of the effective $BF$ theory. We supplement this effective theory by studying possible projective symmetry group of ${\bf Z}_{2}$ spin liquids.   

ESR lineshape for a two-dimensional spin liquid state with spinon Fermi surface

We propose that ESR experiment can be an informative probe of a putative spin-liquid ground state with a spinon Fermi surface. Our proposal is based on the assumption that in addition to strong and frustrated Heisenberg exchange interactions, the spins also interact via an asymmetric Dzyaloshinskii-Moriya interaction (DMI). We argue that in a spin-liquid state the DMI plays the role of a spin-orbit interaction well-known in low-dimensional conductors. Assuming further spin-orbit interaction to be of Rashba type, we calculate the ESR absorption spectrum of a two-dimensional fermion gas subject to Zeeman and spin-orbit fields. Finite spin-orbit coupling translates into a finite absorption spectrum width. Remarkably, the ESR signal diverges as an inverse square-root at the edges of the spectrum.   

Loop condensation in quantum dimer models

The formation of topological order is well understood in terms of the mechanism of loop condensation in systems with loop-like degrees of freedom. Various quantum dimer models posses exotic liquid states, including topologically ordered phases. Dimer models and can be mapped to loop models and these dimer liquid phases may be described as loop condensates. We present a numerical study of the geometric properties of the loop condensates in quantum dimer models and related models using classical Monte Carlo as well as ground state quantum Monte Carlo calculations.   

Gapless fractionalized vortex liquids in frustrated quantum antiferromagnets

The standard theoretical approach to gapless spin liquid phases of two-dimensional frustrated quantum antiferromagnets invokes the concept of fermionic slave particles into which the spin fractionalizes. As an alternate we explore new kinds of gapless spin liquid phases in frustrated quantum magnets with $XY$ anisotropy where the vortex of the spin fractionalizes into gapless itinerant fermions. The resulting gapless fractionalized vortex liquid phases are studied within a slave particle framework that is dual to the usual one. We demonstrate the stability of some such phases and describe their properties.   

Properties of the short ranged RVB wavefunction on non-bipartite lattices via Pfaffian Monte Carlo

We introduce a Monte Carlo scheme to investigate the nearest neighbor version of Anderson's resonating-valence-bond (RVB) spin-$1/2$ wave function on the kagome and on the triangular lattice. For the kagome lattice there exists a parent Hamiltonian for this state, but even in the absence of a known Hamiltonian, wave functions of RVB type are interesting as such. The corresponding RVB wave function on the square lattice has recently enjoyed much attention, and it was shown that earlier findings about the criticality of the { \it dimer}-liquid wave function on the square lattice qualitatively carry over to the analogous {\it spin}-liquid wave function on this lattice. On bipartite lattices, the spin-$1/2$ RVB wave functions are amenable to MC methods based on a loop gas picture. For other lattices, this method has a sign problem. We present a method that is free of this sign problem, making use of a Pfaffian presentation of the wave function in the orthogonal Ising basis. Our results for both open and periodic boundary conditions show that spin-spin and ``dimer-dimer'' type correlation function are exponentially decaying. Time and/or results permitting, we also comment on the behavior of the monomer correlations, and mention possible applications of our method to other problems.   

Exact Chiral Spin Liquid on the Ruby Lattice and Mean-Field Perturbations of Gamma Matrix Models

We report recent results on the study of an exactly solvable spin-3/2 model of the Kitaev type [A. Kitaev, Ann. Phys. 321, 2 (2006)] and related mean-field studies. The model is a Yao-Zhang-Kivelson Gamma Matrix (GM) extension [H. Yao, S.C. Zhang, and S.A. Kivelson, Phys. Rev. Lett.102, 217202 (2009)] on the ruby or rhombihexadeltille lattice. We show that the model admits an exact chiral spin liquid ground state solution with emergent free spinon excitations and interesting bandstructure. Specifically, we find gapped phases with chiral edge modes resulting from topologically non-trivial Chern numbers and gapless phases with interesting spinon Fermi surfaces. We have also studied the addition of perturbations to this and other GM Kitaev systems (kagome, square) which leads to weakly interacting spinons. We have applied a mean-field analysis to explore the interplay between these interactions and the gapless spin liquid phases.   

Session Q9: Focus Session: Complex Bulk Oxide: Doped and Undoped Manganites

Weak ferromagnetism in lightly electron-doped CaMnO$_3$

The origin of the weak ferromagnetism, that is observed in lightly electron-doped CaMnO$_3$, is studied by means of the non-collinear spin density functional theory, including the spin-orbit interaction. We show that the spin-canting in the G-type antiferromagnetic structure is realized by the electron-doping, and the canting angle becomes larger with increase of the doping amount. The estimated canting angle is in a good agreement with the experimental value of the Ce-doped CaMnO$_3$ [1] The spin-canted state is stabilized by the double-exchange interaction, and the spin-orbit interaction does not play a crucial role in this phenomenon. In addition, the spin-canted state shows metallic behavior by the double-exchange transfer that gives a reasonable interpretation for the experimental electronic transport property [2] We also clarify a possibility of the antiferromagnetic-ferromagnetic phase separation [3] that will be realized when doped-electrons are strongly localized.\\[4pt] [1] E.N. Caspi et al., Phys. Rev. B 69, 104402 (2004).\\[0pt] [2] P.-H. Xiang et al., Appl. Phys. Lett. 94, 062109 (2009).\\[0pt] [3] E. Dagotto et al., Phys.Rep. 344, 1 (2001).   

Synthesis, Structural and Magnetic Characterization of Rare Earth Doped SrMnO$_{3}$ Compounds

We report on our ongoing work on the synthesis, characterization and magnetic studies of Rare Earth (RE) containing RE-SrMnO$_{3}$ compounds. The aim of the study is to determine how different RE elements influence the magnetic properties of said materials. We have so far investigated the incorporation of Dy and Yb into the SrMnO$_{3}$ unit cell. To this effect we have employed solid state reaction synthesis methods to fabricate said compounds. The reaction products evolution were monitored as a function of time by XRD, TGA and SEM. Measurements of lattice parameters and Rietveld refinement of the XRD spectra, indicate that Dy and Yb are incorporated substitutionally in SrMnO$_{3}$. Temperature dependent magnetic measurements, on the other hand, reveal a common transition temperature around 41 K for both Dy and Yb doped SrMnO$_{3}$. We are in the process of synthesizing additional materials containing additional RE elements to investigate how the electronic properties of said RE may influence the magnetic properties of these compounds.   

Far-IR spectra of magnons, crystal field transitions, and phonons in hexagonal \textit{RE}MnO$_{3}$ (\textit{RE}=Er, Tm, Yb, Lu) single crystals

Far-IR spectra of hexagonal \textit{RE}MnO$_{3}$ (\textit{RE}=Er, Tm, Yb, Lu) single crystals have been studied between $T$=1.6 K and 300 K using transmission in high magnetic field and rotating analyzer ellipsometry. The symmetry of the IR optical phonons and their oscillator strengths were determined for compounds with different \textit{RE} ions. The temperature dependence of the phonon frequencies revealed a strong spin-phonon interaction in the temperature range below $T_{N}\sim $70 K. The effective g-factors have been determined for the AFM resonances and crystal field transitions using external magnetic fields up to 10 T. The frequency of the AFM resonances around 50 cm$^{-1}$ increases systematically with a decrease of the \textit{RE} ion radius. The observed effects are analyzed taking into account main magnetic interactions in the system including exchange of the Mn$^{3+}$ spins with \textit{RE}$^{3+}$ paramagnetic moments. The magnetic ordering of \textit{RE} ions was observed at low temperatures $T<$3.5 K and in strong magnetic fields.   

Direct observation of collective magnetism at ferroelectric domain walls in multiferroic ErMnO$_{3}$

Multiferroic hexagonal manganities \textit{RE}MnO$_{3}$ (\textit{RE} = Ho, Er, Lu, etc.) have been of great interest because of the coexistence of ferroelectric and magnetic orders. Herein we report cryogenic magnetic force microscopy (MFM) studies of flux-grown ErMnO$_{3}$ single crystals with vortex ferroelectric domain pattern. By uniquely correlating ambient piezo-response force microscopy and low temperature MFM images at the same location, we identified alternating uncompensated magnetic moments at ferroelectric domain walls that correlate over entire vortex network, suggesting collective magnetism at ferroelectric vortex domain walls.   

Maximally localized Wannier functions in LaMnO$_3$ within PBE$+U$, hybrid functionals, and GW: an efficient route to construct ab-initio tight-binding parameters for $e_g$ perovskites

Using the newly developed VASP2WANNIER90 interface we have constructed maximally localized Wannier functions [1] (MLWFs) for the $e_g$ states of the prototypical Jahn-Teller magnetic perovskite LaMnO$_3$ at different levels of approximation for the exchange-correlation kernel. These include conventional density functional theory (DFT) with and without additional on-site Hubbard $U$ term, hybrid-DFT, and single shot GW. By suitably mapping the MLWFs onto an effective $e_g$ tight-binding (TB) Hamiltonian [2,3] we have computed a complete set of TB parameters providing the band dispersion in excellent agreement with the underlying {\em ab initio} and MLWF bands. The method-dependent changes of the TB parameters and their interplay with the electron-electron interaction term are discussed and interpreted, outlining a guidance for more elaborate treatments of correlation effects in effective Hamiltonian-based approaches. \newline [1]\,I.\,Souza,\,N.\,Marzari,\,and\,D.\,Vanderbilt,\,Phys.Rev.B\,65,\,035109\,(2001).\newline [2]\,R.\,Kov\'a\v{c}ik\,and\,C.\,Ederer,\,Phys.Rev.B\,81,\,245108\,(2010).\newline [3]\,R.\,Kov\'a\v{c}ik\,and\,C.\,Ederer,\,Phys.Rev.B\,84,\,075118\,(2011).   

Reverse Monte Carlo Modeling of Pair Distribution Function Data as a Tool for Separating the Coordination Environments of Multiple Atoms Disordered Over a Single Site

The local structures of 8 perovskite compounds which contain equal concentrations of 2 transition metal cations disordered over the $B$-sites have been investigated using reverse Monte Carlo (RMC) modeling of neutron pair distribution function (PDF) data. Such compounds are known to display a number of interesting magnetic and electronic properties which, due to the cation disorder, cannot be correlated with the average long range structure and so remain poorly understood. In compounds with $B$=Mn/Ru there exists a valence degeneracy between Mn$^{3+}$/Ru$^{5+}$ and Mn$^{4+}$/Ru$^{4+}$. We demonstrate that the RMC method can be used as an effective tool to separate out the individual coordination environments of these cations and also to monitor the relative concentrations of the different oxidation states. We find that the valency ratio is governed by the size of the $A$-site cations. In a different series of Sr$_{2}$FeMnO$_{6-x}$ perovskites we find that locally the structures are quite different from the average cubic structures, with the local coordination environments more closely resembling those of the brownmillerite structure. In all compounds the octahedra containing Mn$^{3+}$ are Jahn-Teller distorted, even if this distortion is not evident in the average structure.   

Direct Visualization of Electric-Field-Driven Migration and Decay of Oxygen Vacancy-induced Stripes in Pr$_{0.7}$Ca$_{0.3}$MnO$_{3}$

We report on the microscopic evidence of electric-field driven migration and decay of oxygen vacancy stripes in Pr$_{0.7}$Ca$_{0.3}$MnO$_{3}$ (PCMO30). A local lattice stripe phase associated with oxygen vacancy migrating along the applied electric field was imaged in real time by using \textit{in-situ} imaging with high-resolution transmission electron microscopy (TEM). Such a field-driven dynamic oxygen migration process should be responsible to the transport for the resistance switching effects observed in many metal-oxide-metal structures, thus providing a direct microscopic evidence for the oxygen migration model. A decay of oxygen vacancy stripes with a characteristic decay time has been observed, consistent with measurement of resistance relaxation in the materials.   

Ultrafast pump-probe reflectance study of multiferroic Eu$_{0.75}$Y$_{0.25}$MnO$_{3}$

Time resolved dynamical studies of multiferroic materials help unravel the fundamental interactions between various degrees of freedom. We report an ultrafast pump-probe reflectance study of multiferroic Eu$_{0.75}$Y$_{0.25}$MnO$_{3}$. The material undergoes antiferromagnetic ordering and, upon further cooling, ferroelectric ordering that strongly couples to the material's magnetic state. We measured the pump-probe reflectance in this compound using 400- and 800-nm pump and probe pulses. We found that the amplitude of the photoinduced reflectance increases dramatically with the development of local and long-range spin-spin correlations as the temperature is lowered toward the magnetic ordering transition. We also observe a dramatic increase in the rise time, up to 10s of picoseconds, of the photoinduced reflectance. This time scale is consistent with the long response times of the spin system in manganites. We suggest that the modification of the local exchange coupling around the photoinduced electrons and holes is responsible for the observed reflectance behavior, as the optical properties of manganites are known to couple strongly to the local and long-range spin correlations [1]. \\[4pt] [1] N.N. Kovaleva et al., Phys. Rev. Lett. \textbf{93}, 147204 (2004)   

Multiple Magnetic Transitions and Magnetocaloric Effect in (La,Pr,M)MnO$_{3}$ (M = Ca, Sr, Ba) Mixed Phase Manganites

The manganite compound (La,Pr,Ca)MnO$_{3}$ is a well-studied system that is known to exhibit a complex phase diagram featuring ``strain liquid'' and ``strain glass'' regions in combination with competing ferromagnetic (FM) and charge-ordered antiferromagnetic (CO/AFM) phases. The balance of these phases is sensitive to various perturbations including magnetic and electric field, strain, bandwidth, and A-site cation disorder. The A-site disorder and bandwidth of this compound can be tuned through the replacement of Ca with larger Sr and Ba ions. We report here a systematic study of the influence of cation substitution on the magnetic and magnetocaloric properties of La$_{0.35}$Pr$_{0.275}$M$_{0.375}$MnO$_{3}$ (M = Ca, Sr, Ba). Structural properties, including lattice parameters and Mn--O--Mn bond angles, were determined from X-ray diffraction patterns. DC magnetometry studies reveal multiple magnetic transitions in each sample which are probed by magnetocaloric effect (MCE) and transverse susceptibility (TS) experiments. Increasing the average A-site cationic radius is found to strongly impact the magnetic properties and phase behavior of the system.   

Evolution of antiferromagnetic order during the colossal magnetoresistive transition

Pr$_{0.7}$Ca$_{0.3}$MnO$_3$ (PCMO) displays one of the largest colossal magneto-resistances (CMR) among manganites. Magneto-transport data suggest that an insulating antiferromagnetic to metallic ferromagnetic transition occurs as the system goes through a CMR transition with the application of a high magnetic field (~3-6T). However, the nature of this transition is a mystery. We report the first high magnetic field resonant soft x-ray scattering (RSXS) experiments on PCMO which follow the evolution of the antiferromagnetic superlattice order through the CMR transition. We find that the antiferromagnetic order is first enhanced by several orders of magnitude before melting away into the metallic ferromagnetic phase. Additional high field x-ray magnetic circular dichroism (XMCD) measurements allow us to track the spin and orbital moments and construct a microscopic picture of the competing forces at the heart of CMR.   

Low energy magnetic excitations in phase-separated La5/$8-y$Pr$y$Ca3/8MnO3

La5$/$8-$y$Pr$y$Ca3$/$8MnO3 (LPCMO) ($y= 0.$4) is one of the prototype materials for the study of phase separation. The end members of the series, La5/8Ca3/8MnO3 and Pr5/8Ca3/8MnO3, have a robust low temperature FM metallic and charge ordered insulating states, respectively. Various experimental techniques have shown evidence of two-phase coexistence for intermediate Pr contents. However, a clear understanding of some basic macroscopic signature of phase separation is still lacking. The states of the coexistence phases are different when the system goes through different thermodynamic paths with the application of magnetic field. The zero-field-cooled (ZFC) procedure results in a dominant CO-OO state with little FM clusters at low temperature. Such insulating state is robust against external magnetic field. On the other hand, a zero-field cooled, field warming (ZFC-FW) procedure causes a sudden increase in FM intensity near the glassy transition temperature (TG $\sim $ 25K). In this talk we will present the results of recent elastic and inelastic neutron scattering experiments on a single crystal specimen of LPCMO, which reveal the nature of the complex phase coexistence at low temperatures.   

Anisotropic field-induced melting of orbital ordering phase in Pr0.6Ca0.4MnO3

The orbital degree of freedom in correlated electron systems plays an essential role in creating versatile phenomena via its coupling with charge, spin, and lattice. One extraordinary phase in doped oxide compounds is the charge/orbital-ordered (OO) antiferromagnetic (AF) insulating state, which, interestingly, can be melted to an orbital-liquid metallic state by external magnetic field. By measuring the field-dependent transport behavior of Pr0.6Ca0.4MnO3 single crystal at different temperatures, we have found a field-orientation dependent melting of the charge-orbital ordered state, regardless whether or not the system is in AF phase. The field-induced melting is found stronger when the applied field is in theab (basal)-plane. This can be understood as suppression of the CE-type OO state via spin-orbit coupling induced preference of in-plane orbital direction.   

Paramagnetic Spin Correlations in Colossal Magnetoresistive La$_{0.7}$Ca$_{0.3}$MnO$_{3}$

Inelastic neutron scattering measurements, taken on the ARCS time-of-flight spectrometer, reveal dynamic spin correlations throughout the Brillouin zone in the colossal magnetoresistive system La$_{0.7}$Ca$_{0.3}$MnO$_{3}$ at 265~K ($\approx$1.03~$T_{C}$). Well defined correlations are observed in constant-$E$ scans. The long-wavelength behavior can be attributed to spin diffusion, qualitatively consistent with dynamical scaling theory, with a correlation length of $\approx$10~{\AA}. Dynamic correlations are observed at energies up to at least 28~meV, suggesting persistent short range spin correlations in the paramagnetic phase. An additional and unexpected component of the scattering is observed at lower energies which takes the form of ridges of strong scattering running along ($H$~0~0) and equivalent directions.   

Existence of a New Phase in the Intermediate $J_{\rm AF}$-coupling Regime of the Two-Orbital Model for Manganites

We report the existence of a new exotic state in the two-orbital model for manganites in the intermediate $J_{\rm AF}$ coupling regime, analyzed using the standard Monte Carlo technique based on the exact diagonalization of the electronic sector. At density $x=1/4$, this state shows diagonal ferromagnetic (FM) chains with uniform charge order (CO), stacked in between CE-like zig-zag patterns of spin with less populated staggered CO. The new state exists in a narrow range between the well-known FM metallic and C$_{x}$E$_{1-x}$ insulating states, and provide a realization in the clean limit of the nanoscale phase separation scenario of CMR manganites. The existence of many other competing exotic states in this range of couplings will also be discussed.   

Session Q10: Invited Session: Rare Fluctuation Effects in Strongly Disordered Systems

Rare Fluctuation Effects in the Anderson Model of Localization

Two significant advances in the theory of disordered systems in the past three decades have been (i) the development of large disorder Renormalization Group methods, and (ii) a more concerted effort to study of the effects of rare fluctuations or configurations, such as Griffiths' phenomena. A major problem facing the latter in many-body systems has been the enormous numerical resources needed to see these rare phenomena. In this talk, we examine the issue of rare configuration effects in Anderson's original model of localization (1958). In this talk, we examine the issue of rare configuration effects in Anderson's original model of localization. We show that effects due to resonant tunneling among neighboring sites leads not only to anomalous behavior of electronic eigenstates far in the Lifshitz tail, where the density of states is exponentially suppressed, but also leads to singularities in average properties (i.e. the inverse participation ratio) as a function of energy, where the density of states is large. The singular behavior, which separates resonant, Lifshitz-like states from typical, Anderson-localized states, occurs \emph{in the insulating phase}, and thus is present in \emph{all} dimensions [1]. Using the analytic solution of a toy model, as well as numerical results of the Anderson model for several different disorder distributions in dimensions d = 1, 2 and 3, we show that this separation of eigenstates due to rare fluctuations is a ubiquitous property of the Anderson model with \emph {bounded} disorder. This suggests that the half-century-old model, being solvable in polynomial time, is a prime candidate for detailed numerical studies of rare fluctuation effects in disordered systems. \\[4pt] [1] Sonika Johri and R. N. Bhatt, arXiv1106.1131; and in preparation.   

Electronic Griffiths Phases and Quantum Criticality at Disordered Mott Transitions

The effects of disorder are investigated in strongly correlated electronic systems near the Mott metal-insulator transition. Correlation effects are found\footnote{E. C. Andrade, E. Miranda, and V. Dobrosavljevic, Phys. Rev. Lett., \textbf{102}, 206403 (2009).} to lead to strong disorder screening, a mechanism restricted to low-lying electronic states, very similar to what is observed in underdoped cuprates. These results suggest, however, that this effect is not specific to disordered d-wave superconductors, but is a generic feature of all disordered Mott systems. In addition, the resulting spatial inhomogeneity rapidly increases\footnote{E. C. Andrade, E. Miranda, and V. Dobrosavljevic, Phys. Rev. Lett., \textbf{104} (23), 236401 (2010).} as the Mott insulator is approached at fixed disorder strength. This behavior, which can be described as an Electronic Griffiths Phase, displays all the features expected for disorder-dominated Infinite-Randomness Fixed Point scenario of quantum criticality.   

Gaps and Pseudogaps across the inhomogeneous superconductor to paired insulator transition

The mechanism for the disorder-tuned superconductor to insulator transition (SIT) in thin films and the nature of the resulting insulator are still debated, despite decades of research. We use quantum Monte Carlo simulations [1] that treat, on an equal footing, inhomogeneous amplitude variations and phase fluctuations, and go beyond our earlier Bogoliubov-deGennes analysis [2]. We gain new microscopic insights into the SIT, compare our theory with experiments [3] and make testable predictions for local spectroscopic probes. The energy gap in the single-particle density of states survives across the transition, but coherence peaks exist only in the superconducting state. A characteristic pseudogap persists above the critical disorder and critical temperature, in contrast to conventional theories. Surprisingly, the insulator has signatures of pairing with a two-particle gap scale that vanishes at the superconductor--insulator transition, despite a robust single-particle gap. The impact of rare regions on the gaps will also be discussed. In collaboration with K. Bouadim, Y.L.Loh and N. Trivedi. \\[4pt] [1] K. Bouadim, Y.L.Loh, M. Randeria and N. Trivedi, Nature Phys. 7, 884 (2011). \\[0pt] [2] A. Ghosal, M. Randeria, and N. Trivedi, Phys. Rev. B 65, 014501 (2001). \\[0pt] [3] B. Sacepe et al., Nature Comm. 1, 140 (2010); Nature Phys. 7, 239 (2011); M. Mondal et al., Phys. Rev. Lett. 106, 047001 (2011).   

Infinite-randomness criticality in disordered metals and superconductors

Quantum phase transitions in disordered systems often display unconventional behavior which is dominated by rare strongly coupled spatial regions. In this talk, we investigate magnetic and superconducting quantum phase transitions in disordered metallic systems. We develop a strong-disorder renormalization group method that accounts for both quenched disorder and the dissipation of the critical modes due to the Fermi sea. We find that the quantum phase transition in Heisenberg anti-ferromagnets and the pair-breaking superconductor-metal transition are both governed by non-perturbative infinite-randomness critical points. Even stronger disorder effects arise for metallic magnets with Ising spin symmetry in which the quantum phase transition is completely destroyed by smearing. We determine thermodynamic and transport properties at these transitions and in the associated quantum Griffiths phases. We also discuss the current status of experimental observations of these exotic disorder phenomena in a variety of systems including transition metal compounds, heavy-fermion systems, and superconducting nanowires.   

Session Q11: Focus Session: Graphene Structure, Stacking, Interactions: Infrared and Terahertz Spectroscopy

Collective modes in gapped bilayer graphene

We calculate the polarizability of gapped bilayer graphene using the four-band continuum model. In the presence of a gap the four-band model and the simplified two-band model return bands that are qualitatively different especially at low energies. We find that because of these differences the static polarizability obtained using the four-band model is qualitatively different from the one obtained using the two-band model. We also find that the differences between the two-band model and the four-band model profoundly affect the dynamical dielectric function, and therefore the properties of the plasmon modes. In addition, we study the effect of trigonal warping and find that it qualitatively modifies the density response function.   

Sum-Frequency Vibrational Spectroscopic Studies of Polymer/Graphene Interface

The interest in alignment of polymer on graphene surfaces has been motivated by a desire to gain a fundamental understanding the interaction between molecule and graphene, and for possible application of graphene for surface chemistry. Graphene-polymer interactions also play an important role in graphene-polymer composites, which exhibit greatly improved electrical conductivity, strength, and thermal stability compared with pure polymer material. Theoretical investigation of graphene-polymer interface has been performed previously using molecular dynamics simulations [1]. However, experimental studies of the interfacial characteristics of graphene-polymer composite has been challenging. Here we investigate the molecular orientation at polymer/graphene interface using phase-sensitive-sum-frequency generation spectroscopy. The sum-fequency spectrum shows clear vibration signatures of CH$_{2}$ groups. In particular, it suggests that CH$_{2}$ groups pointing toward the graphene surface interact with graphene strongly, which leads to a red shift of vibration frequency as large as 15 cm$^{-1}$. In this talk I will discuss the implications of our experimental findings. \\[4pt] [1] C. Lv, Q. Xue, D. Xia, M. Ma, J. Xie, and H. Chen, \textit{J. Phys. Chem. C}, \textbf{2010}, $114$ (14), 6588--6594.   

Tunable Quantum-Enhanced Second-Order Optical Nonlinearity From Bilayer Graphene

Bilayer graphene exhibits a tunable band gap when the inversion symmetry is broken. It therefore stimulates much interest on its physical characterization and practical application for mid-infrared (MIR) optoelectronics. Here we focus on its second order nonlinear optical response to the MIR laser excitation under device condition, following a quantum description of nonlinear optical conductivity. Our theoretical study shows that, for a certain laser-frequency range determined by the band-gap, giant second harmonic generation can be excited due to the intrinsic electronic spectrum of bilayer graphene. Electrically tunable $\chi ^{(2)}$ on the order of $10^5pm/V$ can be achieved, 3 orders of magnitude larger than the widely-used nonlinear crystal AgGaSe2.   

Infrared magneto-spectroscopy of graphene-based systems

The results of infrared magneto-spectroscopy of different graphene-based materials will be presented. These systems involve multi- and mono-layers of epitaxial graphene, decoupled graphene flakes on the surface of graphite as well as bulk graphite. The magneto-optical methods serve us mostly as a tool of Landau level spectroscopy. It is used to study the characteristic response due to massless or massive Dirac-type particles and, e.g., to distinguish materials with graphene layers exhibiting rotational or Bernal stacking. Broadening of inter-Landau level transitions has been traced as a function of magnetic field and energy to evaluate the quality of multi-layer epitaxial graphene in terms of scattering time and carrier mobility. From broadening of overlapping Landau levels we find that the scattering rate increases linearly with energy. Complementary to these experiments, inelastic relaxation processes have been studied in pump-and-probe measurements in THz range. The obtained data indicate that the inelastic processes are significantly slower than the elastic ones, and also that the inelastic relaxation is slowed down when the photon energy is tuned to values below the optical phonon frequency. References: M. Orlita et al., PRL, to be published (2011); S. Winnerl et al., PRL, to be published (2011).   

Far-infrared Kerr rotation spectroscopy of graphite and multilayer graphene

Graphite attracts much attention nowadays as a reference 3D material for graphene. Since the early measurements of the cyclotron effect in graphite over fifty years ago [1], a satisfactory quantitative description of this spectacular phenomenon is missing. The analysis of magneto-optical data was hindered either by a limited set of the used photon energies or by the lack of the optical selectivity between electrons and holes. We overcome this issue by measuring the far-infrared magneto-optical Kerr rotation spectra [2] and achieve a highly accurate unified microscopic description of all spectra in a broad range of magnetic fields (0.5 -- 7 T) by taking rigorously the c-axis band dispersion and the trigonal warping into account. We find that the second- and the forth-order cyclotron harmonics are optically almost as strong as the fundamental cyclotron resonance even at high fields. The same effects are expected to strongly influence the magneto-optical spectra of Bernal stacked multilayer graphene and therefore play a major role in the respective applications. \\[4pt] [1] J. K. Galt, W.A. Yager and H.W. Dail Jr., Phys. Rev. \textbf{103}, 1586 (1956) \newline [2] J. Levallois, M.K. Tran and A. B. Kuzmenko, arXiv:1110.2754v2; submitted.   

``Intrinsic'' terahertz plasmons and magnetoplasmons in single layer graphene on SiC

Plasmons in graphene have lately attracted much attention, to great extent, due to promises for novel technologies. Recently, plasmon absorption in graphene was attained in deliberately patterned structures [1]. We measured the magneto-optical absorption and Faraday rotation response of highly doped single layer graphene, epitaxially grown on Si-terminated SiC substrate. The zero-field spectra show a clear plasmon peak at about 2 THz. In magnetic fields, the plasmon peak splits into two branches, thus showing a characteristic magneto-plasmon behavior which was previously observed in periodic dot structures in GaAs two dimensional electron gases [2]. Hence, in large-scale epitaxial graphene on SiC, light can couple to plasmons in the absence of the intentional patterning of graphene. We suggest that optically-active plasmon absorption in this kind of two-dimensional system arises from laterally confined plasmon modes due to``intrinsic'' imperfections of graphene on Si-face of SiC, such as, grain boundaries which we clearly identify with AFM methods. \newline\noindent [1] L. Ju \emph{et al.} , Nature Nanotechnology \textbf{6}, 630 (2011). \newline\noindent [2] A. J. Allen \emph{et al.} , Phys Rev B \textbf{28}, 4875 (1983).   

Enhanced Optical Dichroism of Graphene Nanoribbons

The optical conductivity of graphene nanoribbons is analytical and exactly derived. It is shown that the absence of translational invariance along the transverse direction allows considerable intra-band absorption in a narrow frequency window that varies with the ribbon width, and lies in the THz band for ribbons 10-100nm wide. In this region the anisotropy in the optical conductivity can be as high as two orders of magnitude, which renders the medium dichroic, and allows near 100\% polarizability with just a single layer of graphene. The interplay between the geometrically induced anisotropy with the anisotropy induced by plasmon absorption is also considered and discussed.   

Quasiparticle properties in graphene

The quasiparticle properties in both single layer and bilayer graphene are presented. We study the electron self-energy as well as the quasiparticle spectral function in graphene, taking into account electron-electron interaction in the leading order dynamically screened Coulomb coupling and electron-impurity interaction associated with quenched disorder. Our calculation of the self-energy provides the basis for calculating all one-electron properties of graphene. We provide analytical and numerical results for quasiparticle renormalization in graphene. Comparison with existing angle-resolved photoemission spectroscopy measurements shows broad qualitative and semiquantitative agreement between theory and experiment, for both the momentum-distribution and energy-distribution curves in the measured spectra. We also present the inelastic quasiparticle scattering rate and the carrier mean free path for energetic hot electrons as a function of carrier energy, density, and temperature, including both electron-electron and electron-phonon interactions. Our results are directly applicable to device structures where ballistic transport is relevant with inelastic scattering dominating over elastic scattering.\\[4pt] S. Das Sarma, S. Adam, E. H. Hwang, and E. Rossi, Rev. Mod. Phys. 83, 407 (2011). \\[0pt] E. H. Hwang, Ben Yu-Kuang Hu, and S. Das Sarma Phys. Rev. B 76, 115434 (2007). \\[0pt] E. H. Hwang and S. Das Sarma Phys. Rev. B 77, 081412 (2008). \\[0pt] Rajdeep Sensarma, E. H. Hwang, and S. Das Sarma, Phys. Rev. B 84, 041408(R) (2011).   

Anisotropy of $\pi$-plasmon Dispersion Relation of AA-stacked Graphite

The dispersion relation of optical $\pi$-plasmons of simple hexagonal intrinsic graphite was calculated within the self-consistent-field approximation. The plasmon frequency $\omega_p$ is determined as functions of the wave vector $\textbf{q}_\parallel$ along the hexagonal plane in the Brillouin zone and its perpendicular component $q_z$. These plasmons are isotropic within the plane in the long wavelength limit. As the in-plane wave vector is increased, the plasmon frequency strongly depends on its magnitude and direction ($\phi$). Our results reveal that interlayer interaction could enhance anisotropy of in-plane $\pi$-plasmons. The group velocity for plasmon propagation along the perpendicular direction may be positive or negative depending on the choice of in-plane wave vector.   

Session Q12: Focus Session: Graphene: Growth, Mechanical Exfoliation, and Properties - SiC and Growth Kinetics

From above or from below? Determining how graphene layers form on SiC(0001)

SiC decomposes when heated above 1200 C in vacuum. Silicon desorbs, while the carbon left behind can coalesce to form graphene. Growth of graphene on the SiC(0001) surface (``Si face'') and the SiC(000-1) (``C face'') is very different. On the Si face, graphene growth is epitaxial, while on the C face the growth is generally much less ordered. On the Si face, the observed epitaxy suggests that new graphene layers form under existing one, that is, at the SiC/graphene interface. The lack of epitaxy on the C face suggests that the growth mode on this surface might be different. To test this, we grew ultra-thin epitaxial SiC films (1 nm) on both SiC(0001) and SiC(000-1) via CVD using isotopically pure carbon-13. We then formed graphene via high-temperature thermal decomposition. We used medium energy ion scattering to determine where the carbon-13 was located within the graphene film. For both the Si face and C-face, we find that the carbon-13 is located predominantly in the outmost graphene layer, confirming that graphene grows ``from the inside out'' on both surfaces [1]. This work was performed in collaboration with Matt Copel and Ruud Tromp. \\[4pt] [1] Phys. Rev. Lett. 107, 166101 (2011)   

STM/STS study of ridges on epitaxial graphene/SiC

The graphitization of hexagonal SiC surfaces provides a viable alternative for the synthesis of wafer-sized graphene for mass device production. During later stages of growth, ridges are often observed on the graphene layers as a result of bending and buckling to relieve the strain between the graphene and SiC substrate. In this work, we show, by atomic resolution STM/STS, that these ridges are in fact bulged regions of the graphene layer, forming one-dimentional (nanowire) and zero-dimentional (quantum dot) nanostructures. We further show that their structures can be manipulated by the pressure exerted by the STM tip during imaging. These results and their impact on the electronic properties of epitaxial graphene on SiC(0001) will be presented at the meeting.   

Scalable templated growth of graphene patterns on SiC and their electronic properties

Conventional graphene growth research focuses on SiC on-axis surfaces: SiC (0001) and (000-1). In our previous work, we showed that graphene can be selectively grown on off-axis SiC crystal facets, demonstrated the possibility for templated graphene growth. Here we show scalable production of various devices made with this technique, such as graphene nanoribbons, Hall bars and Aharonov--Bohm rings. Graphene and SiC crystal facets are characterized with SEM and SPM tools. Shubnikov-de Haas oscillations and other phase coherent transport phenomena are observed at low temperature. These observations indicate that the structured epitaxial graphene growth can be a viable method for graphene electronics.   

A study of epitaxial graphene/SiC(0001) functionalized by nitrogen doping

In this work, we have carried out nitridation of epitaxial graphene/SiC(0001) using N$_{2}$ plasma. The effects of processing conditions on the structure of graphene have been investigated by x-ray photoemission spectroscopy and Raman spectroscopy, and changes in the electronic structures of the nitrogen-doped graphene have been studied using scanning tunneling microscopy. We find that the exposure of epitaxial graphene to nitrogen plasma not only leads to N incorporation, but also creates carbon vacancies, resulting in the formation of N-vacancy complexes.   

Creation and sculpting of graphene with ion and electron beams

This talk will cover our recent work on the creation of graphene by ion implantation of carbon into copper substrates followed by a prescribed annealing procedure. We also discuss nanopore nucleation with ion beams and the direct observation of nanopore growth in an aberration corrected TEM. We discuss the cross-sections and knock-on energy transfers required for edge atom removal and demonstrate the controlled growth of monodisperse nanopores in graphene with atomic precision.   

Spatially Selective Graphene Formation on Si Substrate

A uniform large area graphene is useful for applications such as electrode in a touch screen or substrate for growing another material. For applications where graphene is used either as active material (FET for instance) or electrode in a 2-D device array, to form a 2D (electronic) superlattice or photonic crystal, it is critically important to be able to form graphene at selective locations, in desirable size and shape on a substrate, without relying on mechanical cutting. It would be even more significant if the substrate is a Si wafer for coupling with the mature microelectronic technology. We have developed a technique that can achieve these goals. A thin SiC film is first deposited on a Si substrate using MBE. Then, at ambient condition, a focused laser beam is used to convert SiC to graphene at the selected location with the shape and size that can be defined by either a lithographic method or simply by a focused laser beam. The graphene conversion has been verified by structural characterization (TEM, SEM/EDS, etc.) and Raman spectroscopy.   

Surface reconstruction and graphene formation on face-to-face 6H-SiC at 2000 $^{\circ}$C

Improved epitaxial graphene films have been widely reported when the sublimation rate of Si is reduced by ambient Ar gas, vapor phase silane, or confined Si vapor. We describe graphene growth on (0001) 6H-SiC samples annealed ``face-to-face'' [1]; in our modified method the separation is limited only by the flatness of the surfaces. After annealing in 100 kPa Ar gas at 2000 $^{\circ}$C for 300 s, atomic force microscopy (AFM) and electrostatic force microscopy (EFM) show graphene coverage is typically between one and a few layers. Samples without prior hydrogen etching undergo surface reconstruction in the graphitization process, resulting in atomically flat terraces with step bunching. Estimates of the sequestered carbon in the form of graphene are compared to calculated levels due to sublimation and diffusion rates where the sublimated gas is dominated by Si atoms below 2100 $^{\circ}$C. The 2000 $^{\circ}$C samples are contrasted against samples processed between 1700 $^{\circ}$C and 1900 $^{\circ}$C and transport results on large-scale graphene devices are presented.\\[4pt] [1] X.Z Yu, C.G. Hwang, C.M. Jozwiak, A. Kohl, A.K. Schmid and A. Lanzara, New synthesis method for the growth of epitaxial graphene, Journal of Electron Spectroscopy and Related Phenomena 184 (2011) 100-106.   

Imaging grain boundary scattering of graphene in real space

Graphene grain boundaries are unavoidable defects in most growth methods, in particular chemical vapor deposition and thermal decomposition on the SiC(000\underline {1}) surface. How electrons are scattered by those grain boundaries has not been experimentally demonstrated at the nanoscale. Here we report atomic-scale images of grain boundary scattering measured by scanning tunneling potentiometry (STP). Monolayer graphene sheets were synthesized on the SiC(000\underline {1}) surface by thermal decomposition in a background of disilane, using low energy electron microscopy to monitor the graphene thickness during its formation. High resolution scanning tunneling microscopy (STM) reveals graphene grain boundaries and various grain orientations, and STP shows variations in voltage across grains and terraces as current flows across the graphene layer. We have identified two types of grain boundary. One shows a trench structure in STM images; potential mapping shows prominent potential drops. These boundaries between grains appear to be weak links and the dominant scattering locations. The other type of boundary shows a continuous lattice between the grains, with periodic dislocations accommodating the grain misorientation. Potential mapping indicates much weaker scattering despite the grain misorientation. We will discuss transport in polycrystalline graphene based on these measurements.   

Imaging of Electron Beam Induced Current in Epitaxial graphene

It has been observed that there forms a Schottky junction between graphene and SiC in epitaxial graphene due to the work function difference. As a result, it is viable to apply the electron beam induced current (EBIC) technique on epitaxial graphene due to the fact that it needs a built-in field and ample electron generation volume to generate EBIC. EBIC is an important characterization technique, which identifies electrically active impurities/defects, detects local built-in field, and measures minority carrier diffusion length. In this paper, we use a FEI SEM equipped with a current amplifier to investigate the spatial mapping of EBIC. The incident electron beam generates excited electron-hole pairs in SiC and the minority carriers are collected through the Schottky junction before flowing into graphene. EBIC imaging reveals mesoscopic domains of bright and dark contrast areas due to local EBIC polarity and magnitude, which is believed to be the result of spatial fluctuation in the carrier density in graphene. We also investigate the electron energy dependence, which modulates the EBIC magnitude. With an analytical drift-diffusion current model, we are able to extract the minority carrier diffusion length in the SiC, which is on the order of micro meter.   

Writing Graphene Nanoribbons on SiC by Selective Graphitization

We describe a new technique for selective graphene growth onto 4H- and 6H-SiC by ion implan- tation. The presented technique is as easy as patterning (ion implanting) regions where graphene layers are desired followed by annealing to 100 C below the graphitization temperature (T$_{G})$ of SiC. We find that ion implantation of SiC lowers the T$_{G}$ of SiC, allowing selective graphene growth at temperatures below the T$_{G}$ of pristine SiC and above T$_{G}$ of implanted SiC. Presented results provide a new technique to pattern device structures ranging from nanometers to microns in size without using conventional lithography and chemical processing.   

Nucleation of uniform mono- and bilayer epitaxial graphene on SiC(000$\overline{1}$)

Early stage of epitaxial graphene growth on SiC(000$\overline{1}$) has been investigated. Using the confinement controlled sublimation (CCS) method, we has achieved well controlled growth and been able to see the formation of mono- and bilayer graphene islands. The growth features reveal the intriguing growth mechanism. In particular, a new ``stepdown'' growth mode has been identified. Graphene can propagate tens of micrometers across many SiC steps, while, most importantly, step bunching is avoided and the initial regular stepped SiC surface morphology is preserved. The stepdown growth demonstrates a route towards uniform epitaxial graphene in wafer size without sacrificing the initial substrate surface morphology.   

Session Q13: Focus Session: Magnetic Nanostructures-Nanoparticle Synthesis and Magnetism

Synthesis and properties of magnetic ceramic nanoparticles

Magnetic ceramic nanoparticles of the type xIn2O3-(1-x)alpha-Fe2O3, xV2O5-(1-x)alpha-Fe2O3 and xZnO-(1-x)alpha-Fe2O3 (x=0.1-0.7) were synthesized from the mixed oxides using mechanochemical activation for 0-12 hours. X-ray diffraction was used to derive the phase content, lattice constants and particle size information as function of ball milling time. Mossbauer spectroscopy results correlated with In3+, V5+ and Zn2+ substitution of Fe3+ in the hematite lattice. SEM/EDS measurements revealed that the mechanochemical activation by ball milling produced systems with a wide range of particle size distribution, from nanometer particles to micrometer agglomerates, but with a uniform distribution of the elements. Simultaneous DSC-TGA investigations up to 800 degrees C provided information on the heat flow, weight loss and the enthalpy of transformation in the systems under investigation. This study demonstrates the formation of a nanostructured solid solution for the indium oxide, an iron vanadate (FeVO4) for the vanadium oxide, and of the zinc ferrite (ZnFe2O4) for the zinc oxide. The transformation pathway for each case can be related to the oxidation state of the metallic specie of the oxide used in connection with hematite.   

Magnetic Interactions in Binary Nanocrystal Superlattices

The recent development\footnote{A. Dong, J. Chen, P. M. Vora, J. M. Kikkawa, and C. B. Murray, Nature 466, 474 (2010).} of highly ordered three-dimensional assemblies of magnetic nanocrystals (NCs) poses new questions for the study of collective magnetic dipolar interactions. Prior literature has focused on changes in blocking temperature in infinite, random assemblies. Here, we study ordered assemblies with two different magnetic NCs and complex superlattice unit cells. Monte Carlo simulations are compared with data to clarify magnetic behaviors in AB$_{13}$ superlattices consisting of two different-sized (14.3 nm and 7.2 nm) Fe$_{3}$O$_{4}$ NCs, which are superparamagnetic in isolation. This strategy illuminates the individual sublattice properties and their interaction. We show that under certain circumstances, the magnetic response of smaller magnetic NCs may be quenched by the random magnetic field of larger magnetic NCs,\footnote{J. Chen, A. Dong, J. Cai, X. Ye, Y. Kang, J. M. Kikkawa, and C. B. Murray, Nano. Lett. 10, 5103 (2010).} and that trends in blocking temperature with interaction strength depend strongly on both unit cell geometry and boundary conditions.   

Fabrication of Iron Oxide Nanoparticle Monolayers by Electrophoretic Deposition

Magnetic nanoparticle (NP) films are potentially useful in a variety of applications, such as magnetic storage media and ultra-strong permanent magnets. Monolayers of magnetic NPs are specifically interesting as the monolayer geometry maximizes film interactions with dissimilar materials below and above the monolayer. However, many potential commercial and industrial applications of NP films rely on fabrication techniques that are facile, rapid, and site-selective which create homogenous, densely packed, defect-free thin films. Electrophoretic deposition (EPD) is a technique for forming thin films that meets all of these criteria. This work shows, for the first time, EPD's utility in forming monolayers of magnetic NPs. Iron oxide NPs ($\sim $14nm) have been synthesized using a solution phase synthesis technique. Repeated centrifugation of the particles prepares the NPs for EPD. The particles are then deposited onto silicon substrates with EPD using dc electric fields. Analysis of the films using scanning electron microscopy and atomic force microscopy shows the particles deposit as NP monolayers. The monolayer density and deposition rate are controlled by varying the suspension concentration and the deposition time. Future research will focus on creating long-range order within the monolayers.   

Curie temperature reduction in SiO$_{2}$-coated ultrafine Fe$_{3}$O$_{4}$ nanoparticles: Quantitative agreement with a finite-size scaling law

We report high-temperature magnetic measurements for SiO$_{2}$-coated ultrafine Fe$_{3}$O$_{4}$ nanoparticles. The Curie temperatures of the ultrafine Fe$_{3}$O$_{4}$ nanoparticles are significantly reduced and follow a finite-size scaling law predicted from Monte Carlo simulations. Our current result provides the first quantitative confirmation of the finite-size scaling law for quasi-zero-dimensional magnetic systems.   

Magnetic properties of Fe nanoparticles: application of the DFT-Inhomogeneous-DMFT approach

Dynamical Mean-Field Theory (DMFT) in combination with Density Functional Theory (DFT) has been successfully applied to examine the properties of transition metal elements in which correlation plays an important role. It was recently shown that this approach can also be applied to study correlation effects in nanostructures [1]. Here we present results of a combined DFT-inhomogeneous-DMFT approach used to investigate the size dependent magnetic properties of small iron clusters containing 15 to 19 atoms. For the DMFT impurity solver we use the iterated-perturbation theory approximation. The numerical analysis with the code developed in our group allows one to study systems consisting up to several hundred atoms. The optimized structure of the Fe clusters is obtained from spin polarized DFT calculations. We find our approach to yield better agreement with experimental data [2] than that obtained using DFT and DFT+U, which generally overestimates the magnetization. \\[4pt] [1] V. Turkowski, et al, J. Phys.: Condens. Matt. 22, 462202 (2010).\\[0pt] [2] M. B. Knickelbein, Chem. Phys. Lett. 353, 221(2002).   

Finite-size scaling behavior and intrinsic critical exponents of nickel: Consistent with the three-dimensional Heisenberg model

We report high-temperature magnetic measurements of silica-coated nickel nanoparticles. The Curie temperature is found to decrease with decreasing particle size and follow a finite-size scaling relation with the correlation length exponent $\nu$ = 1.06$\pm$0.07. The measured exponent is in excellent agreement with the reported values for nickel nanowires and some nickel thin films. By carefully analyzing the reported thickness dependencies of the Curie temperatures for some nickel films, we show that the intrinsic $\nu$ value for nickel is 0.73$\pm$0.03 while the much larger $\nu$ values (about 1.0) found for some other samples might arise from the presence of long-range correlated disorder near the surface. The intrinsic $\nu$ value together with the experimental values of other critical exponents consistently shows that the three-dimensional Heisenberg model is sufficient to describe the ferromagnetism of nickel. Our current work thus resolves a long standing controversy in this field.   

Self-assembly of Superparamagnetic Nanoparticles with Permanent Magnetization

Magnetic nanoparticles (MNPs) exhibit superparamagnetism when thermal fluctuations overcome the potential barrier for spin reversal set by magnetocrystalline anisotropy. The magnetic moment in such a material oscillates between the easy axes leading to zero net magnetization. Stable colloidal dispersions of MNPs exploit this state to prevent agglomeration. Self-assembly of MNPs presents an excellent bottom up nanofabrication technique due to the wide range of structures that can be formed. A stable dispersion of MNPs is an essential starting point for good control of the process. In this study we explore the theoretical basis for a self-assembled MNP structure with permanent magnetization starting from a dispersion of superparamangetic MNPs. Magnetostatic coupling of dipole moments enhance the potential barrier for magnetization reversals. We use X-Ray microCT and TEM to visualize the self-assembled structures. We use a stochastic form of the Landau-Lifshitz-Gilbert equation to simulate the magnetization dynamics in each MNP. Permanent magnetization in self-assembled structures generated \textit{in situ} promise several significant applications such as targeted drug delivery, tissue engineering and novel soft composites.   

Rate-dependent hysteresis losses in ensembles of magnetic nanoparticle clusters

Hysteresis is ubiquitous in magnetic nanoparticle systems and understanding how it emerges from complex interactions and for different time scales is a long-standing issue in magnetism research. Understanding the phenomenon is most important for engineering magnetic nanoparticle structures of well-controlled properties in magnetic recording, hysteresis loss optimization in hyperthermia cancer treatment in biomedicine, or biological and chemical sensing, to name a few examples. In this work we address one of the general questions related to the influence of thermal activation processes on hysteresis loss. Employing large-scale computational modeling based on the master-equation framework we investigate the influence of dipolar interactions on thermal hysteresis loops in ensembles of magnetic nanoparticle chains and clusters. We show that the directional dependence of dipolar interactions results in enhanced or reduced hysteresis loss, depending on the distribution of particles' anisotropy axes and particle chain orientations with respect to the external field. Additional hysteresis loss reduction occurs in case of particle clusters due to possibility of the frustration phenomenon not present for topologically simpler chains.   

Size dependence and thermal stability of chiral states in ferromagnetic nanoparticles deposited on a ferromagnetic substrate

Chiral magnetization profiles are observed in many low dimensional systems such as nanoscale particles, thin films, or bulk systems such as multiferroic samples, that are characterized by a lack of inversion symmetry. These spiraling spin structures are often size-dependent and can be attributed to the competition between exchange and anisotropic, or parity breaking Dzyaloshinskii-Moriya (DM) terms. To utilize such spiraling magnetization profiles in novel spintronic devices, it is necessary to understand the mechanisms under which these spiral spin configurations form and how they can be harnessed via an external field. Here we present exact analytic solutions for the magnetization profiles and the associated energies and energy barriers for ferromagnetic nanoparticles deposited on a ferromagnetic substrate. Our method allows us to determine the critical length at which spiral solutions are supported in such samples, which we find to be $l_c = (\pi /2) \sqrt{A/K_e}$ for vanishing applied field and a misfit angle of $\pi/2$ between substrate and nanoparticle anisotropy axis. We also demonstrate that in absence of further pinning effects, the nanoparticles are exclusively in a uniform state for $l < l_c$. We show that our theory is in good agreement with recent experiments.   

Magnetic and magnetocaloric properties of NdMnO$_{3}$ nanoparticles

Recently nanosized manganites have attracted considerable attention as the reduction of particle size has exotic effect on their properties. We have studied the magnetic properties and magnetocaloric effect (MCE) of NdMnO$_{3 }$nanoparticles with particle size $\sim $20 and 30nm (denoted as S20 and 30 respectively). In temperature dependence of magnetization, M(T), a paramagnetic to ferromagnetic transition is observed at T$_{C}\sim $ 70K for S20, which is 5K higher than that for S30 indicating enhancement of ferromagnetic interaction with particle size reduction. In addition to this, an anomaly in M(T) is observed at 20K (T$_{CA})$ for both S20 and S30, which is attributed to the stabilization of a canted magnetic state (CMS) due to the ordering of Nd$^{3+}$ . The magnetic entropy change [ -$\Delta $S$_{M}$(T)] is calculated from isothermal magnetization curves using Maxwell relation. There are two maximas in -$\Delta $S$_{M}$(T) at T$_{C}$ and T$_{CA}$ indicating large MCE over both temperature regions. Interestingly, the relative cooling power is enhanced in case of smaller particle size in which the influence of stabilization of CMS on MCE is less pronounced.   

Effect of the size distributions of magnetic nanoparticles on metastability using phonon-assisted transition rates

Experiments show that magnetic nanoparticles have distributions of sizes and shapes, and that the distributions greatly influence static and dynamic properties of the nanoparticles. Therefore, it is critical to understand their properties as a function of the distributions. Previously, we studied an effect of particle size distributions on metastability in magnetization relaxation, using spin $S=1$ Blume-Capel model with Glauber transition rates. The size distributions were simulated using distributions of magnetic anisotropy parameter $D$ with spins fixed. We found that the lifetime of the metastable state is governed by the smallest particle in a given system. In this talk, we present the effect of size distributions on metastability in magnetization relaxation with phonon-assisted transition rates. These transition rates differ from Glauber dynamics and are derived from weak spin-phonon coupling. In the phonon-assisted transition rates, spin-flips occur via emission or absorption of phonons, and so transitions are forbidden between degenerate states. We investigate magnetization relaxation with distributions of $D$ using kinetic Monte Carlo simulations, when the distributions include values with which such forbidden transitions are expected.   

Magnoelastic coupling in magnetic oxide nanoparticles

Phonons are exquisitely sensitive to finite length scale effects in a wide variety of materials. To investigate confinement in combination with strong magnetoelastic interactions, we measured the infrared vibrational properties of MnO and CoFe$_2$O$_4$ nanoparticles and their parent compounds. For MnO, a charge and bonding analysis reveals that Born effective charge, local effective charge, total polarizability, and the force constant are overall lower in the nanoparticles compared to the bulk. We find that the spin-lattice coupling drops from $\sim$7 cm$^{-1}$ in the single crystal to $<$1 cm$^{-1}$ in the nanoparticles. For CoFe$_2$O$_4$, the spectroscopic response is sensitive to the size-induced crossover to the superparamagnetic state, which occurs between 7 and 10 nm, and a spin-phonon coupling analysis supports the core-shell model. Moreover, it provides an estimate of the thickness of the magnetically disordered shell, increasing from 0.4 nm in the 14 nm particles to 0.8 nm in the 5 nm particles, demonstrating that the associated local lattice distortions take place on the length scale of the unit cell. These findings are important for understanding finite length scale effects in magnetic oxides and other more complex functional oxides.   

The specific edge effects of 2D core/shell model for spin-crossover nanoparticles

We analyzed the size effect of spin-crossover nanoparticles at the edges of the 2D square lattices core/shell model, where the edge atoms are constrained to the high spin (HS) state. We performed MC simulations using the Ising-like Hamiltonian, \[ H=-J\sum\limits_{(i,j)} {\sum\limits_{\begin{array}{l} i'=\pm 1; \\ j'=\pm 1 \\ \end{array}} {S\left( {i,j} \right)S\left( {i+i',j+j'} \right)} +\left( {\frac{\Delta }{2}-\frac{k_B T}{2}\ln g} \right)\sum\limits_{(i,j)} {S\left( {i,j} \right)} } \mbox{ } \] The molar entropy change is $\Delta $S$\approx $50J/K/mol, ln$g=\Delta $S/R$\approx $6 (R is the perfect gas constant), energy gap is $\Delta $=1300K. The HS fixed edges were based on the observation of an increasing residual HS fraction at low temperature upon particle size reduction. This specific boundary condition acts as a negative pressure which shifts downwards the equilibrium temperature. The interplay between the equilibrium temperature (=$\Delta $/k$_{B}$ln$g)$ variation and the expected variation of the effective interactions in the system leads to a non-monotonous dependence of the hysteresis loop width upon the particle size. We described how the occurrence condition of the first-order transition has to be adapted to the nanoscale.   

Magnetic Properties of Single Co Nanoparticles Probed by Tunneling and Microwaves

We present tunneling studies of magnetic hysteresis loops of single Co nanoparticles. The magnetic switching field at mK-temperature is strongly reduced as a function of bias voltage. At 10mV bias voltage, the switching field is reduced by 15\%, while the magnetization can be switched by applying a voltage pulse of 10mV. The strong reduction of the switching field is not an artifact due to charge noise or Joule heating, nor it is a result of the electric field dependence of the surface anisotropy. Instead, the reduction represents the case of magnetic excitation driven by the tunnel current. The strength of the effect indicates strongly enhanced coupling between magnetic excitations and the tunnel current in ferromagnets with strongly reduced dimensions. We also present the first measurement of the magnetic relaxation time in a single Co nanoparticle ($\sim$microsecond) , obtained by combining tunneling spectroscopy and microwave pumping.   

Exchange Bias Studies in Core/Shell Structures Nanoparticles

This study is focused on a comparison of magnetic properties of chemically synthesized core/shell structured iron/iron-oxide nanoparticles with different core sizes and comparable shell thickness. Particles were synthesized by high temperature decomposition of iron organometallic compounds. Thermomagnetic data revealed that particles are superparamagnetic at room temperature. The field cooled hysteresis loops showed interesting features of enhanced coercivity and horizontal and vertical shifts along directions of the cooling field, all strongly depend on temperature, indicative of an exchange-bias-like phenomenon. These effects were more pronounced in smaller core size nanoparticles with an exchange bias field of 4098 Oe. The spin-glass-like phase with high-field irreversibility in the iron oxide shells played the role of the fixed phase in the core/shell system and provided the pinning force to the reversible spins. The magnetic domains and higher contributions from the surface anisotropy in the hollow nanoparticles caused enormous magnetic frustration that is the origin of high field irreversibility and vertical shift of hysteresis loop in these particles.   

Session Q14: Focus Session: Spins in Semiconductors - Spin Dependent Transport

Determination of Rashba and Dresslhaus coefficient in InGaAs quantum wells

We report the determination of the intrinsic spin-orbit interaction (SOI) parameters for In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As quantum wells (QWs) from the analysis of the weak antilocalization effect measured at dilution temperature [1]. We found that the Dresselhaus SOI is mostly negligible relative to the Rashba SOI in this system. The intrinsic parameter for the Rashba effect, a$_{\rm SO}\equiv \alpha/\langle E_z \rangle$, is determined to be a$_{\rm SO}m^*/m_e = (1.46-1.51 \times 10^{-17}N_{\rm S}$ [m$^{-2}$]) $e${\AA}$^2$, where $\alpha$ is the Rashba SOI coefficient, $\langle E_z \rangle$ is the expected electric field within the QW, $m^*/m_e$ is the electron effective mass ratio, and $N_{\rm S}$ is the sheet carrier density. The $N_{\rm S}$ dependence of a$_{\rm SO}$ corrsponds to the non-parabolic correction in the effective mass or electron g-factor. These values for a$_{\rm SO}m^*$, which are in good agreement with the thoretical prediction by Kane's ${\bf k\cdot p}$ theory, were also confirmed by the observation of beatings in the Shubnikov-de Haas oscillations in our most asymmetric QW sample.\\[4pt] [1] S. Faniel {\it et. al.}, PHYSICAL REVIEW B {\bf 83}, 115309 (2011).   

Spin-dependent scattering in the presence of polarized nuclei in n-GaAs

We report on all-electrical measurements of the inverse spin Hall effect (ISHE) in epitaxial (100) Fe/GaAs heterostructures with a channel doping (Si) of $n =5\times 10^{16}$~cm$^{-3}$ and highly doped Schottky tunnel barriers. Under measurement conditions of large (10-20\%) spin accumulation at the injection electrode, a significant dynamic nuclear polarization (DNP) enhances the size of the ISHE. The electron spin dynamics are shown to match the predictions of the usual drift-diffusion model, including the applied, hyperfine, and Knight fields. The DNP, however, also enhances the scattering of spin-polarized carriers, which is not understood. To separate the roles of the electronic and nuclear spin systems, we have employed a pump-probe method to vary the nuclear spin polarization $\langle I \rangle$ and electron spin polarization $S$ independently. The size of the ISHE is proportional to $\langle I \rangle$ when the DNP is small, but it eventually saturates. When the nuclear polarization is fixed, the ISHE is linear in $S,$ as expected. We conclude therefore that the measured signal scales linearly with the spin current multiplied by a transport skewness parameter that depends strongly on $\langle I \rangle$.   

Nuclear enhancement of the spin Hall angle in $n$-In$_{x}$Ga$_{1-x}$As

We present measurements of the inverse spin Hall effect in vertical Fe/In$_{x}$Ga$_{1-x}$As heterostructures as identified via a Hanle effect in the local Hall voltage. The spin Hall angle is greatly enhanced in the presence of polarized nuclei, achieving typical values of $\gamma\simeq5\times10^{-2}$. Phenomenological modeling of the observed line-shapes shows that the nuclear polarization acts as a linear prefactor to the standard spin Hall conductivity. This enhancement far exceeds expectations based on the energy splitting of the electron or nuclear spin systems. Our samples are doped just above the Mott transition ($n\simeq3n_c$) where metallic impurity band conduction is dominant. A strong coupling between localized moments and delocalized states is evidenced by the temperature dependence and sensitivity to disorder at higher In concentrations. This leads us to interpret our results using an Anderson-like model of polarized impurities whereby both dynamic nuclear polarization and resonant skew scattering arise as a result of a spin polarized doubly occupied $\left(D^{-}\right)$ impurity band.   

Spin Hall effect for detection of spin-currents -- Realization of a Spin transistor

The realization of a viable semiconductor transistor and information processing devices based on the electron spin has fueled intense basic research of three key elements: injection, detection, and manipulation of spins in the semiconductor microchannel. The inverse spin Hall effect (iSHE) detection of spins manipulated by a gate electrode [1] has recently led to the experimental demonstration of a spin transistor device. [2] Here, the spin injection into a 2-dimensional electron gas (2DEG) was done optically in the depletion layer of a reverse biased pn-junction. [3] The iSHE detection is also used for electrical spin injection from a Fe electrode into a lateral GaAs channel combined with a simultaneous non-local spin valve measurement [4-10]. The spins in the channel are manipulated via the Hanle spin precession induced by an applied magnetic field and via a drift of electrons induced by an applied electric field. The output spin signal is suppressed or enhanced depending on the applied electrical bias rendering the device to a spin transitor different from the Datta Das concept. [11] \\[4pt] [1] S. Datta and B. Das, Appl. Phys. Lett. 56, 665 (1990). \\[0pt] [2] J. Wunderlich, et al., Science 330,1801 (2010). \\[0pt] [3] J. Wunderlich, et al., Nature Phys., 5, 675 (2009). \\[0pt] [4] X. Lou, Nature Phys. 3, 197 (2007). \\[0pt] [5] M. Ciorga, et al., Phys. Rev. B 79, 165321 (2009). \\[0pt] [6] C. Awo-Affouda, et al., Appl. Phys. Lett. 94, 102511 (2009). \\[0pt] [7] M. K. Chan, et al., Phys. Rev. B 80, 161206(R) (2009). \\[0pt] [8] G. Salis, et al., Phys. Rev. B 80, 115332 (2009). \\[0pt] [9] G. Salis, et al., Phys. Rev. B 81, 205323 (2010). \\[0pt] [10] E. S. Garlid, et al., Phys. Rev. Lett. 105, 156602 (2010). \\[0pt] [11] K. Olejnik, et al., submitted.   

Measurement by antilocalization of interactions between InAs surface electrons and magnetic surface species

Weak-antilocalization (WAL) low-temperature magnetotransport measurements are sensitive to electron quantum coherence, and can be used as a sensitive probe of surface quantum states. We experimentally study interactions between surface electrons and local magnetic moments on InAs by comparing WAL on patterned InAs accumulation layers where rare earth ions or Co$^{2+}$, Co-phthalocyanine, Fe$^{3+}$, and Fe-phthalocyanine were deposited, with those where no magnetic species were deposited. The magnetic species modify the magnetic spin-flip scattering, which carries information about magnetic interactions, and modify the spin-orbit (SO) scattering, identified via the WAL signal and characterized over temperature. Experiments indicate a mostly temperature-independent magnetic spin-flip scattering, except for Ho$^{3+}$. The SO scattering also displays a weak temperature dependence, and is increased by the heavy ions, Co$^{2+}$ and Co-phthalocyanine, while suppressed by ferromagnetic Fe$^{3+}$ and Fe-phthalocyanine, in agreement with the expected absence of the WAL in ferromagnets.   

A Quantitative Analysis of the Electrical Detection of Spins Via the Spin Hall Effect and the Non-Local Spin Valve Effect Within a Semiconductor Microchannel

Recently, the manipulation of spins via a gate electrode, and their subsequent detection through the Spin Hall Effect, has led to the experimental realization of a spin-based semiconductor transistor. While in this experiment, spin injection was achieved optically via circularly-polarized light, we consider a similar experiment using electrical injection by means of a ferromagnetic contact into a GaAs microchannel instead. The spin current in a lateral semiconductor channel is then detected through the Spin Hall Effect, while the spin accumulation nearby is simultaneously measured through the Non-Local Spin Valve Effect (using another Fe electrode). The spins within the channel are manipulated through the Hanle Effect via an external magnetic field, and through a drift induced by an applied electrical bias. To analyze these results, we use analytical and numerical solutions to the steady-state drift-diffusion equations with a constant magnetic field and a drift velocity modeled by a Heaviside Theta function. Combining these results with the anomalous Hall response function, which takes into account the geometry of the Hall probe in order to obtain the correct Hall angle, we obtain results that are in quantitative agreement with experiments.   

Spin-gating of a conventional aluminum single electron transistor

We report the realization of a single electron transistor in which electron transport from an aluminum source electrode to an aluminum drain electrode via an aluminum island is controlled by spins in a capacitively coupled magnetic gate electrode. The origin of the effect is in the change of the chemical potential on the gate, formed by the ferromagnetic semiconductor GaMnAs, with changing the direction of the magnetization. In agreement with experimental observations, microscopically calculated anisotropies of the chemical potential with respect to the magnetization orientation are of the order of 10$\mu$V which is comparable to the electrical gate voltages required to control the on and off state of the single electron transistor. Our phenomenon belongs to the family of anisotropic magnetoresistance effects which can be observed in ohmic, tunneling or other device geometries. In our case, the entire phenomenon is coded in the dependence of the chemical potential on the spin orientation which allowed us to remove the spin functionality from all current contacts and channels and place it in the capacitively coupled gate electrode. Our spintronic device therefore operates without spin current.   

Spin injection from into InSb from CoFe

The strong spin-orbit interaction in InSb is an asset for spin manipulation using electric fields. In order to electrically characterize spin injection and detection in InSb, we experimentally investigate spin injection into InSb from ferromagnetic CoFe electrodes, via non-local spin valve measurements at low temperature. We observe non-local transresistance switching around zero in-plane external magnetic field. We characterize the magnetic properties of the CoFe layer by the Hall signal of the fringing fields and confirm 3-state switching. We verify that the non-local signal is not related to the physical or geometrical magnetoresistance due to the CoFe fringing fields. The non-local spin valve signal is, as typical, dependent on the specific CoFe/InSb interfaces, while the temperature dependence points to a contribution beyond the spin coherence length. We further observe a modification of weak-antilocalization by spin injected carriers and the same phenomenon may contribute to the spin valve transresistance (partial support from DOE DE-FG02-08ER46532).   

Top- and Side-Gated InAs Spinfilter Cascades in Magnetic Fields

We present results from transport experiments on two-stage Y-shaped spin-filter cascades fabricated from InAs heterostructures. The first Y junction acts as a generator of two oppositely spin-polarized currents by employing the intrinsic spin-Hall effect. When the second filter that is attached to one of the first filter's outputs in a distance corresponding to a multiple of the spin-precession length, the spin polarization is revealed as a conductance imbalance at the outputs. To achieve the required quasi one-dimensional transport modes we reduce either the effective width of the cascade's five wires by side-gate quantum-point contacts or we reduce the carrier concentration by means of a top gate. The latter yields the advantage to keep the width along the cascade's wires constant and thus, by ensuring higher homogeneity of the potential, reduces spurious effects in the measured conductances. The application of a magnetic field perpendicular to the cascade's plane results in a Lorentz force acting on the electrons in the cascade and thereby changing the measured conductance imbalance and the spin polarization. This can be used to quantify the strength of the spin-Hall effect in InAs heterostructures.   

Tunable Zeeman-like Spin Splitting with Liquid Gated Field Effect Transistors

Generation of spin polarized electrons is the most critical step for developing spintronics applications. As an electric and nonmagnetic way to realize spin polarization in energy bands, spin-orbit interaction (SOI) has been widely used for spin manipulation in two-dimensional systems. For example, Rashba-type energy splitting with in-plane-polarized spins near \textit{$\Gamma $} point of Brillouin zone (BZ) is able to be modulated by electric field through tuning spatial inversion asymmetry. However, Zeeman-type energy splitting with out-of-plane spin polarization is known to be sensitive only to magnetic field and supposed never to be affected by external electric field. In this paper, we theoretically uncover and experimental confirm a perpendicular-electric-field induced giant Zeeman spin splitting at low symmetric $K$ and $K'$ points in a layered chalcogenide, 2H-WSe$_{2}$. \textit{Ab initio} band calculation and spin texture indicate that an electric field can make low-energy carriers spin-polarized in a out-of-plane Zeeman-type way and a tunable SOI is able to selectively control the size of splitting. A gate-induced crossover from weak localization to weak antilocalization in the magnetotransport serves as an experimental proof for the tunable SOI and spin polarization. The splitting energy deduced from quantum correction of magnetoconductance is as large as 120 meV and satisfied well with the band calculation for Zeeman-type splitting. This finding directly provides us with a new path-way for electrically initializing and manipulating electron spins for spintronics applications.   

Anomalous Hall effect in the Presence of Strong Spin-orbit Coupling and Non-trivial Magnetization

AHE in ferromagnets with strong spin-orbit coupling (SOC) and homogeneous magnetization has been studied extensively, using both Kubo formalism and semi-classical Boltzmann equation. In the opposite limit of weak SOC in the presence of non-trivial magnetization texture and strong exchange coupling with the carriers (adiabatic limit), the electron spins always align themselves with the direction of the local magnetization and they experience an effective magnetic field arising from this non-trivial magnetization, giving rise to the topological anomalous Hall effect. We study here the transition between the two limits and the joint effect that a strong SOC and non-trivial magnetic textures have on the AHE. We will report on results from both perturbative analytical approaches and bulk numerical simulations. Some of these effects may be present and exploited in current induced manipulation and detection of domain walls.   

Spin diffusion and precession at the multiferroic interface and InAs quantum wells

We study spin diffusion and precession in a two-dimensional electron gas at the multiferroic interface and InAs quantum wells respectively by means of the kinetic spin Bloch equation approach [Wu {\it et al.}, Physics reports {\bf 493}, 61 (2010)]. At the AlO$_3$/SrTiO$_3$/TbMnO$_3$ heterostructure with a temperature being as low as 15~K, the two-dimensional electron gas at the LaAlO$_3$/SrTiO$_3$ interface interacts with the spiral magnetic moments of Mn$^{3+}$ in TbMnO$_3$ via the Heisenberg exchange interaction. It is demonstrated that the spin diffusion length at the interface is always finite, despite the polarization direction of the injected spins. It is also revealed that the Coulomb scattering plays an important role and effectively suppresses the spin diffusion. The spin precession in InAs quantum wells is investigated with the Rashba spin-orbit coupling being modulated by a gate voltage. The gate-voltage dependence of spin diffusion under different temperatures is studied with all the scattering explicitly included. Our result partially supports the claim of the realization of the Datta-Das spin-injected field effect-transistor by Koo {\it et al.} [Science {\bf 325}, 1515 (2009)]. We also show that the scattering plays an important role in spin diffusion in such a system.   

Enhanced photon-assisted spin transport in a quantum dot attached to ferromagnetic leads

Time-dependent transport in quantum dot system (QDs) has received significant attention due to a variety of new quantum physical phenomena emerging in transient time scale.[1] In the present work [2] we investigate real-time dynamics of spin-polarized current in a quantum dot coupled to ferromagnetic leads in both parallel and antiparallel alignments. While an external bias voltage is taken constant in time, a gate terminal, capacitively coupled to the quantum dot, introduces a periodic modulation of the dot level. Using non equilibrium Green's function technique we find that spin polarized electrons can tunnel through the system via additional photon-assisted transmission channels. Owing to a Zeeman splitting of the dot level, it is possible to select a particular spin component to be photon-transferred from the left to the right terminal, with spin dependent current peaks arising at different gate frequencies. The ferromagnetic electrodes enhance or suppress the spin transport depending upon the leads magnetization alignment. The tunnel magnetoresistance also attains negative values due to a photon-assisted inversion of the spin-valve effect. [1] F. M. Souza, Phys. Rev. B 76, 205315 (2007). [2] F. M. Souza, T. L. Carrara, and E. Vernek, Phys. Rev. B 84, 115322 (2011).   

Session Q16: Heavy Fermions - 1-1-5 Systems

Strong magnetic fluctuations in superconducting state of CeCoIn$_5$

We probe the magnetism inside the superconducting state of CeCoIn$_5$ by locally suppressing superconductivity and investigating the underlying normal state through current-voltage measurements under applied pressure and external magnetic field in the mixed state. We observe that the vortex core resistivity increases sharply with decreasing temperature ($T$) for $T < T_c$ and magnetic field. We attribute this result to the presence of critical spin fluctuations near the Neel temperature inside the vortex core. This behavior is greatly suppressed with increasing pressure, due to the suppressed antiferromagnetic order inside the vortex core. Using our experimental results we construct a three-dimensional phase diagram which provides a direct evidence for a quantum critical line inside the superconducting phase. An experimentally obtained explicit equation for the antiferromagnetic boundary inside the superconducting dome shows the close relationship between quantum criticality, antiferromagnetism, and superconductivity.   

Visualizing the Emergence of Heavy Fermions in a Kondo Lattice (Part I)

The interaction between magnetic moments and conduction electrons is at the heart of many phenomena in condensed matter physics, from the Kondo effect in magnetic alloys and nanostructures to superconductivity in strongly correlated systems. We use the scanning tunneling microscope (STM) to detect the emergence of these heavy excitations with lowering of temperature in a prototypical 115 family of Ce-based heavy fermion compounds. Experiments on different atomically terminated layers and their modeling are used to demonstrate the sensitivity of the tunneling process to the composite nature of these heavy quasiparticles, which arise from quantum entanglement of itinerant conduction and $f-$electrons. The momentum space electronic structure of those heavy excitations will be discussed in the next talk by Pegor Aynajian.   

Visualizing the Emergence of Heavy Fermions in a Kondo Lattice (Part II)

The development of low energy fermionic excitations with heavy mass in compounds with $f$-orbitals is one of the key concepts in the physics of correlated electronic states and fundamental to the mechanism of unconventional superconductivity in such systems. We use spectroscopic mapping with the scanning tunneling microscope (STM) to detect the emergence of these heavy excitations in the Ce-115 heavy fermion compounds. Scattering and interference of the heavy quasiparticles is used to resolve their energy-momentum structure and to extract their mass enhancement, which develops near the Fermi energy with decreasing temperature. This work is funded by a DOE-BES grant. Infrastructure at the Princeton Nanoscale Microscopy Laboratory are also supported by grants from NSF-DMR, Keck Foundation, and NSF-MRSEC. PA also acknowledges support of a fellowship through the PCCM funded by NSF MERSEC.   

Scanning tunneling microscopy studies of heavy fermion compound CeCo(In$_{1-x}$Cd$_{x})_{5}$

Heavy fermion materials, such as those forming in actinide- or lanthanide-based compounds, have a rich variety of phases from unconventional superconductivity to antiferromagnetism to possibly exotic and non-Fermi liquid states. Central to all these ground states is the interaction between the magnetic impurities and the conduction electrons. In the Ce-based heavy fermions compounds (e.g. CeCoIn$_{5})$, the ground state can be tuned by doping or isovalent substitution, for example, Cd doping tunes the system toward antiferromagnetism. We present scanning tunneling microscopy/spectroscopy.measurements on the Cd-doped CeCoIn$_{5}$ heavy fermion compounds as a function of temperature. These results will be analyzed within the context of how tunning the chemical structure impacts the formation of heavy electron band and various ground states of this material system.   

Magnetic penetration depth and skin depth study of superconductivity and quantum criticality in Ce$_{1-x}$R$_x$CoIn$_5$ (R=La and Nd)

A heavy fermion superconductor CeCoIn$_5$ shows different responses to Nd- or La- substitutions for Ce, with the former inducing static magnetic order coexisting with superconductivity for some concentrations. To understand the origin of the differences, we studied the temperature and field dependent in-plane magnetic penetration depth, $\lambda(T)$, in single crystals of (Ce,R)CoIn$_5$ (R=La, Nd). Measurements were performed with a tunnel diode resonator down to 50~mK in a dilution refrigerator, in magnetic field up to 14 T parallel to the $c$-axis. These low-temperature and high field measurements allowed for the exploration for the full domain of superconductivity and quantum criticality in the $T-H$ phase diagram. Some previously unreported features were observed and will be discussed from the point of view of measured differential magnetic susceptibility. Combined with the contact-less measurements of resistivity via normal-state skin depth, these measurements bring new insight into the interplay between superconductivity and magnetism as well as field-tuned quantum critical behavior of doped 115 systems.   

Quantum oscillations study of the Fermi-surface evolution in Yb-substituted CeCoIn$_{5}$

We report results of systematic de Haas-van Alphen (dHvA) studies on Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$ single crystals with varying Yb concentrations $x$. For a low dilution of $x$ = 0.1, the well-documented Fermi surface and the heavy effective masses of CeCoIn$_{5}$ ($x = 0$) remain nearly unchanged. A clear change of the Fermi-surface topology becomes evident for high Yb concentrations of $x = 0.55$, and above. The effective masses are reduced considerably to values between 0.7 and 2.6 free electron masses. Nevertheless, the superconducting transition temperature $T_c$ and upper critical field $H_{\mathrm{c2}}$ are only weakly suppressed with $x$. The angular-resolved dHvA frequencies for YbCoIn$_{5}$ show a good agreement with our density functional theory band-structure calculation with localized 4$f$ electrons and an Yb valence of 2+, which has been used to constructed the Fermi surface.   

Field induced QCP in Yb-doped CeCoIn$_5$

We performed magnetoresistance and Hall effect measurements on Yb-doped CeCoIn$_5$. The longitudinal resistivity data measured in 14 T show that the onset of coherence in the dilute Kondo lattice remains robust with respect to Yb concentration. In addition, we find that the superconducting transition temperature is weakly suppressed with doping ($x\leq 0.2$). Our analysis of the magnetoresistance data allowed us to identify the magnetic field induced quantum critical point and its evolution upon doping. At high Yb concentrations, our Hall effect data point to a possible valence transition of Yb ions. At small doping, our results provide an insight into the nature of the interplay between quantum criticality, magnetism, and unconventional superconductivity, while the behavior of this system at high doping can be characterized by a subtle interplay between Kondo screening on Ce sites and strong valence fluctuations on Yb sites.   

Effect of local electronic tuning in CeCoIn$_{5}$

The relationship between quantum criticality ($QC$), non-Fermi-liquid ($nFl$) behavior and the emergence of unconventional superconductivity ($SC$) in the vicinity of an antiferromagnetic quantum critical point ($QCP$) is one of the important issues in strongly correlated electron physics. Here we report on the effect of electronic tuning on superconductivity and quantum criticality in CeCoIn$_{5}$ driven by electron (Pt and Sn) and hole doping (Hg). We show that both Pt and Sn doping have similar strong effect on superconductivity and push the system slightly away from the $QCP$. The sub-linear power law exponent, even at a high doping level (where the superconductivity is suppressed) could point to the formation of electronic inhomogeneity. Moreover, hole doping by Hg can tune the system back to the $QCP$ as demonstrated by an increase of $T_{c}$ (and subsequently the onset of AFM), a decrease of the coherence temperature $T^{*}$ and an increase of the power law coefficient $n$ stressing the importance of the interplay of electronic tuning and pair breaking effects.   

Doping effects of CeCo$_{1-x}$Ru$_{x}$In$_{5}$

CeCoIn$_{5}$ lies in close proximity to a QCP which can be tuned with chemical doping, pressure or magnetic field. In this work, single crystals of Ruthenium doped CeCoIn$_{5}$ were prepared by means of self-flux in Indium. The lattice structure of CeCo$_{1-x}$Ru$_{x}$In$_{5}$ was identified as tetragonal by powder XRD with slightly increasing lattice constants. The results of electrical resistivity down to 1.8 K reveals that both coherence (T*) and superconducting transition (Tc) temperatures are decreasing monotonically with increasing Ru doping. Antiferromagnetism is anticipated on the basis of both negative chemical pressure and hole doping. Transport and thermodynamic data will be compared and contrasted with results from Rh and Cd doping.   

Effect of Pressure on Superconductivity and the Kondo-Lattice Coherence Temperature in Ce$_{1-x}R_x$CoIn$_5$ with $R$ = Yb, Y, Gd

Generally, rare-earth substitution for Ce in the heavy fermion superconductor CeCoIn$_5$ suppresses superconductivity rapidly. However, it was recently reported that the correlated electron ground state of Ce$_{1-x}$Yb$_x$CoIn$_5$ is stabilized over an anomalously large range in $x$, perhaps because of cooperative valence fluctuations of the Ce and Yb ions. Motivated by this possibility, we studied the effect of applied pressure on the superconducting critical ($T_c$) and Kondo-lattice coherence ($T^*$) temperatures of Ce$_{1-x}R_x$CoIn$_5$ with $R$ = Yb, Y, and Gd in order to compare the effect of Yb substitution with other magnetic and non-magnetic rare-earth ion substitutions. We performed electrical resistivity measurements under pressures up to a maximum of $\sim$2.3 GPa in a piston-cylinder clamped high pressure cell using a 50:50 mixture of $n$-pentane and isoamyl alcohol for the pressure transmitting medium. It was found that the variations of $T_c$ and $T^*$ in Ce$_{1-x}R_x$CoIn$_5$ under pressure were approximately independent of $R$. This result implies that the effect of pressure is independent of the magnetic configuration of the rare-earth ion being introduced.   

Antiferromagnetic Order in Pauli-Limited Unconventional Superconductors

We develop a theory of the coexistence of superconductivity (SC) and antiferromagnetism (AFM) in CeCoIn5. We show that in Pauli-limited nodal superconductors the nesting of the quasiparticle pockets induced by Zeeman pair breaking leads to incommensurate AFM with the magnetic moment normal to the field. We compute the phase diagram and find a first order transition to the normal state at low temperatures, the absence of normal state AFM, and the coexistence of SC and AFM at high fields, in agreement with experiments. We also predict the existence of a new double-Q magnetic phase.   

Staggered moments in the vortex cores of CeCoIn$_5$

Our previous nuclear magnetic resonance measurements revealed that magnetic field can induce an exotic superconducting phase, characterized by the presence of strong antiferromagnetic fluctuations. In the low field superconducting state, NMR spectra are determined by the inhomogeneous field distribution of a vortex lattice. In the exotic superconducting phase the NMR spectra broaden well beyond what is expected on the basis of the vortex lattice distribution. Here we explore the possibility that this extra broadening of the NMR spectra arises from the staggered magnetization induced locally around the vortex cores.   

Knight Shift anomaly in anti-ferromagnetic Heavy Fermion, CeRhIn$_{5}$

Since their discovery, the CeMIn$_{5}$ (M=Ir, Rh, Co) class of heavy fermion superconductors has attracted a lot of attention for their unusual properties. These compounds all have a scaling behavior which Nakatsuji et al (NPF) proposed is best explained by a two-fluid model. Below a characteristic temperature T*, the f-moments delocalize and form a coherent state with the conduction electrons, similar to super-fluid $^{4}$He. One of the central questions in the field is which energy scale correlates with the onset of coherence, T$_{Kondo}$ or T$_{RKKY}$. We will present new data on the Knight Shift anomaly in CeRhIn$_{5}$ which allows us to learn about the spin correlations as we approach the coherent state. By comparing the Knight shift anomaly in the three cousin compounds, we can explore how the characteristic energy scales of these materials change as we transition from a superconducting to an anti-ferromagnetic ground state.   

Strong suppression of superconductivity and Kondo coherence by Yb substitution in CeCoIn$_{5}$ epitaxial films

One of the important issues in strongly correlated electron system is the relationship between unconventional superconductivity and quantum criticality. Among them, the heavy-fermion superconductor CeCoIn$_{5}$ is a key material situated near an antiferromagnetic quantum critical point. When rare-earth ions are substituted for Ce, superconductivity and Kondo-lattice coherence are usually suppressed, but it has been recently pointed out from bulk studies that Yb substitution may be distinguished because of its valence instability. Here we report our recent study on Ce$_{1-x}$Yb$_{x}$CoIn$_{5}$ epitaxial thin films grown by the molecular beam epitaxy, which have high homogeneity. We find that the superconducting transition temperature is suppressed with increasing x much more rapidly than the previous bulk results, and that the coherence temperature is suppressed concurrently. We also observe a systematic reduction of the low-temperature Hall coefficient magnitude with x, establishing that the antiferromagnetic fluctuations fade even by the Yb substitutions.   

Extremely strong-coupling superconductivity in artificial two-dimensional Kondo lattices

Superconductivity with the strongest electron correlations is realized in heavy-fermion system, where almost all of the compounds have three-dimensional nature. It had remained an unanswered question whether superconductivity would persist on reducing the dimensionality of these materials. We succeeded in observing superconductivity in the system of heavy electrons confined within a two dimensional square lattice of Ce atoms, which was realized by fabricating epitaxial superlattices built of alternating layers of heavy-fermion CeCoIn$_{5}$ and conventional metal YbCoIn$_{5}$[1]. The field-temperature phase diagram of the superlattices exhibits a striking enhancement of the upper critical field relative to the transition temperature. This implies that the force holding together the superconducting electron pairs takes on an extremely strong-coupled nature as a result of two-dimensionalization. [1]Mizukami \textit{et al}., Nature Phys. \textbf{7}, 849 (2011).   

Session Q17: Focus Session: Nanostructures and Metamaterials, Growth, Structure, and Characterization -- Improved Materials and Applications I

Metamaterials and Plasmonics: Improved Material Building Blocks

Optical metamaterials are rationally designed and manufactured materials built of nanostructured unit cells, or ``artificial atoms'' much smaller than the wavelength of operating light. These materials can be engineered to exhibit optical properties beyond any naturally occurring materials. This field has been gaining momentum over the past several years, as it continues to provide new fascinating ideas promising a variety of exciting applications including for example super-resolution microscopes, extremely efficient light concentrators and invisibility cloaks. In most metamaterial devices, noble metals (primarily gold and silver) have been used as the constituent material to make subwavelength building blocks. But metals suffer from high optical losses that are much too large to create practical and robust metamaterials devices. A recent approach that could unlock the technological potential of plasmonics and optical metamaterials is to look for better plasmonic materials that have a negative real part of dielectric permittivity. Here we provide an overview of two classes of alternative plasmonic materials - doped semiconductors and intermetallics - that could allow realization of novel transformation optics and metamaterial devices with greatly improved performance operating at near infrared and visible frequencies.   

Bianisotropy Compensation in Metamaterials

The potential scientific and technological applications for metamaterials abound and continue to multiply at an unprecedented rate. However, with applications come non-trivial design challenges. For instance, many metamaterial designs exhibit the phenomenon of bianisotropy, the ability for an incident electric field to excite a magnetic response (and vice versa) in the metamaterial. In many applications, this bianisotropic response is considered a parasitic effect to be avoided whenever possible. Metamaterials can be designed to eliminate bianisotropy at the unit cell level, but the presence of a substrate will inevitably reintroduce bianisotropy into the system. Here, through a judicious choice of unit cell geometry, we have compensated for and removed the effects of substrate-induced bianisotropy in broadside coupled split-ring resonators on a GaAs substrate. We present numerical simulation results, parameter extraction, and experimental measurements at terahertz frequencies to validate this claim.   

Indium Tin Oxide Nanorod Building Blocks for Near-Infra-Red Filter Metamaterials

We report arrays of indium tin oxide (ITO) nanorods function as near-infra-red (NIR) filter metamaterials. We fabricated arrays of rectangular cross-section, plasmonic ITO nanords of varying pitch, width, gap, and height of the nanorods using nanoimprint lithography and chlorine based inductively coupled plasma (ICP) etching processes. The transmission spectrum of the periodic nanorod arrays may be spectrally tuned in the NIR by the geometry of the arrays and the optical response depends on the polarization of the incident light. The nanorod array behaves as an optical nanocircuit. For illumination by an E-field vector parallel to the nanorod array, the array functions as a parallel L-C circuit, acting as a bandpass filter. For illumination by an E-field vector perpendicular to the nanorod array, the array functions as a series L-C circuit, acting as a bandstop filter. We show good agreement between optical measurements of fabricated nanorod arrays and simulations using equivalent circuit theory and finite-difference time-domain (FDTD) methods. The optical properties of the ITO nanorod circuit may be further tuned by filling the gap between the nanorods using various dielectric materials.   

Measurement of Resonant Frequencies and Modes of Freestanding Nanoparticle Monolayers

We recently showed that freestanding membranes of ligated nanoparticles can be assembled in a one-step drying-mediated process [1]. These 10nm thin membranes can stretch over holes up to 100 microns in diameter and are supported by a substrate only along their outer edge, thereby freely suspending of the order of 100 million close-packed particles [2]. Previous work has focused on quasi-static mechanical properties [1-3]. Here we present the first investigation of the full dynamic response of freely suspended nanoparticle membranes, utilizing a high frequency laser interferometer with picometer sensitivity. This instrument allows us to rapidly measure the dynamical properties of freestanding nanoparticle monolayers for the first time including resonant frequencies, quality factors, and images of different modes.\\[4pt] [1] Klara E. Mueggenburg et al., ``Elastic membranes of close-packed nanoparticle arrays,'' Nature Materials 6, 656-660 (2007). \\[0pt] [2] Jinbo He et al., ``Fabrication and Mechanical properties of large-scale freestanding nanoparticle membranes,'' Small 6, 1449-1456 (2010).\\[0pt] [3] Pongsakorn Kanjanaboos et al., ``Strain Patterning and Direct Measurement of Poisson's Ratio in Nanoparticle Monolayer Sheets,'' Nano Letters 11, 2567-2571 (2011).   

Metamaterial Based Terahertz Detector

We have designed, fabricated, and characterized metamaterial enhanced bimaterial cantilever pixels for far-infrared detection. Local heating due to absorption from split ring resonators (SRRs) incorporated directly onto the cantilever pixels leads to mechanical deflection which is readily detected with visible light. Highly responsive pixels have been fabricated for detection at 95 GHz and 693 GHz, demonstrating the frequency agility of our technique, and their subwavelength nature enables their use as a focal plane array (FPA) to image near the diffraction limit. We have obtained single pixel responsivities as high as 16,500 V/W and noise equivalent powers of 10-8~W/Hz1/2~with these first-generation devices, which were achieved at room temperature and pressure. Consequently, MMs hold great promise for facilitating the development of a ``versatile'' THz detector which can a) strongly absorb THz radiation; b) operate at room temperature; c) function as a multi-pixel array for imaging applications; and d) be lightweight and low cost.   

Experimental observation of strong microwave-induced force in parallel-plate metallic cavity

It has long been known that light induced forces have an impact on matter. These forces, albeit small, have found various applications in physics, chemisty and biology. The magnitude of this induced force is directly related to the momentum carried by light. With a much longer wavelength than visible light, microwave rediation is commonly regarded to having negligible mechanical impact on macroscopic objects. Here we present the first experimental demonstration of a strong repulsive force induced by incident microwave radiation in parallel centimeter-sized metallic plates. We found that the microwave radiation induced force can be significantly stronger than the usual photon pressure exerted by the incident beam when the cavity is excited at resonance, as strong electromagnetic energy is trapped inside the cavity walls. There is good agreement between experimental measurement and calculations using a boundary element method and the Maxwell stress tensor formalism. Our effort may bring new applications of microwave manipulations in the microwave and metamaterial communities.   

Geometrical structure, multifractal spectra and localized optical modes of aperiodic Vogel spirals.

We present a numerical study of the structural properties, photonic density of states and bandedge modes of Vogel spiral arrays of dielectric cylinders in air. Specifically, we systematically investigate different types of Vogel spirals obtained by the modulation of the divergence angle parameter above and below the golden angle value ($\approx $137.507 degrees). We found that these arrays exhibit large fluctuations in the distribution of neighboring particles characterized by multifractal singularity spectra and pair correlation functions that can be tuned between amorphous and random structures. We also show that the rich structural complexity of Vogel spirals results in a multifractal photonic mode density and isotropic bandedge modes with distinctive spatial localization character. Vogel spiral structures offer the opportunity to create a novel photonic devices that leverage radially localized and isotropic bandedge modes to enhance light-matter coupling, such as optical sensors, light sources, concentrators, and broadband optical couplers.   

Geometrically Structured Dynamic Shadowing Lithography: Structural Growth and Control

Sphere lithography (SL), or nanosphere lithography (NSL), stands out as a versatile technique capable of producing 2D periodic micro- and nanostructures using colloidal crystal as deposition mask. Many of the fundamental aspects of the features produced by SL have been extensively investigated, including the optical, magnetic, electronic, and catalytic behaviors with emphasis toward applications in biosensing, ultrasensitive spectroscopy, and nanodevice fabrication. Previous work has primarily focused on 2D patterning, however, with little attention paid to vertical growth of the SL features. In this work, we will demonstrate the 3D structural evolution of metal dot arrays by SL-based geometrically structured dynamic shadowing lithography (GSDSL). The resulting structure is highly dependent on the nature of the metal that is used as evaporative source. We will specifically focus on the difference in the grain size of several typical metals and illustrate the ability in control of the structural growth through experiment and modeling. We believe that knowledge of the detailed geometry will enable us to understand further information on the physical and chemical properties of the SL substrates.   

Omni-directional active pillar arrays for emission extraction and on-chip generation of optical vortices at 1.55$\mu$m

We engineer deterministic aperiodic structures (DAS) for omni-directional light extraction, emission profile shaping and direct orbital angular momentum generation from Si-based light emitting devices operating at telecom wavelengths. Omni-directional diffraction is achieved through the use of structures with circularly symmetric Fourier space and is well suited for extracting light from devices, such as LEDs or lasers. To exploit the unique light scattering properties of these structures we have fabricated active pillar arrays of Erbium (Er) doped Silicon-Rich Nitride (SRN) using electron beam lithography (EBL) and reactive ion etching (RIE) while varying geometry to optimize extraction enhancement around 1.55$\mu$m. We find that aperiodic spiral arrays with continuous circular Fourier space give over 10 times extraction enhancement and outperform Archimedean lattices, which are the standard structures commonly utilized for omni-directional extraction. Additionally we directly image the real and reciprocal space of the emitted radiation at 1.55$\mu$m and demonstrate direct generation of optical vortices with well-defined values of orbital momentum. These results offer the opportunity to engineer novel optical devices that leverage the control of structured light on optical chips, such as novel laser sources, broadband optical couplers and concentrators.   

Synthesis and Structural Characterization of Orthorhombic Vanadium Oxide Nanorods

Nanorod structures for Li storage are of interest for rechargeable battery applications. Vanadium pentoxide is a promising battery cathode material and in this work we report on the synthesis of V$_{2}$O$_{5}$ orthorhombic single crystal and polycrystalline nanorods by the sol-gel polymerizing acryl amide method via ethylenediamine tetra acetic acid EDTA assisted hydrothermal process. In order to determine the thermodynamic stability of nanostructured polymorphs vanadates, heat treatments were performed from 450 \r{ }C to 500 $^{\circ}$C with annealing times ranging from 48 to 72 h. The morphologies and structures of the nanorods were characterized by XRD, SEM and HRTEM. Thermo Gravimetric Analysis (TGA) was employed to monitor reaction mass losses during the course of the synthesis. Nanorod diameters ranging from 50 to 150 nm were observed. The lengths and diameter of the rods depended on the conditions of the preparation, such as concentration, and reaction time.   

Nonlinear metamaterials through enhanced impact ionization in GaAs at terahertz frequencies

We report the experimental observation of a nonlinear response in metamaterial split ring resonators on semi-insulating GaAs at terahertz frequencies. Using metamaterials with narrow gaps (down to 1$\mu $m), a local in-gap THz field of 3.5 MV/cm was achieved with a field enhancement of $\sim $20 on resonance. With increasing THz electric field the metamaterial resonance is gradually quenched as the capacitive gap is shorted due to a large change in the local conductivity in the gap. This indicates an increase of the local carrier density by ten orders of magnitude resulting from impact ionization. Hybrid metamaterials with intense local electric fields not only have the potential to serve as a new tool to study nonequilibrium transport phenomena in materials, but also provide a new way to explore nonlinear metamaterials at terahertz frequencies.   

Mode nonorthogonality in nonhermitian PT-symmetric optical resonators

PT -symmetric optical resonators combine absorbing regions with active, amplifying regions. The latter are the source of radiation generated via spontaneous and stimulated emission, which embodies quantum noise and can result in lasing. We calculate the frequency-resolved output radiation intensity of such systems and relate it to a suitable measure of excess noise and mode nonorthogonality The lineshape differs depending on whether the emission lines are isolated (as for weakly amplifying, almost hermitian systems) or overlapping (as for the almost degenerate resonances in the vicinity of exceptional points associated to spontaneous PT -symmetry breaking). The calculations are carried out in the scattering input-output formalism, and are illustrated for a quasi one-dimensional resonator set-up.   

Elastic metamaterials and effective medium theory

The unusual properties of a metamaterial are induced by the resonance in its building blocks. We derived an effective medium theory for elastic metamaterials in two dimensions, which is capable of predicting the wave propagation behavior inside the metamaterial near resonances of the building-block. It reveals the connection between resonances and negativities in effective medium parameters. Based on the EMT, we design two types of elastic metamaterials consisting of different resonance structures in their building blocks that can exhibit multiple negative dispersion bands with special characteristics. One is able to produce negative shear modulus and negative mass density simultaneously over a frequency regime, and the other is super-anisotropic. All of these unusual properties are demonstrated by multiple-scattering theory or finite element simulations.   

Session Q18: Focus Session: Interfaces in Complex Oxides - Electronic, Magnetic and Optical Properties

First principles insights into electronic, magnetic, and dynamic effects at and across oxide interfaces

The recent experimental capacity to create high quality epitaxial oxide/oxide interfaces has opened new avenues for research and provides examples of novel materials properties that emerge at the interfaces and in some cases only exist at the interfaces. Furthermore, a coherent, high-quality interface allows degrees of freedom in the two materials to be coupled to each other across the interface thereby creating artificial multi-functional materials systems. Ab initio theoretical approaches can provide key understanding of these complex systems as they can directly describe the interfacial chemical and structural effects on the electronic properties without assumptions or empirical parameters that are derived from bulk properties. Here, we will provide recent examples from our work showing how the presence and structure of the interface can modify the electronic, magnetic, or transport properties. For example, at a ferroelectric/manganite interface we see how the ferroelectric polarization couples to and strongly modifies the magnetism in the manganite. Another example involves dynamic coupling across an insulator/manganite interface where structural fluctuations in the insulator modify the conductivity in the manganite. In part, we will be focusing on the types of structural distortions present at such interfaces, how they are different from or non-existent in the bulk, and which type of distortions create uniquely interfacial phenomena.   

Digital Layered-Manganites: Madelung Energy Effects on Atomic Structure and Properties

The atomic monolayer control of molecular beam epitaxy allows one to explore non-equilibrium dopant-cation configurations in correlated oxide thin films, enabling new electronic phases and magnetic properties to emerge. We report the effects of digital A-site cation doping on electronic phase stability and competition in perovskite-derived manganites. In such digitally synthesized films, Madelung energy constraints are expected to play a primary role in minimizing local Coulomb forces. We correlate changes in the electrical and magnetic properties of the ordered manganites and the resulting crystal structures (Mn-O bond lengths and O-Mn-O bond angles) to the compositionally equivalent control films, i.e. those with randomly distributed A-site dopant-cations. DFT calculations predict that these different layering patterns produce different local and extended crystallographic distortions, including a potential multiferroicity induced by a hitherto unknown mechanism. Synchrotron surface X-ray diffraction measurements in combination with COherant Bragg Rod Analysis at the Advanced Photon Source is used to investigate the resulting atomic structure of the different layering variants, while Second Harmonic Generation and Piezoforce Microscopy investigate the ferroelectric properties.   

Reduced dimensionality and pseudogap formation in (LaMnO$_{3}$)$_{2n}$(SrMnO$_{3}$)$_{n}$ superlattices

(LaMnO$_{3}$)$_{2n}$(SrMnO$_{3}$)$_{n}$ superlattices, composed of the antiferromagnetic insulators LaMnO$_{3}$ (LMO) and SrMnO$_{3}$ (SMO), are ferromagnetic and metallic for n $<$ 3. By increasing the separation between LMO/SMO interfaces for n $\ge$ 3, the system goes through a transition from a metallic to insulating ground state whose origin remains unresolved. We present ARPES measurements of LMO$_{2n}$SMO$_{n}$ superlattices grown by MBE. The electronic structure of states near the Fermi level is similar to the random alloy La$_{2/3}$Sr$_{1/3}$MnO$_{3}$ for small n, but as n is increased we observe the formation of a more 2D state with a preferential occupation of $x^2-y^2$ orbitals. As the system passes into the insulating state at n = 3, a pseudogap forms at the Fermi level: charge carriers are suppressed over a scale of hundreds of meV but without substantial changes to the overall bandstructure. This pseudogap begins to fill as the temperature is increased, but a large suppression in spectral weight at the Fermi level remains at room temperature. Our observations indicate that the insulating state for large-n superlattices is related to strong many-body effects within this system, enhanced by the reduced dimensionality of an interfacial two-dimensional electron liquid.   

Cross-sectional Scanning Tunneling Microscopy (XSTM) Investigation on (SrMnO$_{3})_{n}$/( LaMnO$_{3})_{n}$ Heterostructures

Recent advances in obtaining heterostructures between dissimilar transition-metal oxides with atomically sharp interfaces have revealed emerging exotic electronic and magnetic phases in the vicinity of the interface, which are qualitatively different from the parent compounds. In this study, we have grown (SrMnO$_{3})_{n}$/( LaMnO$_{3})_{n}$ heterostrcuture superlattice, with $n$ being varied from 2 to 8, by laser MBE system with the assistance of the reflection high-energy electron diffraction (RHEED) intensity oscillations on (001) SrTiO$_{3}$ single-crystal substrates. The variation of the density of states across the vicinity of the SrMnO$_{3}$-LaMnO$_{3}$ interfaces were investigated by scanning tunneling microscopy (STM) to reveal the spatial modulation of the electronic properties arising from formation of the two-dimensional electron system at the interfaces. The effects of the layer number, $n$, on this electronically-induced contrast, which is generally ascribed to result from the differences in the energy band gaps, carrier concentrations, as well as electron affinities between SrMnO$_{3 }$and LaMnO$_{3}$, will be discussed.   

Magnetoelectric coupling at the interface of manganite thin films grown on strontium titanate

Oxide heterostructures of PbZr0.2Ti0.8O3/La0.8Sr0.2MnO3/SrTiO3 (PZT/LSMO/STO) have been shown to undergo a large charge-driven magnetoelectric coupling. Switching the polarization state of the ferroelectric PZT layer induces a spin reconstruction in the top atomic layer of the magnetic LSMO layer, changing from ferromagnetic to antiferromagnetic ordering [1]. In this work, the LSMO layer is several unit cells thick. In order to enhance this magnetic switching effect, we have reduced the thickness of the active LSMO layer, replacing part of the LSMO film with LaMnO3 (LMO), a bulk antiferromagnetic insulator. To carry out this approach, we use oxide molecular beam epitaxy (MBE) to control the composition of thin films of LMO and LSMO/LMO heterostructures on SrTiO3(001) with atomic layer precision. Heterostructures grown in this way show a large deviation from the expected behavior for a simple combination of the individual components. We compare measurements of the magnetization for epitaxial LMO on SrTiO3 and heterostructures of LSMO/LMO grown on SrTiO3. Using this approach, one can optimize the properties of the ferromagnetic layer and improve the magnetoelectric switching properties of the PZT/LSMO/STO system. [1] CAF Vaz, et al. Phys. Rev. Lett. 104, 127202 (2010); doi:10.1103/PhysRevLett.104.127202   

Density-functional Study of Suppressed Magnetism at La$_{0.7}$Sr$_{0.3}$MnO$_{3}$/SrTiO$_{3}$ Interfaces

The experimentally observed magnetism suppression at interfaces of La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ has attracted increasing attention. Here we report density-functional calculations for the interface systems of La$_{0.7}$Sr$_{0.3}$MnO$_{3}$/SrTiO$_{3}$. Two interface models are employed to isolate and identify different effects coming from epitaxial strain, symmetry-breaking, charge redistribution, and oxygen vacancy segregation. We found that the strain effect from SrTiO$_{3}$ substrate is not significant enough to cause magnetism suppression at the interface. Although the symmetry is broken at interfaces, this effect leads only to a local ground state and does not cause the observed suppression either. The choice of interface termination does have an effect: moderate magnetism suppression is found for SrO/MnO$_{2}$ termination. Finally, we considered the effect of oxygen vacancy segregation at the interface. In the scenarios we have tested, oxygen vacancies do not suppress the interfacial magnetism. Thus, a complicated mechanism is needed to explain the suppressed magnetism at La$_{0.7}$Sr$_{0.3}$MnO$_{3}$/SrTiO$_{3}$ interfaces.   

Optical Measurements on Magnetoelectric LSMO/PZT Bilayers

Fairly weak magnetoelectric coupling observed in the only single phase material (BeFiO$_{3})$ exhibiting magnetism and ferroelectricity at room temperature has pushed scientists to consider alternative systems. Multilayers prove promising theoretically and experimentally, however, most modern techniques are blind to the interfacial mechanisms causing the coupling. Without a full understanding of the physical mechanism for these effects, significant improvements in the design and multiple potential applications of magnetoelectric coupling will be difficult to achieve. Optical measurements including second harmonic generation are crucial tools to solve this problem, as they provide complementary insight into the magnetic/ferroelectric properties and resulting carrier dynamics. For example, angular dependence SHG of magnetic LaSrMnO$_{3}$ and ferroelectric PbZrTiO$_{3}$ bilayers indicates the symmetry and magnetization as we vary thicknesses of the magnetic and ferroelectric layers and its implication to magnetoelectric coupling.   

Mn valences in La$_{0.7}$Sr$_{0.3}$MnO$_{3}$/PbZr$_{0.2}$Ti$_{0.8}$O$_{3}$ Heterostructures

Magnetoelectric (ME) coupling---the electrical control of magnetic properties or vice versa---has promising applications in computer memory and logic, magnetic sensing and energy scavenging. Understanding the coupling mechanisms in a variety of magnetoelectric material systems is an important step as it will allow us to design better magnetoelectric systems. Our group studies the interfacial properties of the known magnetoelectric system of a ferromagnetic La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ (LSMO) and a ferroelectric PbZr$_{0.2}$Ti$_{0.8}$O$_{3}$ (PZT). Through photoemission electron microscopy imagining, ME coupling was confirmed at the interface. X-ray absorption spectroscopy of Mn was taken across wedged samples of varying ferroelectric and ferromagnetic thicknesses. Here, we will show the changes of Mn valences at different thicknesses of LSMO and PZT, which helps to understand ME coupling and impact of thickness on the ME properties.   

Magnetic coupling at vertical perovskite-spinel epitaxial interface

Interfaces in complex oxides have been the focus of scientists because of their intriguing and unique properties that cannot be found in bulk. Vertical nanostructure is one of the most interesting heterostructure that has been studied for interface phenomena due to its high interface-volume ratio. In this study, (La,Ca)MnO3 (LCMO) (perovskite, matrix) / CoFe2O4 (CFO) (spinel, pillars, 50-200 nm in size) vertical nanostructure has been taken as model system to investigate the interface magnetic coupling with X-ray absorption spectroscopy and photoemission electron microscopy (PEEM), taking the advantages of their element sensitivity and spatial resolution. Matrix and pillars were studied separated with the photon energy set to different absorption edges. The magnetic order and valence states as well as site occupancy in CFO pillars were characterized by XMCD measurements at Co and Fe L-edges with the application of external magnetic fields. In order to investigate the exchange coupling at the interface, we combined this XMCD study with angular dependent XMLD measurements at Fe and Mn L-edges, which give us the information of orbital order in LCMO, while CFO pillars are magnetized in different directions. Similarly, XMCD studies at the Mn L-edges provide detailed insights into the magnetic order of the LCMO matrix, the Mn valence state and elucidate the impact of the CFO pillars. In addition, PEEM measurement provides spatially resolved XMCD/XMLD images that give more insight of the magnetic coupling at the matrix-pillar interface.   

Transport Properties of Films of Prussian Blue Analogues and Manganites

The CoFe Prussian blue analogue (PBA) is a coordination polymer, A$_j$Co$_k$[Fe(CN)$_6$] (A = K, Rb, Cs), that exhibits a photoinduced charge transfer.\footnote{O. Sato \emph{et al}., Science \textbf{272} (1996) 704.} The resulting changes in the magnetization and in the lattice parameter have been used to successfully apply stress on other pressure-sensitive materials, achieving photocontrol of the magnetic response.\footnote{ D.M. Pajerowski \emph{et al}., J. Am. Chem. Soc. \textbf{132} (2010) 4058.} The metal-to-insulator transition (MIT) is a prominent feature of the manganites, whose transition temperature can be tuned by applying various stimuli such as pressure or magnetic field.\footnote{H. J. Jeen and A. Biswas, Phys. Rev. B \textbf{83} (2011) 064408.} By coupling a layer of PBA over a thin film of manganite, the temperature for the MIT can be altered by the light-induced changes in the CoFe PBA.   

Enhanced magnetoresistivity of modulation-doped manganite superlattices

Modulation-doped epitaxial superlattices of La$_{1-x}$Ca$_{x}$MnO$_{3}$ and La$_{1-y}$Ca$_{y}$MnO$_{3}$ layers alternating with x=1/3 and y=1/2 on (001) LaAlO$_{3}$ substrates have been grown by magnetron sputtering. The magnetoresistivity (MR) has been greatly enhanced over a wide temperature range in comparison with the parent compounds. The MR is -50{\%} at 0. 5 Tesla and -90{\%} at 4 Tesla. At low temperatures, a quantum interference effect (QIE) was observed, as manifested by a resistivity minimum considered to be incurred by the 3D e-e interactions. The modulation-doping approach is an enabling strategy to boost the sensitivity of colossal magnetoresistive oxides in response to an applied magnetic field.   

Induced magnetism at complex oxide interfaces

Modified bonding at complex oxide interfaces may be at the bottom of the appearance of interesting novel behaviours not appearing in the bulk constituents. The possibility of tailoring the electronic structure of interfaces has driven an important effort towards the design of interfaces with specific functionalities. We have examined novel interfacial magnetic states originating at the modification of the orbital occupancy resulting from the modified bonding at the interface. We discuss the effect of these low dimensional magnetic states in determining the macroscopic magnetic response and in tailoring specific functionalities of heterostructures.   

Photostriction-Magnetostriction Coupled Epitaxial Nanostructures

Extensive research on complex oxide thin films and heterostructures suggest new possibilities to create and design devices with tantalizing functionalities by taking the advantages of the interplay between lattice, charge, orbital, and spin degrees of freedom. Recently, the self-assemble vertical nanostructures have drawn considerable attentions due to the strong coupling mediated by high interface-to-volume ratio to tailor the properties of oxide nanostructures. However, most studies have been stressing on the controllability of heterostructues through external electric or magnetic fields. In this study, we have synthesized SrRuO3 (SRO)-CoFe2O4 (CFO) nanostructures to introduce light as other external control parameter, where the light-controlled properties are enabled by ultrafast photostriction of SRO and the magnetostriction of CFO. Through a combination of ultrafast-optics, magnetic force microscopy, and soft Xray absorption spectroscopy, the coupling between SRO and CFO is clearly revealed. When illuminating CFO-SRO nanostructures, SRO matrix inflates its volume via expanding its c-axis; the elongated SRO matrix relaxes the out-of-plane compressive strain in CFO pillars effectively reduces the magnetic anisotropy thereof; the reduce magnetic anisotropy resets the preferred magnetization direction of CFO pillars; after removing the illumination, the magnetic anisotropy is re-installed and CFO pillars choose to reverse their magnetization. Our study paves a way to ultrafast optical-coupled functionalities.   

Session Q19: Invited Session: The Scientific Legacy of Edward Purcell (1912-2012)

Purcell and NMR

In 1946 and 1947 the author carried out research at Harvard University under the guydance of Professor Edward M.Purcell. The results were communicated in a frequently cited paper,often referred to as BPP, after the authors Bloembergen, Purcell and Pound. The same material appeared in my 1948 Ph. D. Leiden thesis ``Nuclear Magnetic Relaxation.'' Some personal interactions with Ed Purcell and Bob Pound in these early and in later years at Harvard will be recounted.   

Purcell and the Development of Radioastronomy

``Join me for a ride on an electron, as we fly through electric and magnetic fields.'' With those words, Ed Purcell began a course in Electromagnetic Theory. I had a front row seat. Ken Bainbridge recommended I take the course and get to know Ed. Ed's wisdom and lucidity of thought soon gave the course, and Ed, a special place in my learning experience. I did not take notes in class. I was in awe at Ed's ability to present the subject with such clarity and simplicity. Ed's broad scope of interests and ability to present simple solutions to complex issues quickly led to my identification of Ed as the supreme mentor on any and all subjects. While working with Norman Ramsey to obtain an external beam from the Harvard Cyclotron, I consulted with Ed on the subject of available options. He suggested I scatter the beam off a target that could be remotely positioned, and catch it in a tunnel shielded from the magnetic field of the Cyclotron. When I had a problem with implementation I would, `` Ask Ed.'' During a visit to the Lab by Fermi, he commented on the simplicity of the solution. He was not surprised to learn that Purcell provided critical guidance. When I suggested Meteorology as a subject for my Oral Test, Purcell said it was not a science and I should pick another subject. I argued it was a science. Ed asked that I loan him some books on the subject and the Oral would be in two weeks. When I walked into the room for the Oral, I noticed that Ed had invited all seven authors of the books I had loaned to him. A simple Purcell answer to a problem. When I asked about his recommendations concerning doctorate dissertation topics, he said the selection must be based on my interests not his. I provided a brief summary: Mathematics, Quantum Mechanics, Meteorology, and Astronomy. Within two weeks, Ed proposed I look into the Hydrogen Line. After a joint review of the papers by Van deHulst and Shklovski we concluded that: van de Hulst had clearly shown the line was undetectable, Shklovski had claimed the line was detectable, however, there was an error in his calculations. We noted, however, that the topic fit my interests. Purcell had a simple solution. I would proceed with a ``negative thesis,'' the goal to measure the level of non-detectability. As with all other joint ventures, Ed was always there when I needed help. His guidance was always simple and embarrassingly obvious. For my doctorate oral exam, Ed invited Van deHulst as the only other participant. Purcell began by asking if I had any questions. I asked Van deHulst why the line was detectable. Purcell then announced that I had my doctorate and could leave at any time, while he and Van deHulst worked on the answer to my question. Many of us became terribly alone on March 7, 1997, when we learned we could no longer ``Ask Ed.''   

On small things in water moving around: Purcell's contributions to biology

I went to see Purcell after finishing my course work for the Ph.D. (1961) to ask whether I might join his group. ``But I don't have any graduate students,`` he said. ``Why is that?'' I asked. ``I can't think of anything to do,'' he replied. That was a wipe out. After I had finished my Ph.D. with Ramsey on the hydrogen maser (1964), Ed and I came up with an idea that led to work on sedimentation field-flow fractionation (\textit{PNAS} 1967). We had hoped this method would be useful for biology, but problems of adsorption of proteins to surfaces stood in the way. Then I moved over to the biology department and got interested in the motile behavior of bacteria (1968). Here was a subject that I thought Ed would really enjoy. There were wonderful movies made by Norbert Pfennig of experiments done by Theodor Engelmann in the 1880's. We found a 16-mm projector and looked at these movies on Ed's office wall. Ed's first comment proved seminal, ''How can such a small cell swim in a straight line?'' We thought about how cells count molecules in their environment and wrote ``Physics of chemoreception,'' (\textit{Biophys. J}.,1977). In the meantime, Ed gave a memorable lecture at Viki Weisskopf's retirement symposium, his classic ``Life at low Reynolds number'' (\textit{Am. J. Phys.} 1977). Ed really wanted to understand what it would be like to swim like a bacterium! He wasn't very interested in what the literature had to say about such a problem, he wanted to think it through for himself. My role was straight man. I very much enjoyed the ride.   

Purcell's Work Helping the Government

I worked closely with Ed Purcell from 1956 through 1975 or so, largely through our joint membership on and consulting with the President's Science Advisory Committee (PSAC) and working with the ``Land Panel'' on reconnaissance satellites. Purcell's work with the government had begun long before, with his 5-year service at the MIT Radiation Laboratory, and his advisory role had included, in particular, important work of the Technological Capabilities Panel (TCP) of the predecessor to PSAC. I will try to capture the flavor of Ed's contributions and the context of the times in which he was involved. His style and impact are well characterized by this quote from the book of Eisenhower's Science Advisor and PSAC Chair, James~R.~Killian, ``When Eisenhower was later to speak in memorable tribute of `my scientists' he was surely recalling among others this quiet, modest, lucid man. Robert Kreidler [one of Killian's staff], in an interview I had with him in preparing for this memoir spoke almost with awe of his [Purcell's] impact on PSAC, `Ed Purcell did not speak often,' he said, `but when he did there would be enormous silence in the room, because everybody knew that whatever he said was going to be worth listening to with careful attention.''' I give some examples why it was so worthwhile listening to Ed Purcell.   

Purcell the Teacher: In and Out of the Classroom

As a high school student Edward Purcell read articles by K.K. Darrow from his series, ``Advances in Contemporary Physics.'' Many years later, Purcell, referring to those articles, said they remind us ``that great teaching does not require a classroom{\ldots}.'' Many of Purcell's choices were motivated by his devotion to teaching: the undergraduate courses he preferred to teach at Harvard, the textbooks and pedagogical papers he wrote, and the professional activities he engaged in. He delighted in explaining complex phenomena in simple ways -- a mark of a great teacher.   

Session Q20: Invited Session: Robust Energy Storage with Engineered Si

Silicon Nanowire Anodes: Materials and Composites

Silicon nanowires (SiNWs) have the potential to perform as anodes for lithium-ion batteries with a much higher energy density than graphite. Previously, we have shown that reversible capacities $>$3,000 mAh/g can be obtained by using an electrode geometry consisting of SiNWs grown on metallic current collector substrates using the CVD-based vapor-liquid-solid (VLS) method. These electrodes consisted of SiNWs directly attached and vertically oriented off of the current collector. SiNWs can be synthesized in large quantities using the supercritical-fluid-solid (SFLS) method. Slurries were prepared composed of silicon nanowires synthesized using the SFLS method mixed with amorphous carbon or carbon anotubes and binder and coated onto Cu foil. Recent results regarding the cycling behavior of the SiNWs using different experimental conditions will be presented. The performance of these composite electrodes will also be compared with our previous work using the VLS SiNWs to determine how the electrode architecture affects the electrochemical performance.   

Strain-tolerant High Capacity Silicon Anodes via Directed Lithium Ion Transport for High Energy Density Lithium-ion Batteries

Energy storage is an essential component of modern technology, with applications including public infrastructure, transportation systems, and consumer electronics. Lithium-ion batteries are the preeminent form of energy storage when high energy / moderate power densities are required. Improvements to lithium-ion battery energy / power density through the adoption of silicon anodes--with approximately an order of magnitude greater gravimetric capacity than traditional carbon-based anodes--have been limited by $\sim$300\% strains during electrochemical lithium insertion which result in short operational lifetimes. In two different systems we demonstrated improvements to silicon-based anode performance via directed lithium ion transport. The first system demonstrated a crystallographic-dependent anisotropic electrochemical lithium insertion in single-crystalline silicon anode microstructures. Exploiting this anisotropy, we highlight model silicon anode architectures that limit the maximum strain during electrochemical lithium insertion. This self-strain-limiting is a result of selecting a specific microstructure design such that during lithiation the anisotropic evolution of strain, above a given threshold, blocks further lithium intercalation. Exemplary design rules have achieved self-strain-limited charging capacities ranging from 677 mAhg$^{-1}$ to 2833 mAhg$^{-1}$. A second system with variably encapsulated silicon-based anodes demonstrated greater than 98\% of their initial capacity after 130+ cycles. This anode also can operate stably at high energy/power densities. A lithium-ion battery with this anode was able to continuously (dis)charge in 10 minutes, corresponding to a power / energy density of $\sim$1460 W/kg and $\sim$243 Wh/kg--up to 780\% greater power density and 220\% higher energy density than conventional lithium-ion batteries. Anodes were also demonstrated with areal capacities of 12.7 mAh/cm$^2$, two orders of magnitude greater than traditional thin-film silicon anodes.\\[4pt] In collaboration with Michael W. Cason and Ralph G. Nuzzo.   

Understanding the Degradation of Silicon Electrodes for Lithium-Ion Batteries Using Acoustic Emission and Fracture Mechanics

Silicon is a promising anode material for lithium-ion battery application due to its high specific capacity, low cost, and abundance. However, when silicon is lithiated at room temperature, it can undergo a volume expansion in excess of 280{\%}, which leads to an extensive fracturing. This is thought to be a primary cause of the rapid decay in cell capacity routinely observed. We have developed a special cell design which allows us to monitor acoustic emissions stemming from mechanical events in the cell and allow for detailed structural analysis using X-ray diffraction with an internal standard. The combined result from acoustic emissions and X-ray diffraction allow for a first of its kind detailed look at how silicon anodes degrade and together with presented theories of fracture mechanics enable a material engineering approach to optimize its long term behavior. In collaboration with Kevin Rhodes and Sergiy Kalnaus.\\[4pt] Parts of this research were performed at the High Temperature Materials Laboratory, a national user facility sponsored by the same office.   

Reversible Cycling of Silicon and Silicon Alloys

Lithium ion batteries typically use a graphite negative electrode. Silicon can store more lithium than any other element and has long been considered as an attractive replacement for graphite. The theoretical lithium storage capacity of silicon is nearly ten times higher than graphite volumetrically and three times higher gravimetrically. The equilibrium Si-Li binary system is well known. Completely new phase behaviors are observed at room temperature. This includes the formation of a new phase, Li15Si4, which is the highest lithium containing phase at room temperature [1]. The formation of Li15Si4 is accompanied by a 280 percent volume expansion of silicon. During de-alloying this phase contracts, forming amorphous silicon. The volume expansion of alloys can cause intra-particle fracture and inter-particle disconnection; leading to loss of cycle life. To overcome issues with volume expansion requires a detailed knowledge of Li-Si phase behavior, careful design of the composition and nanostructure of the alloy and the microstructure of the negative electrode [2]. In this presentation the phase behavior of the Li-Si system will be described. Using this knowledge alone, strategies can be developed so that silicon can be reversibly cycled in a battery hundreds of times. Further increases in energy density and efficiency can be gained by alloying silicon with other elements, while controlling microstructure [2]. Coupled with negative electrode design strategies, practical negative electrodes for lithium ion cells can be developed based on bulk materials, with significant energy density improvement over conventional electrodes. \\[4pt] [1] M.N. Obrovac and L.J. Krause, J. Electrochem. Soc., 154 (2007) A103. \\[0pt] [2] M.N. Obrovac, Leif Christensen, Dinh Ba Le, and J.R. Dahn, J. Electrochem. Soc., 154 (2007) A849   

Pair Distribution Function Analysis and Solid State NMR Studies of Silicon Electrodes for Lithium Ion Batteries: Understanding the (De)lithiation Mechanisms

The crystalline-to-amorphous phase transition that occurs on electrochemical Li insertion into crystalline Si, during the first discharge, hinders attempts to link the structure with electrochemical performance. We apply a combination of local structure probes, in situ and ex situ 7Li nuclear magnetic resonance (NMR) studies, and pair distribution function (PDF) analysis of X-ray data to investigate the changes in short-range order that occur during the initial charge and discharge cycles. The distinct electrochemical profiles observed subsequent to the first discharge have been shown to be associated with the formation of distinct amorphous lithiated silicide structures. The first process seen on the second discharge is associated with the lithiation of the amorphous Si, forming small clusters. These clusters are broken in the second process to form isolated silicon anions. The (de)lithiation model helps explain the hysteresis and the steps in the electrochemical profile observed during the lithiation and delithiation of silicon. At deep discharge states a highly reactive lithium excess Li15Si4 phase is detected by in situ NMR which undergoes a self-discharge process in electrolyte.   

Session Q21: Novel Superconductivity in New and Low Dimensional Materials

Superconductivity in ThCoC$_{2}$

We report bulk superconductivity in the metallic carbide compound ThCoC$_{2}$. This compound crystallizes in the orthorhombic CeNiC$_{2}$ prototype structure, a non-centrosymmetric system. Despite the presence of Cobalt and the lack of inversion symmetry, we find bulk superconductivity with a critical temperature of T$_{c}$-2.6K. Details of the superconducting state with specific heat, magnetization, and resistivity measurements will be presented. This study was made possible by the generous support of AFOSR MURI ``Search for New Superconductors for Energy and Power Applications.''   

Superconductivity in ScGa$_3$ and LuGa$_3$

We are reporting low-temperature superconductivity in single crystals of ScGa$_3$ and LuGa$_3$. While the latter compound had been listed as a superconductor before, superconductivity in the former compound had never been observed, and characterization of the low-temperature state was lacking in both compounds. By measurements of magnetization, specific heat and resistivity, we show that RGa$_3$ (R = Sc and Lu) are conventional BCS superconductors with T$_c$ around 2.3 K and the upper critical field less than 240 Oe. The experimental results agree with band structure calculation estimate of the critical temperature.   

Physical properties of single crystalline SrSn$_{4}$ and BaSn$_{5}$ superconductors

We present the growths and detailed thermodynamic and transport measurements on single crystals of the recently discovered binary intermetallic superconductors, SrSn$_{4}$ and BaSn$_{5}$. Their superconducting transition temperatures T$_{c}$ are found to be 4.8 K and 4.4 K respectively. Both materials are strongly-coupled, possibly multi-band superconductors. Hydrostatic pressure causes a decrease in the superconducting transition temperature at the rate of $\approx \quad -$0.068 K/kbar for SrSn$_{4}$, and $\approx \quad -$0.053 K/kbar for BaSn$_{5}$. Band structure and upper superconducting critical field anisotropy of SrSn$_{4}$ suggest complex, multi-sheet Fermi surface formed by four bands. De Hass-van Alphen oscillations are observed in BaSn$_{5}$, which indicates a more complex topology of Fermi surface.   

Synthesis, Structure, Physical Properties of several Zirconium Chalcogenides

Compounds of KxZr2Se6, RbxZr2Se6 and ZrTe1.3As0.7 have been fabricated by high temperature solid state synthesis technique. All these compounds have the same space group Immm. They can be generally considered as the compounds derived from ZrSe3 and ZrTe3, which accommodate the quasi 2D type structure composed by (Zr2Se2)(Se4) and (Zr2Te2)(Te4) Layers. KxZr2Se6 and RbxZr2Se6 could be considered as the anionic layers [(Zr2Se2)(Se4)]x- intercalated with alkali cations. One the other hand, ZrTe1.3As0.7 isn't a layered compound. The compound has the same structure with NbPS, with disordered As and Te occupying the P sites. This structure could be considered as a derivative structure of ZrTe3 with the retained (Zr2Te2) layers interspersed with linear (Te0.3As0.7) chains. We also measured the magnetic and transport properties of these samples. We shall present and discuss their interesting structural and physical properties.   

Superconductivity in Pd, Ir, and Pt chalcogenide

Large spin-orbit coupling in materials with heavy chalcogens can result in unique quantum states or functional properties such as topological insulator, giant thermoelectric power, and superconductivity. When materials contain heavy cations in addition to heavy chalcogens, spin-orbit coupling can be further enhanced. For these reasons, we have studied the superconductivity of Pd, Ir, and Pt tellurides and selenides. In the exploration of these chalcogenides, we have focused on the competition between superconductivity and charge density wave that is associated with superlattice reflections.   

Elementary excitations and elusive superconductivity in palladium hydride -- \textit{ab initio} perspective. I. Paramagnons

\newcommand{\el}{\textit{et~al}.} Motivated by a experimental reports on possible high temperature superconductivity in palladium hydride [Tripodi \el, \textit{Physica C} \textbf{388-389}, 571 (2003)], we present a first principle study of spin fluctuations, electron-phonon coupling and critical temperature in PdH$_{x}$, $0 \leq x \leq 1$. A prerequisite for any qualitative study of exchange-enhanced materials is the knowledge of spin flip fluctuation spectrum. It is generally believed [Berk \& Schrieffer, \textit{Phys. Rev. Lett.}, \textbf{17}, 433 (1966)] that the ferromagnetic-like paramagnons of Pd are destructive for the conventional, i.e.\ $s$-wave, superconductivity. We describe them using linear response time dependent density functional theory, recently implemented to study complex metals [Buczek \el, \textit{Phys. Rev. Lett.} \textbf{105}, 097205 (2010)] . We find that hydrogenation suppresses the intense spin fluctuations of pure Pd, driving it away from a magnetic critical point. Under the assumption of $s$-wave pairing, this could lead to the formation of the superconducting state. The \textit{ab-initio} estimated electron-phonon coupling is strong enough to support superconductivity. Please look for the complementary contribution of Christophe Bersier.   

Elementary excitations and elusive superconductivity in palladium hydride -- \textit{ab initio} perspective. II. Phonons

Motivated by a experimental reports on possible high temperature superconductivity in palladium hydride [Tripodi et al., \textit{Physica C} \textbf{388-389}, 571 (2003)], we present a first principle study of spin fluctuations, electron-phonon coupling and critical temperature ($T_{c}$) in PdH$_{x}$ , $0 < x < 1$. Our results described in terms of (i) electronic structure, (ii) phonon density of states and (iii) Eliashberg function show that the hydrogenation of Pd clearly enhance the electron-phonon coupling in this material. Assuming phonons to be the driving force for superconductivity, fcc Pd features a vanishingly small $T_{c}$, while for the stochiometric $x=1$ PdH the resulting $T_{c}$ is around 10K in agreement with experiment. It is generally believed [Berk \& Schrieffer, \textit{Phys. Rev. Lett.}, \textbf{17}, 433 (1966)] that intense spin-\&flip fluctuations of Pd are destructive for the conventional, i.e. $s$-wave, superconductivity. However, the H doping leads to a drastic reduction of spin-flip scattering. Please look for complementary presentation of Pawe\l{} Buczek.   

Structural and Electronic properties of the 2D Superconductor CuS covellite with 113-valent Copper

Hexagonal CuS has recently been reported to superconduct at 40 K. At the same time, earlier experiments had found superconductivity at 1.5 K. Some authors reported local magnetic moments in this compound, while others observe pure Pauli paramagnetism. It exhibits a rather unusual for a good metal symmetry-lowering transition at 55 K of unknown origin. Even the Cu valency in CuS has been debated, with suggested ionic models such as $(Cu^{+1})_3(S_2^{-2})(S^{-1})$ and $(Cu^{+1})_3(S_2^{-1})(S^{-2})$, as well as noninteger valencies. To gain more insight, we've performed DFT calculations and found that the actual valency of Cu is 4/3 (2), so that the Cu d band is not sufficiently ionized in the ideal compound to provide enough proximity to Mott dielectric for either local moments or unconventional superconductivity. On the other hand, the reason that Cu in not divalent here is that some sulfurs form covalent S$_2$ molecules with the effective S$_2^{-2}$ valency. If some of these covalent S-S bonds are broken, local moments $can$ form, and in that case superexchange in the hexagonal lattice can induce $f-$wave pairing. Finally, regarding the structural transition, it is well reproduced in DFT calculations. Possible microscopic origin of this transition will be discussed in the talk.   

Moving Beyond Quantum Mechanics in Search for a Generalized Theory of Superconductivity

Though there are infinite number of theories currently in the literature in the search for a generalized theory of superconductivity (SC), there may be three domineering mechanisms for the Cooper pair formation (CPF) and their emergent theories of SC. Two of these mechanisms, electron-phonon interactions and electron-electron correlations which are based on the quantum theory axiom of action-at-a distance, may be only an approximation of the third mechanism which is contact interaction of the wavepackets of the two electrons forming the Cooper pair as envisaged in hadronic mechanics to be responsible for natural bonding of elements. The application of this hydronic --type interaction to the superconducting cuprates, iron based compounds and heavy fermions leads to interesting results. It is therefore suggested that the future of the search for the theory of SC may be considered from this natural possible bonding that at short distances, the CPF is by a nonlinear, nonlocal and nonhamiltonian strong hadronic-type interactions due to deep wave-overlapping of spinning particles leading to Hulthen potential that is attractive between two electrons in singlet couplings while at large distances the CPF is by superexchange interaction which is purely a quantum mechanical affairs.   

Material Specific Design for Room Temperature Superconductivity

The transition temperature, Tc, of superconductors has been increased sevenfold from 23K in Nb$_{3}$Ge to 164K in Hg-1223. A further two-fold increase would get us to above room temperature superconductivity. Studying high temperature superconductors (HTSCs), we have developed a formula that expresses Tc in terms of electronegativity, valence electrons, Ne, atomic number, Z, formula mass and a coupling constant, Ko. We observe an increasing linear relationship between Tc and Ko. Ko also correlates with formula mass and atomic number and the number of atoms in the compound. By our formula, Hg-1223 has Ko = 70. We propose, using our design algorithm, that room temperature superconductivity may be realized in a system with ko = 160; electronegativity = 2.5, Ne/Sqrt Z = 0.8. We proceed to show combinations of oxides and elements that will yield the required parameters for synthesizing reproducible room temperature superconductivity.   

Thermopower and Resistivity in the Spin Density Wave- Metal co-existence regime of (TMTSF)2PF6

The organic conductor (TMTSF)2PF6 is studied in the pressure regime where it is believed to exhibit co-existence between Metallic and Spin Density Wave domains. In this pressure regime, an anisotropy in the superconductivity transition - seen previously in resistivity data on separate samples in different experimental runs - Is here reproduced using both resistivity and thermopower as probes, on three slices of the same crystal measured simultaneously. The simultaneous use of these two measurements along the a ,b and c axes , enables us to extract complementary information about the remarkable anisotropy in the superconducting transition and may shed light on the possibly inhomogeneous ground states in the co-existence regime of (TMTSF)2PF6.   

Non-analytical Angular Dependence of the Upper Critical Magnetic Field in a Quasi-One-Dimensional Superconductor

We have derived the so-called gap equation, which determines the upper critical magnetic field, perpendicular to conducting chains of a quasi-one-dimensional superconductor. By analyzing this equation at zero temperature, we have found that the calculated angular dependence of the upper critical magnetic field is qualitatively different than that in the so-called effective mass model. In particular, our theory predicts a non-analitical angular dependence of the upper critical magnetic field, $H_{c2}(0) - H_{c2}(\alpha) \sim \alpha^{3/2}$, when magnetic field is close to one of the crystallographic axes and makes an angle $\alpha$ with the axis. We discuss possible experiments on the superconductor (DMET)$_2$I$_3$ to discover this non-analytical dependence.   

Hidden Reentrant and Larkin-Ovchinnikov-Fulde-Ferrell Superconducting Phases in a Magnetic Field in (TMTSF)$_{2}$ClO$_{4}$

We solve a long-standing problem about a theoretical description of the upper critical magnetic field, parallel to conducting layers and perpendicular to conducting chains, in (TMTSF)$_{2}$ClO$_{4}$ superconductor. In particular, we explain why the experimental upper critical field, H$^{b}_{c2}$ = 6T, is higher than both the quasi-classical upper critical field and Clogston paramagnetic limit. We show that this property is due to the coexistence of the hidden Reentrant and Larkin-Ovchinnikov-Fulde-Ferrell phases in a magnetic field in a form of three plane waves with non-zero momentums of the Cooper pairs. Our results are in good qualitative and quantitative agreement with the recent experimental measurements of H$^{b}_{c2}$ and support a singlet d-wave-like scenario of superconductivity in (TMTSF)$_{2}$ClO$_{4}$.   

$^{1}$H NMR Spin-Lattice Relaxation Study of $\kappa$-(ET)$_{2}$Cu[N(CN)$_{2}$]Br

The discovery of an anomalous Nernst signal in the organic superconductor $\kappa$-(ET)$_{2}$Cu[N(CN)$_{2}$]Br suggests the presence of magnetic flux vortices above T$_{c}^{[1]}$. Previous studies below the transition temperature have shown that the additional fluctuating field created by vortices dramatically increases the $^{1}$H NMR spin-lattice relaxation rate$^{[2]}$. We revisit $^{1}$H spin-lattice relaxation in $\kappa$-(ET)$_{2}$Cu[N(CN)$_{2}$]Br and provide new evidence of inhomogeneous behavior both above and below $T_{c}$. $^{[1]}$M. S. Nam et al, Nature 449, 584-587 (2007) $^{[2]}$H. Mayaffre et al, Phys. Rev. Lett. 76, 4951-4954 (1996) Work at UIUC supported by NSF DMR 10-05708 and the Center for Emergent Superconductivity, USDOE Award No. DE-AC0298CH1088. Work at Argonne supported by UChicago Argonne, LLC, Operator of Argonne National Laboratory, DOE Contract No. DE-AC02-06CH11357.   

$^{13}$C NMR Study of Slow Motions in $\kappa$-(ET)$_2$Cu[N(CN)$_2$]Br

Like the high-$T_{C}$ cuprates, the 2D organic superconductor $\kappa$-$\mathrm{(ET)_{2}Cu[N(CN)_{2}]Br}$ ($T_{C}=11.9$~K) exhibits a pseudo-gapped phase above the superconducting transition, as indicated by the $^{13}\mathrm{C}$ spin-lattice relaxation rate ($1/T_{1}T$) peak at about 50~K. While $^{13}\mathrm{C}$ NMR has been used extensively to probe the pseudo-gapped regime, $T_{1}$ is only sensitive to fast motions in the MHz scale (Larmor frequency), and $T_{2}$ remains relatively constant in the pseudo-gapped regime. Neither $T_{1}$ nor $T_{2}$ give us any clue about any possible slow motions. We report measurements using the stimulated echo pulse sequence\footnote{L. R. Becerra, C. A. Klug, C. P. Slichter, and J. H. Sinfelt, J. Phys. Chem. \textbf{97}, 12014 (1993).} which is capable of providing more detailed information on possible slow motions in the pseudo-gapped regime.   

Session Q22: Focus Session: Fe-based Superconductivity - Doped and Undoped BaFe2As2

Nature of phase transitions in the parent and lightly electron doped BaFe$_{2}$As$_{2}$ compounds

We present a combined high-resolution x-ray diffraction and x-ray resonant magnetic scattering study of as-grown BaFe$_{2}$As$_{2}$. The structural and magnetic transitions must be described as a two-step process. The undoped BaFe$_{2}$As$_{2}$ parent compound manifests a second-order structural transition from the high-temperature paramagnetic tetragonal structure to a paramagnetic orthorhombic phase and a first-order antiferromagnetic transition from the paramagnetic orthorhombic phase to an antiferromagnetic orthorhombic phase at slightly lower temperature. As electrons are introduced by Co or Rh, the phase transitions evolve toward second-order transitions. Using these results, we provide an estimate of the position of a tricritical point in the phase diagram of Ba(Fe$_{1-x}$Co$_{x})_{2}$As$_{2}$.   

Neutron powder diffraction studies on Ba$_{1-x}$A$_{x}$Fe$_{2}$As$_{2}$ (A=Na, K)

In the so-called 122 iron pnictide superconductors, the SDW is suppressed and superconductivity can be induced by various means including charge doping, pressure, and isovalent substitution. Using neutron powder diffraction and SQUID magnetization measurements, we have investigated the effects of both potassium and sodium substitution on superconductivity, structural transformation and magnetic ordering in Ba$_{1-x}$A$_{x}$Fe$_{2}$As$_{2 }$(A=K,Na) producing detailed phase diagrams of both systems. We present a comparison of the similarities and differences in the various internal atomic and magnetic structural parameters as a function of temperature and composition of these two hole-doped systems.   

Neutron diffraction study of the development of incommensurate magnetic order in Ba(Fe$_{1-x}M_{x}$)As$_{2}$ ($M=$ Co, Ni, Cu)

We employ neutron diffraction and electronic structure calculations using both virtual crystal and coherent potential approximations to investigate the conditions for incommensurate magnetism in several electron-doped compounds Ba(Fe$_{1-x}M_{x}$)As$_{2}$ with $M=$Co, Ni, Cu. Incommensurate order is observed for $M=$ Co and Ni with $x \approx 0.06$ and 0.03, respectively. Assuming each Co (Ni) ion donates one (two) additional electrons, the appearance of incommensurate magnetism in the Co and Ni doped systems occurs at similar electron concentrations. For $M=$ Cu, Cu should donate three electrons and one expects that incommensurate magnetism will appear at $x \approx 0.02$. However, we find that the magnetism remains commensurate until it disappears at $x \approx 0.05$. Thus, Cu doping behaves differently than either Co or Ni, as can be explained from the electronic structure.   

Magnetic moment in single crystalline BaFe$_{2-x}$Zn$_{x}$As$_{2}$

Nature of the magnetism for iron-based superconductors (FeSCs) has been actively studied since the discovery of this new family of compounds in 2008, largely owing to its significance for interpreting the paring mechanism. The approach through impurity substitution to shed light into this issue is always one of major ways. The substitution shows distinct responses to species of impurities, where partially replacement of Fe in parent FeSCs with a variety of $d$-metals like Co, Ni Ru, Rh, Pd, Ir, and Pt generally results in superconductivity, while recent progress in Zn doped FeSCs gives rather contrary result, where Zn severely degenerates the $T_{C}$. Herein we show the magnetic and electrical studies on BaFe$_{2-x}$Zn$_{x}$As$_{2}$ single crystals. Nonmagnetic Zn doping progressively suppresses the SDW without resulting in superconductivity, while it alternatively develops the spin-glass state, possibly suggestive of local magnetic moment around the Fe sites induced by Zn. The characterizations by X-ray diffraction, magnetic and electrical transport properties, specific heat capacity, and Hall coefficient have been done and the results will be discussed in detail.   

75As-NMR studies on Ba(Fe1-xNix)2As2 single crystals

75As nuclear magnetic resonance (NMR) were measured for Ba(Fe1-xNix)2As2 single crystals with x = 0.05 and x = 0.1 under 0 GPa and 1.5 GPa, respectively. For the optimal doped sample with x = 0.05, the superconducting transition temperature Tc is strongly suppressed from 18 K to 5 K, while for the over-doped sample with x = 0.1, it is turned from the superconducting ground state to a disordered paramagnetic state under 1.5 GPa. Our experimental results show that the antiferromagnetic spin fuctuations are suppressed as well as Tc. The experimental results can be explained with the two-band model. As a result, the electronic band is downward shifted with increase of pressure and the electrons become the dominant carriers in the system.   

Do Transition Metal Substitutions Dope Carriers in Iron Based Superconductors?

We investigate the currently debated issue concerning whether transition metal substitutions dope carriers in iron based superconductors. From first-principles calculations of the configuration-averaged spectral function [1,2] of BaFe$_2$As$_2$ with disordered Co/Zn substitutions of Fe, important doping effects are found beyond merely changing the carrier density. While the chemical potential shifts suggest doping of a large amount of carriers, a reduction of the coherent carrier density was found due to the loss of spectral weight. Therefore, none of the change in the Fermi surface, density of states, or charge distribution can be solely used for counting doped coherent carriers, let alone presenting the full effects of the disordered substitutions. Our study highlights the necessity of including disorder effects in the studies of doped materials in general. [1] W. Ku, T. Berlijn. and C.-C. Lee, Phys. Rev. Lett. 104, 216401 (2010) [2] T. Berlijn, D. Volja and W. Ku, Phys. Rev. Lett. 106, 077005 (2011)   

X-ray absorption spectroscopy study in the BaFe2As2 family

One of the representative Fe-based superconductor families, BaFe2As2 (Tc =38K) is a semimetal with the same number of hole and electron carriers, and is in a spin density wave state below 139K. It has been reported that various types of ``doped'' BaFe2As2 systems can obtained by substitution of Ba, Fe, and As atoms. However, an important issue has been recently raised regarding whether each type of substitution indeed induces effective charge doping or not. It is essential to clarify whether each type of substitution indeed induce an effective doping in BaFe2As2 system. To clarify the carrier doping issue, we performed high resolution X-ray absorption spectroscopy experiment on Ba(Fe,Co)2As2, Ba(Fe,Ru)2As2, BaFe2(As,P)2 which are representative ``doped'' BaFe2As2 systems.   

Competing Magnetic Phases in Ba(Fe$_{0.925}$Mn$_{0.075}$)$_2$As$_2$

Inelastic neutron scattering measurements on Ba(Fe$_{0.925}$Mn$_{0.075}$)$_2$As$_2$ show broad, diffusive spin fluctuations at two different propagation vectors corresponding to stripe magnetic order and conventional N\'eel antiferromagnetic order. Below {\it T} = 80\,K long-range stripe magnetic ordering occurs and sharp spin wave excitations appear at the stripe propagation vector while diffusive spin fluctuations remain at the N\'eel propagation vector. These results suggest that low concentrations of Mn dopants introduce a competing magnetic phase that may prevent the development of superconductivity in Ba(Fe$_{1-x}$Mn$_{x}$)$_2$As$_2$.   

Infrared pseudogap in P- and Co-doped BaFe$_{2}$As$_{2}$ superconductors

We investigated the in-plane electronic response of P- and Co-doped BaFe$_{2}$As$_{2}$ compounds using infrared spectroscopy. We found hallmarks of the normal-state pseudogap in the optical spectra of the BaFe$_{2}$As$_{2}$ system, which are very similar with those of the cuprates. Based on the evolution of the electronic response with doping and across the superconducting transition, we suggest that the antiferromagnetic fluctuations can be a possible origin of the infrared pseudogap in the iron pnictides. We will also discuss implications of our results for the origin of the pseudogap in the cuprates.   

Effects of disordered isovalent substitution in Fe-based superconductor

Using a recently developed first-principles method for disordered materials [1-2], we investigate the effect of isovalent substitution in Fe-based superconductors, BaFe$_2$(As$_{1-x}$P$_x$)$_2$, FeTe$_{1-x}$Se$_x$, and Ba(Fe$_{1-x}$Ru$_x$)$_2$As$_2$. For anion substitutions (the first two cases) effects of impurity scattering are found mostly in the anion bands. By contrast, the Ru substitution introduces much stronger scattering in the Fe bands. Surprisingly, in all the cases, the pockets near the chemical potential are the least affected, due to the low density of states near the chemical potential. Together, our results suggest an interesting scenario of enhancing superconductivity.\\[4pt] [1] T. Berlijn, D. Volja, W. Ku, Phys. Rev. Lett. 106, 077005 (2011).\\[0pt] [2] W.Ku, T. Berlijn, CC. Lee, Phys. Rev. Lett. 104, 216401 (2010).   

Electron Injection and ``Oxygen Effect'' in BaFe$_{2}$As$_{2}$: M\"{o}ssbauer Studies

It is widely believed that a few percent substitution of Co (with d7) or Ni (with d8) for Fe (with d6) in BaFe$_{2}$As$_{2}$ results in donation~of electrons, killing of magnetism, and thereby induction of superconductivity. We are exploring the possibility of injecting electrons by physico-chemical techniques instead of substitutions.~ We have also discovered that traces of chemisorbed oxygen can change drastically the magnetic behavior in polycrystalline BaFe$_{2}$As$_{2}$ at low temperatures. BaFe$_{2}$As$_{2}$ exhibits considerable hysteresis~behavior as well that of thermal history.   

Effects of annealing on Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ and Ba(Fe$_{1-x-y}$Co$_x$TM$_y$)$_2$As$_2$ (TM=Mn,Cr) single crystals

Single crystals of Ba(Fe$_{1-x-y}$Co$_x$TM$_y$)$_2$As$_2$ (TM=Cr, Mn) have been grown and characterized by structural, magnetic and transport measurements, both in the as-grown state (quenched from $\sim 1000^{\circ}$~C) as well as after post-growth annealing. This phase space has many parameters and is rich and complex, with superconducting transition temperatures depending upon x and y, as well as annealing temperature and time. In this talk, we will present T-x and T-y, as well as T-time and T-T (for annealing) phase diagrams and discuss the implications for future research into these complex materials.   

Infrared conductivity of BaFe$_2$As$_2$ superconductors: Effects of in-plane and out-of-plane doping

We measured the \emph{in-plane} optical conductivity of a nearly optimally doped ($T_{c}$ = 39.1 K) single crystal of Ba$_{0.6}$K$_{0.4}$Fe$_{2}$As$_{2}$. Upon entering the superconducting state the optical conductivity vanishes below $\sim$ 20 meV, indicating a fully gapped system. A model with two different isotropic gaps is required to describe the optical response of this material. The temperature dependence of the gaps indicate a strong interband interaction, but no impurity scattering induced pair breaking is present. This contrasts to the large residual conductivity observed in optimally doped Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$ and strongly supports an $s_\pm$ gap symmetry for both compounds.   

Ultrafast Probing of Antiferromagnetism and Dynamic Critical Behaviors in Iron Pnictide

Iron pnictide superconductors and their parent compounds exhibit superconductivity, antiferromagnetism, poor conductivity in undoped phase, structural instabilities, and additional peculiarities. Much of the complexity originates from strong interactions among the spin, charge, lattice degrees of freedom, where correlated excitations and self-organization among them occur and cause exotic cooperative behaviors. Time-resolved magneto-optical spectroscopy has been developed as a power tool to dynamically disentangle various degrees of freedoms by exploring their responses to fs photoexcitation. Using femtosecond optical and magneto-optical technique, we were able to measure and decoupling dynamics of AFM, structure and electronic excitations in parent BaFe$_{2}$As$_{2}$ and also underdoped sample (Co=4.7{\%}). The technique demonstrated provides an extremely powerful tool to reveal fs dynamics and critical behaviors of various order parameters in the iron pnictide system.   

Session Q23: Superconductivty Theory III: Mainly Cuprates

Grand-canonical variational study for the Gutzwiller-projected BCS wave function

We study the Gutzwiller-projected BCS wave function in the 2D extended t-J model using a variational Monte Carlo method. To take into account the effect of Gutzwiller projection, a fugacity factor proposed by Laughlin and Anderson has been included into the coherence factor of the BCS state. We show that the ground-state energy and excitation spectra calculated in the grand-canonical picture are essentially the same as previous results in the canonical scheme if the free energy is used for minimization. Except for La-214 materials, we find that the doping dependence of chemical potential is consistent with experimental findings on several cuprates. We have investigated the asymmetry of tunneling conductance observed by scanning tunneling spectroscopy becomes much stronger as decreasing doping. A very huge enhancement of phase fluctuation in the underdoped regime has been found.   

Fluctuating Bond Model of cuprate superconductivity.

The fluctuating bond model(FBM),an empirical model based on a strong,local coupling of electrons to the square of the planar oxygen vibrator amplitudes, provides explainations of the d-wave pairing mechanism\footnote{Nature phys. 3, 184-191 (2007)} and the pseudogap\footnote{Phys. Rev. B 83, 144503 (2011)} of cuprate superconductivity. The d-wave pairing is mediated by the anharmonic phonon (planar oxygen vibrator) which is also responsible for the pseudogap when the C4 symmetry of the oxygen vibrator is broken. Here we present calculations of gap and T{\_}c in a unitary framework involving pseudogap as a competing order parameter, with the help of ab initio simulations.   

d-wave superconductivity from correlated hopping interactions determined by angle-resolved photoemission spectroscopy

Starting from a generalized Hubbard model, in which correlated-hopping interactions are considered in addition to the on-site repulsive Coulomb one, we solve numerically two coupled integral equations [1] within the Bardeen-Cooper-Schrieffer formalism, in order to quantify the doping effects on the critical temperature ($T_{c})$, $d$-wave superconducting gap, and the electronic specific heat. Within the mean-field approximation, we have determined the single and correlated electron hopping parameters for La$_{2-x}$Sr$_{x}$CuO$_{4}$ compound by using angle-resolved photoemission spectroscopy (ARPES) data [2]. The resulting parametrized Hubbard model is able to explain the experimental $T_{c}$ variation as a function of the doping level ($x)$. In addition, the observed power-law behavior of the superconducting specific heat is reproduced by this correlated-hopping Hubbard model without adjustable parameters. [1] L.A. P\'{e}rez, J.S. Mill\'{a}n, C. Wang, \textit{Int. J. Mod. Phys. B} \textbf{24}, 5229-5239 (2010). [2] T. Yoshida, \textit{et al}., \textit{Phys. Rev. B} \textbf{74,} 224510 (2006).   

Role of the charge reservoir layer in cuprate superconductors

The high pressure measurements of Jorgensen et al., which show that T$_c$ increases as the apical oxygen distance from the CuO$_2$ plane decreases, is at odds with current theoretical predictions of T$_c$. Furthermore, the unusually close T$_c$ (and similar NMR signatures) of Hg and Tl based families of cuprates, in addition to the facts that their T$_c$ is significantly higher than superconductors without charge reservoir layers (CRLs), suggest that CRLs play a significant role in determining T$_c$. Based on recent studies of S. Raghu et al. on the effects of longer ranged interactions on unconventional superconductivity, we discuss the possibility of the generic role that the CRLs may have in enhancing T$_c$ by considering their role in screening short-range repulsive Coulomb interactions within the CuO$_2$ plane.   

Phase separation instabilities and pairing modulations in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$

There is a growing evidence that the unconventional spatial inhomogeneities accompanied with the pairing of electrons, subsequent quantum phase transitions (QPTs), and condensation control coherent states in doped high-Tc cuprate superconductors, iron pnictide and telluride materials. We show that these superconducting states can be obtained from the phase separation instabilities near the quantum critical points. We examine electron coherent and incoherent pairing instabilities using our results on exact diagonalization in pyramidal and octahedron Hubbard-like clusters under variation of chemical potential (or doping), interaction strength, temperature and magnetic field. We also evaluate the dependence of the energy gap function in the vicinity of the sign change (nodes) as a function of position of the apical oxygen atom, due to vibration of apical atom and variation of inter-site coupling. The developed approach provides a simple microscopic explanation of (correlation) supermodulation of the coherent pairing gap observed recently in the scanning tunneling microscopy experiments at atomic scale in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$.   

Pairing Correlations in the two-layer attractive Hubbard Model

Quantum Monte Carlo (QMC) is used to study pairing correlations in a two-layer Hubbard Model in which one layer is attractive ($U<0$), and the other uncorrelated ($U=0$). We provide a detailed characterization of how superconductivity in the $U<0$ layer induces pairing in the $U=0$ layer, as a function of the interlayer hopping, density, temperature, and on-site attraction strength in the $U<0$ layer. QMC data are complemented by calculations within the Bogoliubov - de Gennes approximation.   

Pair-Density-Wave Superconducting Order in Two-Leg Ladders

We show, using bosonization and Renormalization Group methods, that Pair Density Wave (PDW) state happens in the system of two extended Hubbard-Heisenberg models on two leg ladders. Two different models are discussed in detail. In even legged ladder system we find that PDW state is the dominant instability for certain filling factors and some range of parameters. We show that phase diagram of the spin gap regime is composed of two dual phases: PDW and uniform Superconducting (SC) states. The phase transition between uniform SC and PDW in this model is shown to be in the Ising universality class. The idea has been generalize to the case of other commensurate fillings where we find higher order commensurate PDW states. Then we consider a two leg ladder system with nonzero flux $\Phi$ per plaquette. This system is commensurate for wide range of the electron fillings when $\Phi=\pi$. We show that commensurate PDW and incommensurate CDW are some of the phases present in the phase diagram of this model. We show how formation of PDW order in the ladder embodies the notion of intertwined orders.   

Numerical Investigations of Spontaneous Orbital Currents in the Three-Orbital Hubbard Model

Recent experiments show that the pseudogap regime of the cuprate superconductors could be characterized by a phase where the time-reversal symmetry is spontaneously broken but the translational symmetry remains intact. One possible but still highly disputed theory involves a circulating current looping around the Cu and O atoms. To address this issue, we perform large-scale exact diagonalization using a three-orbital Hubbard model on a Cu8O16 cluster. We find that the current-current correlations fall off quickly and show no signs of particular orbital current patterns. We also extend our calculations by adding explicitly a perturbative orbital current term into the Hamiltonian to study its experimental consequences. Using the magnetic moment measured in neutron scattering to constrain the strength of this perturbation, we compute the dichroic signals of various photon-spectroscopies to provide experimental benchmarks to test the existence of such a circulating current phase.   

Momentum-Resolved d-wave Eliashberg Calculation Using The Spin Excitation Spectrum for LSCO Superconductors

We solve the momentum resolved d-wave Elishberg equation employing the magnetic excitation spectrum from the inelastic neutron scattering on the LSCO superconductors reported by Vignolle et al. [1]. The magnetic excitation spectrum exhibits 2 peaks: a sharp incommensurate peak at 18 meV at momentum ($\pi,\pi\pm\delta$) and ($\pi\pm\delta,\pi$), and another broad peak near 40$\sim$70 meV at momentum ($\pi,\pi$). Above 70 meV, the magnetic excitation spectrum has a long tail that is shaped into a circle centered at ($\pi,\pi$) with $\delta '$. The sign of the real part of the total self-energy $\Sigma(\vec{k},\omega)+X(\vec{k},\omega)$ is determined by the momentum position of the peaks of the magnetic excitation spectrum and bare dispersion $\xi(\vec{k})$. We will discuss the effects of the each component of the magnetic excitation spectrum on the self-energy $\Sigma(\vec{k},\omega)$ the renormalization of the band dispersion $X(\vec{k},\omega)$, the pairing function $\phi(\vec{k},\omega)$, and the spectral function $A(\vec{k},\omega)$.\\[4pt] [1] B.Vignolle et.al., Nature Physics 3,163-167 (2007)   

Superconducting Instabilities in Electronic Liquid Crystal Phases

We discuss the superconducting instabilities in a two dimensional fermionic system in uniform electronic liquid crystal phases which cause the Fermi surfaces (FS) to become distorted. We study the case of fermions in a time-reversal broken nematic-like state with $l=3$ in the charge channel, and the $l=2$ state in the spin channel. We discuss the competition between singlet and triplet superconducting states with pair density wave states.   

Odd-frequency triplet pairing in mixed-parity superconductors

We show that mixed-parity superconductors may exhibit equal-spin pair correlations that are odd-in-time and can be tuned by means of an applied field. The direction and the amplitude of the pair correlator in the spin space turn out to be strongly dependent on the symmetry of the order parameter, and thus provide a tool to identify different types of singlet-triplet mixed configurations. We suggest that odd-in-time spin-polarized pair correlations can be generated without magnetic inhomogeneities in superconducting/ferromagnetic hybrids with non-centrosymmetric superconductor or when parity mixing is induced at the interface. Paola Gentile, Canio Noce, Alfonso Romano, Gaetano Annunziata, Jacob Linder, Mario Cuoco, arXiv:1109.4885   

Common Fermi-liquid origin of T2 resistivity and superconductivity in n-type SrTiO3

SrTiO3 is a semiconductor which, when doped with a low density of electrons, becomes a good conductor with relatively high mobility and strong temperature dependence of the electrical resistivity and the infrared optical conductivity. At low temperatures the material becomes superconducting with a maximum reported Tc below 1 K with a dome-shaped doping dependence of Tc, both in the 3D bulk material and at the 2D LaAlO3/SrTiO3 interface. The DC resistivity below 100 K has a T$^2$ temperature dependence. The quasiparticles are in the anti-adiabatic limit with respect to electron-phonon interaction, which renders the interaction mediated through phonons effectively non-retarded. We apply Fermi-liquid theory for the T$^2$ term in the resistivity, and combine this with expressions for Tc and with the Brinkman-Platzman-Rice (BPR) sum-rule to obtain Landau parameters of n-type SrTiO3. These parameters are comparable to those of liquid 3He, indicating interesting parallels between these Fermi-liquids despite the differences between the composite fermions from which they are formed.   

Time Reversal Invariant Topological Superconductor in Rashba System

Recently, topological superconductors (TSCs) have been intensively studied as one of the topologically nontrivial phases. TSCs are characterized by topological numbers classified by their symmetries and dimensions. In the previous proposals on TSCs in Rashba systems, Zeeman splitting is necessary and therefore time reversal symmetry (TRS) is broken. We consider instead a bilayer Rashba system, e.g., a two-interface system, where hybridization causes a band gap. As for the single layer case, it has been shown experimentally that at the interface of SrTiO$_{3}$/LaAlO$_{3}$, two dimensional electron gas with Rashba spin-orbit interaction and superconductivity is formed. We find that the hybridization in bilayer system leads to topological phase without breaking TRS. This system belongs to the class characterized by Z$_{2}$ index. We obtain the conditions for odd-parity pair potentials by analyzing relations between strength of interactions and types of pair potentials. TSCs are attained in the case when the system has an odd-parity pair potential and the Fermi energy lies in the hybridization gap. We analytically calculate a topological number in a bulk system, and explicitly confirm the bulk-edge correspondence by performing numerical calculation in a finite system with edges.   

Pairing Theories in Very High Magnetic Fields: Effects of Condensed and Non-condensed Pairs

In this talk we focus on the interplay of pseudogap effects with high magnetic fields. Our work is built on reformulating the Gor'kov equations in the non-linear regime into a Landau level basis. Here we explore two distinct fermionic pairing schemes associated with the Abrikosov lattice in real and reciprocal space. We show how both have antecedents in the literature and both can be extended to accommodate non-condensed pairs. With this formulation, we can calculate quantities including the local density of states and $H_{c2}$ in this regime. Importantly, both pairing theories yield gapless excitations which should be relevant to cuprate magneto-oscillatory experiments. The additional implications for the high field diamagnetic susceptibility are discussed.   

Quantum oscillations in vortex-liquids

Motivated by observations of quantum oscillations in underdoped cuprates [1], we examine the electronic density of states (DOS) in a {\em vortex-liquid} state, where long-range phase coherence is destroyed by an external magnetic field $H$ but the local pairing amplitude survives. We note that this regime is distinct from that studied in most of the recent theories, which have focused on either a Fermi liquid with a competing order parameter or on a d-wave vortex lattice. The cuprate experiments are very likely in a resistive vortex-liquid state. We generalize the $s$-wave analysis of Maki and Stephen [2] to $d$-wave pairing and examine various regimes of the chemical potential, gap and field. We find that the $(1/H)$ oscillations of the DOS at the chemical potential in a $d$-wave vortex-liquid are much more robust, i.e., have a reduced damping, compared to the $s$-wave case. We critically investigate the conventional wisdom relating the observed frequency to the area of an underlying Fermi surface. We also show that the oscillations in the DOS cross over to a $\sqrt{H}$ behavior in the low field limit, in agreement with the recent specific heat measurements. [1] L.~Taillefer, J.~Phys.~Cond.~Mat.~{\bf 21}, 164212 (2009). [2] M.~J.~Stephen, Phys.~Rev.~B {\bf 45}, 5481 (1992).   

Session Q24: Fractional Quantum Hall Effect II

Fractional Quantum Hall Effect of Rydberg-Polaritons

Dark-state-polaritons (DSP) are bosonic quasiparticles arising in the interaction of light with 3-level atoms under conditions of electromagnetically induced transparency (EIT). They can be exposed to artificial magnetic fields, strong enough to enter the lowest Landau level regime [Otterbach et. al., Phys. Rev. Lett. 104 (2010)]. We take into account interactions between the DSPs via Rydberg dipole-dipole interactions and discuss the realization of the $\nu=1/2$-Laughlin state and its anyonic excitations (quasiholes) in such systems. The DSPs can be prepared in the correct total angular-momentum subspace by using orbital angular momentum light beams. A numerical and semi-analytical evaluation of the quasihole-gap is presented.   

Compressible and incompressible phases in lattice fractional quantum Hall systems

We study lattice fractional quantum Hall (FQH) systems in the presence of local potential traps using the exact diagonalization technique. By implementing an array of local potential traps, we show that the system undergoes a series of phase transitions. As the strength of potential traps is increased, the FQH state turns into a compressible metallic state, and then into a topologically trivial insulator. We present the phase diagram as well as convincing numerical evidences which we use to identify these phases and phase transitions, including the energy spectrum, the fidelity metric, the Chern number, and the entanglement spectrum. In addition, we also compare the topological trivial insulator observed in our systems with Anderson insulators, which are expected in ordinary fractional quantum Hall systems in 2D electron gases in the presence of strong impurities.   

Tailoring Fabry-Perot Interferometers for Fragile Fractional Quantum Hall States

Depending on the relevance of Coulomb interactions, electronic Fabry-Perot interferometers can exhibit two qualitatively different types of interference, each of which can shed light on the unique physics of quantum Hall systems. Long observed in the integer quantum Hall (IQH) regime, the so-called ``Coulomb-dominated'' interference has only recently been confirmed in the fractional quantum Hall (FQH) regime, where its observation has remained limited to the simplest and most robust FQH states. Building on our recent observation and analysis of this type of interference at several fractional filling factors, we report on interferometer design improvements yielding greater visibility, most notably for weaker FQH states. We find that parameters such as the distance from the gates defining the interferometer to the 2DEG, gate layout, and wafer structure affect the visibility much more in the FQH regime than in the IQH regime. High sensitivity to such parameters is also a characteristic of the second type of interference, believed to arise from a pure Aharonov-Bohm effect, which has been clearly observed only in the IQH regime; we discuss efforts to observe this behavior in the FQH regime.   

Multipartite wavefunctions for the second Landau level FQHE

We study the multipartite wave functions of composite fermions, in which the composite fermions within each partition are correlated differently than those across partitions. These include the Pfaffian wave function at 5/2 and the Rezayi-Read wave function at 13/5. Neutral and charged excitations of this state are modeled as neutral and charged excitations created in the individual partitions. We investigate how accurate these wave functions are for certain model three and four body interactions, and whether they are adiabatically connected to the Coulomb solutions. In particular, 5/2 state for an odd number of particles, which contains at least one unpaired composite fermion, will be considered. We also test how multiple degeneracy arises in this model for quasiparticles and quasiholes.   

Excitons in FQH states

Fractional quantum Hall (FQH) states are the first experimentally realized systems that exhibit topological order. For a full understanding of these systems it is crucial to be able to describe not only their ground states and quasihole excitations, but in fact the full low-energy sector. The lowest energy excitations are believed to be neutral quasihole-quasielectron pairs. We present a description of these excitations for a wide range of FQH states. Our method allows us to variationally change the model states without changing any of their topological properties.   

Geometrical Description of fractional quantum Hall quasiparticles

We examine a description of fractional quantum Hall quasiparticles and quasiholes suggested by a recent geometrical approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, where the local excess electric charge density in the incompressible state is given by a topologically-quantized ``guiding-center spin'' times the Gaussian curvature of a ``guiding-center metric tensor'' that characterizes the local shape of the correlation hole around electrons in the fluid. We use a phenomenological energy function with two ingredients: the shear distortion energy of area-preserving distortions of the fluid, and a local (short-range) approximation to the Coulomb energy of the fluctuation of charge density associated with the Gaussian curvature. Quasiparticles and quasiholes of the 1/3 Laughlin state are modeled as ``punctures'' in the incompressible fluid which then relax by geometric distortion which generates Gaussian curvature, giving rise to the charge-density profile around the topological excitation.   

Model wavefunctions for fractional quantum Hall collective modes

We examine the collective modes of primary fractional quantum Hall states which can be represented by Jack polynomial wavefunctions, in particular the $\nu$ = 1/3 Laughlin and the $\nu$ = 1/2 (or 5/2) Moore-Read states. Using the extension of Jack Polynomial states (B. A. Bernevig and F. D. M. Haldane, Phys. Rev. Lett. 102, 066802 (2009)) to describe states with excited quasiparticles as well as quasiholes, we model the collective mode as a dipole formed by the combination of a single elementary quasiparticle with a single quasihole. In the Laughlin case, this neutral collective excitation is bosonic, while in the Moore-Read case, it has two forms, one bosonic and one fermionic. For small electric dipole moment (also small momentum and wavenumber) the (variational) energy of this mode lies above the threshold of the continuum of roton-pair (Laughlin) or neutral-fermion-pair (Moore-Read) excitations. In the long-wavelength limit the bosonic mode is a ``spin-2'' excitation that has an analogy to the ``graviton'' suggested by a recent geometric approach (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)) to FQH systems, while the neutral fermionic mode (present if the ``odd-denominator rule'' is violated) has ``spin-3/2'', and has a possible analogy to the ``gravitino''.   

Determination of counter-propagating edge modes in the $\nu$ = 5/2 fractional quantum Hall state

Determining the wavefunction that describes the fractional quantum Hall state at $\nu$ = 5/2 remains an unresolved question. Two main candidates are the Pfaffian and anti-Pfaffian states. A major difference between the two is the chirality of their neutral Majorana fermion modes, which in the former run parallel to the charged modes and in the latter, anti-parallel. We consider the recent experiment [Bid, A., et al. Nature, 466, 585-590 (2010)], in which counter-propagating, neutral edge modes in the $\nu$ = 5/2 state were detected as a change in shot noise at an inter-edge quantum point contact (QPC) when current was injected at a point downstream of the QPC. We present a theoretical description of this experiment. We model the injection by coupling one edge to an external field and determine that the change in noise is incompatible with a parallel-propagating neutral mode. We also consider the injection as heat transfer to the neutral mode and reach the same conclusion. In agreement with experiment, these results are strong evidence in favor of any state with counter-propagating edge modes, such as the anti-Pfaffian, as a model for the $\nu$ =5/2 state.   

Geometry of the fractional quantum Hall effect

Unlike the integer effect, the incompressible electron fluid that exhibits the fractional effect is {\it not} invariant under ``area-preserving diffeomorphisms'' of the guiding-center degrees of freedom. Instead (F. D. M. Haldane, Phys. Rev. Lett. 108, 116801 (2011)), it has a shear modulus that characterizes the energy cost of distortions of the correlation hole around the electrons, and a ``guiding-center metric tensor'' that exhibits quantum zero-point fluctuations around a preferred shape. In a simple (one-component) fluid, electronic charge-density fluctuations relative to the background set by the magnetic flux density are given by $\delta \rho$ = $(e^*/2\pi)\bar s K$, where $e^*$ is the elementary fractional charge, $\bar s$ is an integer or half-integer ``guiding-center spin'' that is topologically quantized by the Gauss-Bonnet theorem, and $K$ is the local Gaussian curvature of the guiding-center metric. These results provide a simple explanation of the seminal 1985 results of Girvin, MacDonald and Platzman on the FQH structure factor and collective mode, which remained unexplained in previous proposed narrative explanations of FQH incompressibility (Ginzburg-Landau Chern-Simons theory, composite fermions, and non-commutative Chern-Simons field theory).   

Microscopic nature of the backward propagating neutral edge modes of the ``negative'' flux FQHE states

It is believed that FQHE states that require antiparallel vortex attachment, e.g. 2/3, have neutral modes propagating in the backward direction. Recent experiments have observed signatures of such modes. We study the edge excitations of the fully spin polarized as well as spin singlet 2/3 state both from exact diagonalization and from the microscopic composite fermion (CF) theory, to gain insight into the microscopic nature of the neutral edge modes. We investigate the validity of the CF theory for the edge modes, and also study the dependence on the form of the interaction and the background potential. We further evaluate the spectral weights and compare them with the predictions from the effective bosonic description.   

Braiding statistics of the Gaffnian through the coherent state representation

Certain quantum Hall states have trial wave functions that can be connected to non-unitary conformal field theories, and arguments exist implying that such wave functions cannot describe gapped states. For these trial wave functions, the question arises whether braiding statistics may still be well defined through a formal Berry phase calculation. In essence, this corresponds to assuming an artificial gap to ``non-zero modes'' introduced by non-local terms in the Hamiltonian. The presence of long ranged correlations may still foil the emergence of well defined statistics. However, assuming that this is not the case, the question of what such statistics would be, and how they compare to those defined in terms of conformal block monodromies, can be analyzed using a recently developed coherent state Ansatz based on the thin torus limit. We report pertinent results for the Gaffnian state. Time and/or results permitting, we also present developments on the application of this method to a state by Thomale \emph{et al.}, the associated conformal field theory of which is currently unknown. [References: S. Simon \emph{et al.}, Phys. Rev. B 75, 075317 (2007), J. Flavin and A. Seidel, arXiv:1108.2734v1, N. Read, Phys. Rev. B 79, 045308 (2009)]   

Gapless excitations in the Haldane-Rezayi state: The thin-torus limit

We study the thin-torus limit of the Haldane-Rezayi state. Eight of the ten ground states are found to assume a simple product form in this limit, as is known to be the case for many other quantum Hall trial wave functions. The two remaining states have a somewhat unusual thin-torus limit, where a ``broken'' pair of defects forming a singlet is completely delocalized. We derive these limits from the wave functions on the cylinder, and deduce the dominant matrix elements of the thin-torus hollow-core Hamiltonian. We find that there are gapless excitations in the thin-torus limit. This is in agreement with the expectation that local Hamiltonians stabilizing wave functions associated with non-unitary conformal field theories are gapless. We also use the thin-torus analysis to obtain explicit counting formulas for the zero modes of the hollow-core Hamiltonian on the torus, as well as for the parent Hamiltonians of several other paired and related quantum Hall states. [Reference: A. Seidel, K. Yang, PRB 84, 085122 (2011)]   

Dependence of pinning modes of 2D electron system on short-ranged alloy disorder

A 2D electron system (2DES) in a low Landau filling ($\nu )$ pinned Wigner solid state exhibits a striking resonance in its rf or microwave spectrum. The resonance is understood as a pinning mode, in which the electrons oscillate about their pinned positions, and the frequency (f$_{pk})$ increases for larger disorder. We report on microwave spectroscopy of the low-$\nu $ Wigner solids in Al$_{x}$Ga$_{1-x}$As-Al$_{0.1}$Ga$_{0.9}$As heterojunctions with x=0.4 and 0.8{\%}. The 2DES resides mainly in the dilute Al$_{x}$Ga$_{1-x}$As, and the alloy disorder has been shown to be randomly distributed [1]. We compare the pinning modes of the samples as density ($n$, controlled by backgates) and magnetic field are varied. For example, with densities around $n\sim $6.5$\times $10$^{10 }$cm$^{-2}$ (in sample state with no indication of a 1/5 fractional quantum Hall effect) f$_{pk} \approx $ 5.93 and 8.55 GHz at $\nu \sim $0.2 for x=0.4 and 0.8{\%} respectively.\\[4pt] [1] W. Li \textit{et al}., Appl. Phys. Lett., 83, 2832 (2003).   

Local Thermometry of Neutral Modes on the Quantum Hall Edge

A system of electrons in two dimensions and strong magnetic fields can be tuned to create a gapped 2D system with one dimensional channels along the edge. Interactions among these edge modes can lead to independent transport of charge and heat, even in opposite directions. Measuring the chirality and transport properties of these charge and heat modes can reveal otherwise hidden structure in the edge. Here, we heat the outer edge of such a quantum Hall system using a quantum point contact. By placing quantum dots upstream and downstream along the edge of the heater, we can measure both the chemical potential and temperature of that edge to study charge and heat transport, respectively. We find that charge is transported exclusively downstream, but heat can be transported upstream when the edge has additional structure related to fractional quantum Hall physics.   

Real Space Entanglement Spectrum of Fractional Hall States

The entanglement spectrum has been shown by Li and Haldane to provide a reliable tool to detect the topological order of Hall states. For example, bi-partitioning the system in orbital space produces the signature count of Hall edge states. The spectrum, however, appears to bear no resemblance to the linear spectrum conjectured by Kitaev and Preskill analogous to the actual edge mode dispersion. Here we employ two types of cuts: a real space and a modified particle bi-partitioning. On the sphere, we obtain the entanglement spectrum for the Laughlin, Moore-Read and Read-Rezayi states for both. We also consider the filled Landau level with a real space cut and show that the Laughlin state for $\nu$=1/3 has the same count of levels, which agrees with the chiral CFT (for up to $\Delta M=N/2$, $\Delta M=L_{\rm max}-L_z$). Moreover, the entanglement spectrum of the Laughlin state approaches a linear spectrum, similar to the filled Landau level, as the size of the system increases.   

Session Q25: Focus Session: Simulation of Matter at Extreme Conditions - Phase Transitions

Metallization of FeO at High Temperatures and Pressures: DFT-DMFT Computations and Comparisons with Experiments

DFT+Dynamical Mean Field Theory (DMFT) was applied to FeO as a function of pressure and temperature. We use an LAPW basis set, and the lattice terms are evaluated using the WIEN2K LAPW code. The impurity model is solved using continuous time quantum Monte Carlo (CTQMC). Temperature enters explicitly, so we made special efforts to understand high temperature behavior. The computations are fully self-consistent, including the impurity levels and crystal field splitting, and the total energy is evaluated using the full potential and charge density of the lattice plus impurity models. We find with increasing pressure in paramagnetic FeO in a cubic lattice and U=8 eV a high-spin low-spin transition, with a wide transition region between characterized by intermediate occupancies of the t2g and eg states between. We find that at 300K cubic FeO remains insulating to a factor of two compression (over 600 GPa), except for a small region of high spin metal. However, at high temperatures (e.g. 2000K) a metallic state is found. We find excellent agreement with recent high temperature high pressure experiments (Ohta et al.). We are now studying the antiferromagnetic ordering and effects of lattice strain.   

Finite-temperature solid phases and melting of denser lithium

There has been a lot of recent interest in lithium at high pressure, in particular, in relation to deviations from simple metallic behavior, non-intuitive structural changes, and its anomalous melting curve. Most of the theoretical studies have been limited to 0 K static lattices and liquid properties with classical ions. In this talk, we will present results for the stability of lithium up to 250 GPa and finite temperature, as well as its melting curve. Comparison with experimental measurements and the significance of quantum ion dynamics for the observed properties will be discussed.   

Study on the release process of $\gamma $ and $\alpha $ phase transition in cerium material

Cerium has lots of phase transition in high pressure and temperature. A volume change of about 15{\%} occurs when Cerium is subject to high pressure ($\sim $0.7GPa) and $\gamma \to \alpha $ phase change takes place. The phase transition and constitutive model of Cerium can be respectively obtained by calculating the experiment results and taking account of the multi-phase equation of state (EOS). The calculated results indicate that in loading condition the phase transition pressure of Cerium is higher than quasi-static compression. The calculated results indicate that the phase transition under release is difficultly described because the $\alpha \to \gamma $ phase reversal is great influenced by plastic flow. Based on multi-phase equation of state, constitutive model and non-equilibrium phase transition equation, introducing quasi-elastic unloading rule simulated the phase transition under release. The calculated result is according with the experiment.   

Stability of dense liquid carbon dioxide

We have used first-principles molecular dynamics to identify a transition from molecular liquid CO2 to a new polymeric liquid phase under compression. The phase transition is first-order and unlike other such transitions, is not accompanied by metallization. The region near the liquid-liquid-solid triple point is particularly interesting as it coincides with pressure-temperature conditions inside the Earth's mantle. We have characterized the stability of CO2 under these conditions; contrary to previous studies, our calculations show that CO2 does not phase separate into carbon and oxygen. Comparisons with and alternative interpretations of previous measurements will be presented. Routes for experimental detection of our predictions will also be discussed.   

On the stability of body-centered cubic Fe at Earth's core conditions

Elucidation of Earth's core content and structure is extremely important for understanding Earth's behavior influencing human life, from geodynamics to earthquakes. Though cosmochemical and geochemical studies strongly suggest that solid Fe is the main constituent of the inner core, its exact content and crystal structure are still a matter of debate. The recent experiments reported controversial results of phase stability. Dubrovinsky \textit{et al.} showed stabilization of the body centered cubic (bcc) phase of Fe$_{ }$alloyed with 10 at. {\%} of Ni at pressures above 225 GPa and temperatures over 3400 K [1]. Tateno \textit{et al. }on pure Fe at up to 377 GPa and 5700 K, no bcc phase was observed [2]. We offer a resolution of this contradiction based on finite temperature first-principles molecular dynamics calculations of elastic properties of both bcc Fe and Fe$_{90}$Ni$_{10}$ alloy at high-temperature high-pressure conditions. We indicate the stability range for the bcc phase of high-pressure high-temperature Fe and show how experimental conditions may cause diverse phase stabilization. REFERENCES [1] L. S. Dubrovinsky \textit{et al.} Body-centered cubic iron-nickel alloy in Eath's core. \textit{Science} \textbf{316}, 1880-1883 (2007). [2] S. Tateno,K. Hirose, Y. Ohishi, Y. Tatsumi. The structure of iron in Earth's inner core. \textit{Science} \textbf{330}, 359-361 (2010).   

Thermoelastic Properties of Olivine and its High Pressure Polymorphs at High Pressures and Temperatures: A First-Principles Study

We combine density functional theory (DFT) within the local density approximation (LDA), the quasiharmonic approximation (QHA), and a model of vibrational density of states (VDoS) to calculate aggregate elastic moduli and sound velocities of olivine ($\alpha-$phase) (Fe$_x$,Mg$_{1-x}$)$_2$SiO$_4$, and its high pressure polymorphs, wadsleyite ($\beta-$phase) and ringwoodite ($\gamma-$phase), the most abundant minerals of the Earth's upper mantle (UM) and transition zone (TZ). Comparison of results with high-pressure and room-temperature data and ambient-pressure and high-temperature data shows very good agreement. Using our findings, we investigate the discontinuities in elastic moduli and velocities associated with the $\alpha$ to $\beta$ and $\beta$ to $\gamma$ transformations at pressures and temperatures relevant to seismic discontinuities near 410 km and 520 km depth. This information offers clearly defined reference values to advance understanding of the role that chemical composition and temperature play in these mantle boundary layers.   

Fate of MgSiO3 post-perovskite at multi-Mbar pressures

The discovery of the post-perovskite (PPV) transition of MgSiO$_{3}$ in 2004 invited a new question: What would be the next phase transition from the PPV phase? The importance of this question has increased, since many terrestrial exoplanets with masses of a few to 10 times Earth's (super-Earth) have been recently discovered. Here we predict the new class of phase transitions of MgSiO$_{3}$ PPV under ultrahigh pressure by first-principles calculations combined with the adaptive genetic algorithm, which is a powerful tool for blind structural searches for systems with the large number of atoms. We discuss implications of these new phase transitions in modeling of interiors of terrestrial exoplanets.   

Raman study of the Verwey transition in Magnetite at high-pressure and low-temperature; effect of Al doping

We report high-pressure low-temperature Raman measurements of the Verwey transition in pure and Al --doped magnetite (Fe$_{3}$O$_{4})$ Al-doped magnetite Fe$_{2.8}$Al$_{0.2}$O$_{4}$ (T$_{V}$=116.5K) displays a nearly linear decrease of the transition temperature with an increase of pressure yielding dP/dT$_{V}$=-0.096$\pm $0.013 GPa/K. In contrast pure magnetite displays a significantly steeper slope of the PT equilibrium line with dP/dT$_{V}$ = -0.18$\pm $0.013 GPa/K. Contrary to earlier high pressure resistivity reports we do not observe quantum critical point behavior at 8 GPa in the pure magnetite. Our data indicates that Al doping leads to a smaller entropy change and larger volume expansion at the transition. The trends displayed by the data are consistent with the mean field model of the transition that assumes charge ordering in magnetite.   

Magnetic and Thermal Fluctuations in Fe and (Fe,Ni) alloys at Earth Core Conditions

Several lines of evidence suggest that the earth's inner core is dominated by an iron rich (Fe,Ni) alloy. In this study we address the influence of magnetic and thermal fluctuations as driving forces for phase transitions in Fe and Fe$_{7}$Ni structures at inner core pressure and temperature conditions. Bcc iron is stable at ambient conditions due to its ferromagnetic nature which highlights the importance of magnetism for structural stability. \textit{Ab-initio} electronic structure calculations are used to study the thermal and magnetic fluctuations in Fe and (Fe,Ni) alloys up to pressures and temperatures expected in the earth's inner core. The variable cell shape molecular-dynamics simulations include the magnetic moment and thermal fluctuations. Our preliminary results show a phase transformation in hcp-Fe$_{7}$Ni alloy that occurs after 2.5 ps, well after equilibration. The correlation of magnetic and thermal fluctuations suggests that the residual magnetism is too weak to induce the observed transition. Instead, large thermal fluctuations at the onset of the transition provide a likely driving force.   

Mechanism of body-centered cubic phase stabilization in Fe and He at high pressure and temperature

We have investigated the stabilization of the body-centered cubic phase in Fe and He at high P and T by means of ab initio and classical molecular dynamics. These phases are dynamically unstable at high P and low T, however, they become dynamically stable at high T. We calculated the phonon density of states for Fe and He phases and observed that the bcc PDOS contains long-wavelength phonon states (absent in the close packed phases) that contribute to the free energy. This observation is consistent with the mechanism of stabilization proposed earlier (P. Loubeyre, J.-P. Hansen, PRB 31, 634 (1985); B. L. Holian et al., JCP 59, 5444 (1973)). Direct ab initio simulations of Fe crystallization and classical co-existence simulations for He indicate that the bcc phase is a submelting phase at high P. Previous calculations of the free energy in the bcc phase have been performed on small samples and could not adequately take the long-wavelength correlated motion into account.   

Computation of free energy of liquids and its application to melting of CO$_2$ and N

A computationally efficient method is proposed to compute the free energy of liquids with accuracy comparable to {\it ab initio} thermodynamic integration. The method has been applied to predict melting curves of CO$_2$ and N over a wide range of pressure using the solid-liquid phase coexistence approach. The calculated melting lines are compared with available experimental data and the crossing of the geotherm and melting line of CO$_2$ is determined.   

Melting behaviour of high pressure Na. An ab initio study

The melting curve of sodium for a pressure range up to 120 GPa has been evaluated by the orbital free ab initio molecular dynamics method. This method uses the electronic density as the basic variable and scales almost linearly with system size which allows to perform simulations with a large number of particles and for long simulation times. For various pressures and temperatures we have calculated some static properties (pair distribution functions, static structure factors and short-range order parameters), dynamic properties (mean square displacement, velocity autocorrelation functions and dynamic structure factors) and transport coefficients (self-diffusion, adiabatic sound velocities and shear viscosities). The calculated melting curve reproduces the main qualitative features found in the experiment.   

Session Q26: Focus Session: Computational Frontiers in Quantum Spin Systems I

Computing Entanglement Entropy in Quantum Monte Carlo

The scaling of entanglement entropy in quantum many-body wavefunctions is expected to be a fruitful resource for studying quantum phases and phase transitions in condensed matter. However, until the recent development of estimators for Renyi entropy in quantum Monte Carlo (QMC), we have been in the dark about the behaviour of entanglement in all but the simplest two-dimensional models. In this talk, I will outline the measurement techniques that allow access to the Renyi entropies in several different QMC methodologies. I will then discuss recent simulation results demonstrating the richness of entanglement scaling in 2D, including: the prevalence of the ``area law''; topological entanglement entropy in a gapped spin liquid; anomalous subleading logarithmic terms due to Goldstone modes; universal scaling at critical points; and examples of emergent conformal-like scaling in several gapless wavefunctions. Finally, I will explore the idea that ``long range entanglement'' may complement the notion of ``long range order'' for quantum phases and phase transitions which lack a conventional order parameter description.   

Scaling of entanglement entropy in the 2D Heisenberg ground state

We use a Loop-Ratio Valence Bond quantum Monte Carlo algorithm to study the scaling of the bipartite Renyi entanglement entropy in the 2D Heisenberg ground state. We uncover the surprising result that finite-size scaling supports a logarithmic correction to the entropic area law even with the absence of corners in the entangled region. In addition, examining the scaling within a single system, we observe an aspect-ratio dependent scaling term resembling the ``conformal distance'' term that appears in one-dimensional systems with conformal symmetry.   

Entanglement scaling of the 2D RVB wavefunction

The resonating valence bond (RVB) state on a two-dimensional lattice is a superposition of all permutations of singlet spin pairs. This wavefunction was first proposed by Anderson as a simple spin liquid ground state, showing no long range order at T=0. Using a loop-algorithm Monte Carlo method that samples all nearest-neighbor singlet pairs, we examine the entanglement entropy of the nearest neighbor SU(2) RVB wavefunction on the square lattice. In addition to the area law, we show that the entanglement entropy splits into two branches, due to the different topological sectors of the RVB wavefunction. These branches individually scale with a logarithmic dependence on the size of the entangled region, the functional form of which appears to be similar to the conformal distance observed in scaling at conformal critical points in 1D. We comment on the implication for the search for topological order, and on generalizations of this wavefunction, including models involving SU(N) spins.   

Entanglement entropy at the quantum critical point of the 2D transverse field Ising model

Entanglement entropy is a quantity that is desirable to examine at quantum critical points in condensed matter systems, because it is expected that sub-leading scaling terms should contain universal coefficients. In dimensions higher than one, these universal coefficients (that are sub-leading to the area law) may possibly be used to identify the universality class of the quantum critical point, much like the central charge in 1D systems. The recent development of zero temperature projector methods for the transverse field Ising model in combination with replica methods for stochastic series expansion quantum Monte Carlo (QMC) allows us to examine this idea, using measurements of Renyi entanglement entropies. We compare zero- and finite- temperature QMC results with series expansion, and discuss the scaling of the Renyi entropies at the 2D critical point in the transverse field Ising model.   

Finite entanglement scaling at novel phase transitions in the Bose-Hubbard model with pairing terms

With the introduction of pair hopping, the 1+1D Bose-Hubbard model contains string like defects and half vortices in addition to the familiar vortices that drive the Kosterlitz - Thouless (KT) transition. Recent work [1] proposed the existence of a novel phase transition directly from the insulating to superfluid phase which is partly of an Ising, rather than KT type, contrary to expectations based on symmetry. To characterize the transition we demonstrate an approach to the study of 1+1D critical phenomena using infinite matrix product state algorithms (iMPS), in which critical fluctuations are cut off not by a finite system size, but by the finite entanglement of the iMPS ansatz. Starting from the ``finite entanglement'' scaling of the correlation length [2], we show that scaling and correlation functions also admit a universal ``finite entanglement'' collapse, avoiding boundary effects and validating an elegant alternative to finite size scaling methods for critical phases. \\[4pt] [1] Shi, Lamacraft and Fendley, arxiv:1108.5744v1\\[0pt] [2] Pollmann, Mukerjee, Turner and Moore, Phys. Rev. Lett. 102, 255701 (2009)   

Renormalization of tensor-network states

We have discussed the tensor-network representation of classical statistical or interacting quantum lattice models, and given a comprehensive introduction to the numerical methods we recently proposed for studying the tensor-network states/models in two dimensions. A second renormalization scheme is introduced to take into account the environment contribution in the calculation of the partition function of classical tensor network models or the expectation values of quantum tensor network states. It improves significantly the accuracy of the coarse grained tensor renormalization group method. In the study of the quantum tensor-network states, we point out that the renormalization effect of the environment can be efficiently and accurately described by the bond vector. This, combined with the imaginary time evolution of the wave function, provides an accurate projection method to determine the tensor-network wave function. It reduces significantly the truncation error and enables a tensor-network state with a large bond dimension, which is difficult to be accessed by other methods, to be accurately determined.   

Cluster update for tensor network states

We propose a novel recursive way of updating the tensors in projected entangled pair states by evolving the tensor in imaginary time evolution on clusters of different sizes. This generalizes the so-called simple update method of Jiang et al. [Phys. Rev. Lett. 101, 090603 (2008)] and the updating schemes in the single layer picture of Pizorn et al. [Phys. Rev. A 83, 052321 (2011)]. A finite-size scaling of the observables as a function of the cluster size provides a remarkable improvement in the accuracy as compared to the simple update scheme. We benchmark our results on the hand of the spin 1/2 staggered dimerized antiferromagnetic model on the square lattice, and accurate results for the magnetization and the critical exponents are determined. Reference L. Wang and F. Verstraete, arXiv:1110.4362.   

The spin 1/2 J1-J2 Antiferromagnetic Heisenberg model on Square Lattice

We studied the spin 1/2 J1-J2 Heisenberg antiferromagnets on square lattice using the recently proposed cluster update for tensor network states [arXiv:1110.4362]. Ground state wavefunction with tensor network bond dimension upto $D=9$ was obtained. Through a finite size scaling analysis, we observe a second order phase transition from an antiferromagnetic ordered state to a paramagnetic phase with plaquette valence bond order at a coupling constant ratio J2/J1~ 0.44. The ground state energies in the thermodynamic limit are in the order of 10$^{-3}$J1 per site difference from the state of art exact diagonalization study [Eur. Phys. J. B 73, 117 (2010)].   

The spin-$1/2$ $J_1-J_2$ Heisenberg antiferromagnet on a square lattice:a plaquette renormalized tensor network study

We apply the plaquette renormalization scheme of tensor network states [Phys. Rev. E, \textbf{83}, 056703 (2011)] to study the spin-1/2 frustrated Heisenberg ${J}_{1}$-${J}_{2}$ model on an $L\times L$ square lattice with $L$=8,16 and 32. By treating tensor elements as variational parameters, we obtain the ground states for different $J_2/J_1$ values, and investigate staggered magnetizations, nearest-neighbor spin-spin correlations and plaquette order parameters. In addition to the well-known N\'{e}el-order and collinear-order at low and high ${J}_2/{J}_1$, we observe a plaquette-like order at ${J}_2/J_1\approx 0.5$. A continuous transition between the N\'{e}el order and the plaquette-like order near $J_2^{c_1}\approx 0.40 J_1$ is observed. The collinear order emerges at ${J}_2^{c_2} \approx 0.62J_1$ through a first-order phase transition.   

MERA Study of Spatially Anisotropic Triangular Antiferromagnets

We report variational calculations for the ground states in the spatially anisotropic triangular antiferromagnets. The variational wave function is based on the tensor network with an entanglement renormalization [1]. The entanglement renormalization improves the ability of describing a quantum state. We construct a three-dimensional MERA tensor network for the triangular lattice models. The model in this study has two groups of the antiferromagnetic Heisenberg couplings on a triangular lattice: one on links along a lattice axis and the other on other links. $J_1$ and $J_2$ denote the coefficient of their couplings, respectively. We calculate the ground states of finite lattices ($N=114, 2166$) and an infinite lattice. We confirm a magnetic phase in the region of $0.7 < J_2/J_1 \le 1$. The magnetic structure is incommensurate, and the wave vector is not consistent with that of a classical model except for $J_1=J_2$.\\[4pt] [1] G. Vidal, Phys. Rev. Lett. 99, 220405 (2007).   

General framework of non-Abelian SU(N) symmetries for matrix product states

We present a generic numerical framework for the treatment of an arbitrary set of non-abelian quantum symmetries within the matrix product states (MPS) approach and generalization thereof. The framework is based on the simple observation that Clebsch Gordan coefficient spaces can be split off as tensor products for all objects relevant within MPS [1]. As such it is applicable, for example, to the numerical as well as the density matrix renormalization group (NRG or DMRG, respectively). The framework is applied to a generalized SU(3) channel-symmetric Anderson impurity model within the NRG. This model of a fully screened spin $S=\frac{3}{2}$ Anderson model has been suggested recently as the effective microscopic Kondo model for Fe impurities in gold or silver [2]. Results are presented on the explicit treatment of U(1)$\otimes$SU(2)$\otimes$SU(3) for charge, spin, and channel, respectively. This is compared to the alternative description in terms of SU(2)$^{\otimes4}$ symmetries for total spin and particle-hole symmetry in every channel. \\[1ex] [1] Singh et al, PRA {\bf 82}, 050301 (2010) \\{} [2] Costi et al, PRL {\bf 102}, 056802 (2009).   

Reducing Memory Cost of Exact Diagonalization using Singular Value Decomposition

We present a modified Lanczos algorithm to diagonalize lattice Hamiltonians with dramatically reduced memory requirements. In contrast to variational approaches and most implementations of DMRG, Lanczos rotations towards the ground state do not involve incremental minimizations, (e.g. sweeping procedures) which may get stuck in false local minima. The lattice of size N is partitioned into two subclusters. At each iteration the rotating Lanczos vector is compressed into two sets of $n_{{\rm svd}}$ small subcluster vectors using singular value decomposition. For low entanglement entropy $S_{ee}$, (satisfied by short range Hamiltonians), the truncation error is bounded by $\exp(-n_{{\rm svd}}^{1/S_{ee}})$. Convergence is tested for the Heisenberg model on Kagom\'e clusters of 24, 30 and 36 sites, with no lattice symmetries exploited, using less than 15GB of dynamical memory. Generalization of the Lanczos-SVD algorithm to multiple partitioning is discussed, and comparisons to other techniques are given. Reference: arXiv:1105.0007   

An efficient basis for the modeling of doped and undoped S=1/2 antiferromagnet

We formulate an efficient numerical basis to model both doped and undoped S=$\frac{1}{2}$ Heisenberg antiferromagnet (AFM) with two-dimensional periodic boundary condition (2DPBC). Using a linear combination of Slater determinants with total-spin symmetries, a variational approach is developed to systematically and combinatorially decreases the Hilbert space of the problems, allowing the application of exact diagonalization to record-breaking system sizes. We can now model explicitly the wavefunction of an undoped 64-spin AFM square lattice with 2DPBC. For the doped scenarios, we solve a half-filled lattice with 32 coppers and 64 oxygens with one or two electrons removed. This allows, for the first time, a direct comparison of 32-unit-cell exact diagonalization between multi-band model and the t-J model, quantifying several oxygen-specific properties relevant to the lightly doped cuprate structures.   

Session Q27: Invited Session: DCMP Prize Session: Buckley, Isakson, MGM

Oliver E. Buckley Condensed Matter Prize Lecture: Topological Insulators

A topological insulator is a material that is an insulator on its interior, but has special conducting states on its surface. These surface states are unlike any other known two dimensional conductor. They are characterized by a unique Dirac type dispersion relation and are protected by a topological property of the material's underlying electronic band structure. In this talk we will outline our path to the theoretical discovery of this phase and describe the physical properties of the two dimensional topological insulator - also known as a quantum spin Hall insulator - as well as its three dimensional generalization. We will then go on to discuss more recent developments, including the topological classification of point and line defects in topological insulators and superconductors. The latter may provide a venue for observing Majorana fermion states and for realizing proposals for topological quantum computation.   

HgTe as a Topological Insulator

HgTe is a zincblende-type semiconductor with an inverted band structure. While the bulk material is a semimetal, lowering the crystalline symmetry opens up a gap, turning the compound into a topological insulator. The most straightforward way to do so is by growing a quantum well with (Hg,Cd)Te barriers. Such structures exhibit the quantum spin Hall effect, where a pair of spin polarized helical edge channels develops when the bulk of the material is insulating. Our transport data provide very direct evidence for the existence of this third quantum Hall effect, which now is seen as the prime manifestation of a 2-dimensional topological insulator. To turn the material into a 3-dimensional topological insulator, we utilize growth induced strain in relatively thick (ca. 100 nm) HgTe epitaxial layers. The high electronic quality of such layers allows a direct observation of the quantum transport properties of the 2-dimensional topological surface states.   

Oliver E. Buckley Condensed Matter Prize Lecture: Topological insulators and superconductors

In this talk I shall briefly review the basic concepts of topological insulators and superconductors, and recall the history of the discovery of the first topological insulator in nature, the HgTe material. I will then describe some striking physical properties of topological insulators and their possible applications. \\[4pt] X. L. Qi, S. C. Zhang, Phys. Today 63, 33 (2010). \newline X. L. Qi, S. C. Zhang, Rev. Mod. Phys. 83, 1057 (2011).   

Frank Isakson Prize for Optical Effects in Solids Lecture: Infrared nano-spectroscopy and nano-imaging of Dirac plasmons in graphene

We have applied antenna-based infrared (IR) nano-spectroscopy and nano-imaging to investigate Dirac plasmons in monolayer graphene. This experimental technique enables IR imaging with nano-scale spatial resolution, and also allows one to investigate electromagnetic phenomena at wave-vectors on the order of the Fermi wave-vector in gated graphene. Nano-spectroscopy and nano-imaging experiments have uncovered rich optical effects associated with the Dirac plasmons of graphene [\textit{Fei et al. Nano Letters 2011}]. We were able to directly image Dirac plasmons propagating over sub-micron distances and reflecting from the edges of graphene flakes, all with a spatial resolution far exceeding the plasmon wavelength. Furthermore, we employed new IR nano-optics capabilities to demonstrate the gate-tunable plasmonic properties of graphene and to investigate the coupling between Dirac plasmons and the phonon modes of polar substrates.   

Maria Goeppert Mayer Award Lecture: Spectroscopy of Hybrid Superconductor-Carbon Nanostructure Systems

The electronic properties of carbon nanotubes and graphene have excited much interest, for both fundamental science and technological applications. In this talk, I will discuss how coupling superconductors to these carbon nanostructures can enable new spectroscopic tools. In particular, I will discuss our experiments demonstrating that superconducting probes on carbon nanotube quantum dots can enhance weak spectroscopic features. I will also show how superconducting tunnel probes enable direct measurements of electron-electron interactions in carbon nanotubes. Finally, I will present data showing that connecting graphene to superconductors allows for the spectroscopy of individual, tunable superconducting (Andreev) bound states.   

Session Q28: Applications of Semiconductors, Dielectrics, Complex Oxides

Anatomy of a Nanoscale Conduction Channel Reveals the Mechanism of a High-Performance Memristor

Two major challenges for resistance memory devices (memristors) based on conductivity changes in oxide materials are better performance and understanding of the microscopic picture of the switching. After researchers' relentless pursuit for years, tantalum oxide-based memristors have rapidly risen to be the top candidate, showing fast speed, high endurance and excellent scalability. While the microscopic picture of these devices remains obscure, by employing a precise method for locating and directly visualizing the conduction channel, here we observed a nanoscale channel consisting of an amorphous Ta(O) solid solution surrounded by crystalline Ta$_{2}$O$_{5}$. Structural and chemical analyses of the channel combined with temperature dependent transport measurements revealed a unique resistance switching mechanism: the modulation of the channel elemental composition, and thus the conductivity, by the cooperative influence of drift, diffusion and thermophoresis, which seem to enable the high switching performance observed. (Miao*, Strachan*, Yang* \textit{et al.}, Advanced Materials. DOI: 10.1002$/$adma201103379 (2011))   

Low-frequency noise properties in nanodiodes

Terahertz (THz) detection by a novel type of unipolar nanodiodes, known as self-switching diodes (SSDs), has recently been demonstrated at room temperature up to 1.5 THz (App. Phys. Lett. Vol. 98, 223501, 2011). Since noise property is also of great importance for THz detection, here we have fabricated thousands of SSDs connected in parallel in order to increase the signal-to-noise ratio. Because of the planar nature of the SSDs, no specific metal interconnects are needed, and hence the device speed and voltage sensitivity are unaffected. We study the low-frequency noise spectra and noise equivalent power (NEP) at room and elevated temperatures. The exceptional possibility for the SSD to have an intrinsic zero threshold voltage enables very low noise at frequencies below 1 kHz, without being much affected by 1/$f $noise. We find that the NEP is comparable to the commercial Schottky diode detector. The activation energy extracted from the temperature dependence is approximately 0.27 eV, which we will compare with the barrier height in the SSD channel as well as the conduction band offset in the InGaAs/InAlAs structure used in this work. We show evidence that the observed 1/$f$ noise properties at room and elevated temperatures seem to support Hooge's mobility fluctuation theory.   

Understanding the resistive switching in thin-film Ta-O memristors by their d.c. switching characteristics

Tantalum oxide (Ta-O) memristor is a promising candidate for resistive switching memory (RRAM) technology as they have demonstrated outstanding features such as high endurance, high speed, and low power. However, the responsible mechanisms remain vague partly due to difficulties in characterizing the amorphous film structure, nanoscale active regions, coupled ionic and electronic transport, and intertwined electrochemical and thermochemical processes. Rich information about Ta-O memristors has been revealed by microscopic structural and chemical characterizations of Ta-O conduction channels combined with temperature-dependent transport measurements. As an alternative approach, we took perspectives from a statistical study of the switching behavior under d.c. excitation. We identified distinctive behaviors in device switching characteristics depending on the chemical compositions of conductance channel, and found close correlations with previous temperature-dependent transport measurements and X-ray photoemission (XPS) characterizations. We were able to gather further insight into the microscopic switching mechanisms based on these observations, revealing the granularity of the switching phenomena.   

\textit{In-situ} MBE and ALD deposited HfO$_{2}$ on In$_{0.53}$Ga$_{0.47}$As

The semiconductor industry is calling for innovative devices offering high performance with low power consumption. High-$\kappa $ dielectrics/metal gates on high carrier mobility channels are now strong contenders in the post Si CMOS application. Hafnium-based oxide has been employed as the gate dielectric in Si CMOS since 45 nm node and InGaAs is a leading candidate for channel materials. However, reports of HfO$_{2}$ on InGaAs are scant, and surface treatments using H$_{2}$S or trimethylaluminum are claimed to be required for achieving high quality HfO$_{2}$(high-$\kappa )$/InGaAs interface. In this work, HfO$_{2}$ has been \textit{in-situ} deposited on $n$- and $p$-In$_{0.53}$Ga$_{0.47}$As using both molecular-beam-epitaxy (MBE) and atomic-layer- deposition (ALD), without using any interfacial passivation layer or surface treatments. The HfO$_{2}$/In$_{0.53}$Ga$_{0.47}$As metal-oxide-semiconductor capacitors (MOSCAPs) all exhibit outstanding thermal stabilities ($>$ 800$^{\circ}$C), low leakage currents ($\sim $ 10$^{-8}$ A/cm$^{2}$ at 1 MV/cm), and good CV characteristics. Moreover, the MOSCAPs have shown spectra of interfacial trap densities (D$_{it}$'s) with no discernible peaks at mid-gap, confirmed by temperature-dependent conductance method.   

\textit{In-situ} photoemission analyses of ALD-oxide/In$_{x}$Ga$_{1-x}$As (001) interfaces

High-$\kappa $ dielectrics on high carrier mobility channels, such as In$_{x}$Ga$_{1-x}$As, are now being considered for CMOS technology beyond 15 nm node. The initial bonding of high-$\kappa $/InGaAs determines the value and the distribution of interfacial density of states (D$_{it})$ within the In$_{x}$Ga$_{1-x}$As band gap, key to the device performance. In this work, atomic layer deposited (ALD) HfO$_{2}$ and Al$_{2}$O$_{3}$ on MBE-grown In$_{x}$Ga$_{1-x}$As (001) have been \textit{in-situ} and \textit{ex-situ} carried out to investigate the initial stage of interfacial reactions by high resolution photoemission spectroscopy using synchrotron radiation and monochromatic Al Ka x-ray sources. Comparing the results with the corresponding electrical measurements (C-V and G-V at various temperatures), Fermi level unpinning in the oxide/In$_{x}$Ga$_{1-x}$As hetero-structure may be attributed to the exclusion of the As-As and the As-O bonding during the initial interfacial formation.   

High Temperature Seebeck Coefficient and Electrical Resistivity of Ge$_{2}$Sb$_{2}$Te$_{5}$ Thin Films

Phase-change memory (PCM) is a promising memory technology in which a small volume of a chalcogenide material can be reversibly and rapidly switched between amorphous and crystalline phases by an electrical pulse that brings it above crystallization ($\sim $ 150-200 C) or melting ($\sim $ 700 C) temperature. The large temperature levels involved and small dimensions of PCM devices give rise to very large temperature gradients ($\sim $ 10 K/nm and higher) which result in strong thermoelectric effects. High-temperature characterization of the temperature-dependent thermoelectric properties of these materials is therefore critical to understand for the operation of these devices but to date there is only limited experimental data available. We have performed simultaneous measurements of Seebeck coefficient and electrical resistance of thin films of GST with different thicknesses, deposited on silicon dioxide, from room temperature to $\sim $ 600 C, under small temperature gradients. Two-point current-voltage (I-V) measurements were performed using a semiconductor parameter analyzer. The resistance of the material and the Seebeck voltage (open-circuit voltage) are calculated from the slope and intercept of the I-V characteristics. The details of the measurements and S(T) and R(T) results for the GST thin film samples will be presented and discussed.   

Thermoelectric Effects in Simulations of Phase Change Memory Mushroom Cells

Phase change memory is a potential candidate for the future of high-speed non-volatile memory, however significant improvements in cell design is crucial for its success in the mainstream market. Due to the asymmetric geometry of phase change mushroom cells and the high temperature gradients generated, thermoelectric effects play a key role in determining energy consumption, cell performance, and reliability. In this study, rotationally symmetric 2D finite element simulations using COMSOL Multiphysics are implemented for GeSbTe (GST). Temperature dependent material parameters (electrical conductivity, thermal conductivity, heat capacity, and Seebeck coefficient) are included in the model for accuracy. Switching the direction of current shows a large change in peak molten volume within the cell, as well as current and power consumption.   

Light-controlled plasmon switching using hybrid metal-semiconductor nanostructures

We show a method for the dynamic control over the plasmon resonance frequencies in a hybrid metal-semiconductor nanoshell structure with silver core and TiO$_{2}$ coating. We temporarily change the dielectric function of TiO$_{2}$ using pump laser pulse operating at bandgap or above. This generates free electron-hole pairs in TiO$_{2 }$that alter the dielectric environment for the silver core. The probed surface plasmon frequency lying below bandgap appears to be blue-shifted due to the altered dielectric environment. We calculate the magnitude of the plasmon resonance wavelength shift as a function of electron-hole pair density and obtain shifts up to 126 nm at wavelengths of around 460 nm. Using these results, we propose a model of a light-controlled surface plasmon polariton (SPP) switch.   

Direct-bandgap infrared light emission from tensilely strained germanium nanomembranes

Silicon, germanium, and related alloys, which provide the leading materials platform of electronics, are extremely inefficient light emitters because of their indirect fundamental energy bandgap. This basic materials property has so far hindered the development of group-IV photonic active devices, including diode lasers, thereby significantly limiting our ability to integrate electronic and photonic functionalities at the chip level. We show that Ge nanomembranes can be used to overcome this materials limitation. Theoretical studies have predicted that tensile strain in Ge lowers the direct energy bandgap relative to the indirect one. We demonstrate [1] that mechanically stressed nanomembranes allow for the introduction of sufficient biaxial tensile strain to transform Ge into a direct-bandgap, efficient light-emitting material that can support population inversion and therefore provide optical gain. \\[4pt] [1] J. R. S\'{a}nchez-P\'{e}rez, C. Boztug, F. Chen, F. Sudradjat, D. M. Paskiewicz, RB. Jacobson, M. G. Lagally, and R. Paiella, PNAS web published Nov, 14, 2011   

A Tunable Terahertz Detector Based On Self Assembled Plasmonic Structure on a GaAs 2DEG

The use of tunable gated gratings on 2DEG structure has been well known methods for compact frequency sensitive THz detection based on the resonant absorption of the 2D Plasmon. The resonant frequency is dependent on system dimension and the tunability of that dimension by depletion gating. Here we attempt to improve detector sensitivity, tunability and remove polarization dependence through the development of a gated grid design. To satisfy the requirement for imaging applications of device dimensions on the order of $<$ 1 micron over a detector area of 4 mm$^{2}$, we have fabricated gated grid plasmonic structure on 2DEG material by using nanosphere self-assembly lithography. This fabrication method has not been widely developed for III-V processing but allows us to achieve large area sensitive detectors with tunability in the 1-4 THz range. In this paper we will discuss the characterization of the devices as a function of gate bias, magnetic field, and temperature using FTIR and THz time domain measurements.   

Time-resolved second harmonic generation study of buried semiconductor heterointerfaces using soliton-induced transparency

The transient second harmonic generation (SHG) and linear optical reflectivity (LOR) signals measured simultaneously in reflection from GaAs/GaSb/InAs and GaAs/GaSb heterostructures revealed a new mechanism for creating self-induced transparency in narrow bandgap semiconductors at low temperatures, which is based on the dual-frequency electro-optic soliton propagation. The mechanism takes account of the photo-Dember field solitary wave, which traps both the fundamental and SHG pulses, slowing their velocity down to that of the solitary wave. The trapped light pulses maintain the amplitude of the solitary wave and hence create a condition, at which the self-reinforcing nonlinear optical polarization (dual-frequency electro-optic soliton) can propagate through the semiconductor. This allows the ultrafast carrier dynamics at buried semiconductor heterointerfaces to be studied.   

Room temperature ballistic transport in InSb quantum well structures

We report significant advancements in InSb/AlInSb quantum well (QW) heterostructures for room temperature nanoelectronic applications. InSb/AlInSb heterostructures have phenomenally high room temperature mobility but display intrinsic parallel conduction in the buffer layer limiting exploitation for nanostructured devices where deep isolation etch processing is impractical. We demonstrate a strategy to reduce the parasitic conduction by the insertion of a pseudomorphic barrier layer of wide-band-gap alloy below the QW.\footnote{A.M. Gilbertson, P.D. Buckle, T. Ashley, L.F. Cohen, Phys Rev B \textbf{84}, 075474 (2011).} Mesoscopic geometric nanocrosses fabricated from such material clearly demonstrate ballistic transport at room temperature, as evidenced by very significant negative bend resistance (NBR). We have studied the interplay between sidewall and bulk scattering at 300K in relation to quantum calculations. DC measurements in the non-equilibrium (hot carrier) regime reveal that electrons remain ballistic at current densities in excess of 10$^{6}$ A/cm$^{2}$.   

Spectral and Spatial Response of Sulfur-Hyperdoped n+/p Silicon Photodiodes

Pulsed laser melting of implanted silicon can enable doping well above equilibrium concentrations. Sulfur doping leads to a deep donor state that may form an impurity band at high enough concentrations. Photodiodes formed from sulfur-hyperdoped n+ layers on a p-type wafer have shown external quantum efficiency of much greater than 100\%, as well as enhanced infrared response. In this paper we report on optoelectronic characterization of diodes prepared by implantation of 10$^{15}-10^{16}$ sulfur/cm2 into a p-type wafer, followed by nanosecond pulsed laser melting and recrystallization. Experimental results from wavelength-dependent diode response, spatial quantum efficiency mapping, intensity dependent efficiency, and current-voltage techniques will be reported. We will also discuss potential models for the observed behavior.   

The mesoscopic chaotic cavity as a rectifying heat engine

We present an exactly solvable model of a mesoscopic heat engine that works using the principle of rectifying thermal fluctuations applied to a nonlinear system. The system is a chaotic mesoscopic cavity where the contact transmission to leads is energy-dependent. This energy-dependence is generic in mesoscopic conductors, and leads to an intrinsic nonlinearity. The cavity is coupled capacitively to another conductor, held at a different temperature. The nonlinear cavity rectifies the thermal fluctuations, leading to a hot spot rectified electrical current that is proportional to the asymmetry in the energy-dependence of the contacts, and to the temperature difference. We will discuss the maximum power produced by the system, as well as the efficiency of the engine by comparing it to the heat current that passes between the coupled systems. Possible practical energy-harvesting applications will be proposed.   

Thermal properties of CuGaS$_2$ from first principles

We have investigated in the past the specific heats of monatomic and binary semiconductors and their dependence on temperature and isotopic mass, both experimentally and theoretically. The theoretical calculations were performed \textit{ab initio} with LDA exchange correlations. We are at present carrying over these investigations to ternary materials, in particular to those with chalcopyrite structure. We present here results involving the dependence of the specific heat and other physical properties (lattice parameters, volume thermal expansion, phonon dispersion) of the chalcopyrite CuGaS$_2$ on temperature and on the isotopic masses of the three constituent atoms. Particular emphasis is paid to the maxima of $C_p/T^3$ found at low temperatures which correspond to the deviation of Debye's law related to transverse acoustic phonons near the zone boundary. The calculations were performed with the ABINIT and VASP codes within the local density approximation for exchange and correlation. The results are shown to be in excellent agreement with the experimental data. Correlation with similar compounds such as CuAlS$_2$ and CuInS$_2$ is discussed.   

Session Q29: Focus Session: Topologically Protected Qubits II

Topological superconducting states and protected qubit manipulations

Topological superconducting states supporting Majorana fermion excitations have been recently proposed as platforms for topological quantum computation. Of particular importance are semiconductor-superconductor and topological insulator-superconductor heterostructures, which have been shown to support Majorana fermions at order parameter defects under appropriate external conditions. Here I will focus on topologically non-trivial properties of two-dimensional semiconductors and one-dimensional quantum wires placed adjacent to superconductors, and discuss the possible protected qubit manipulations that may eventually lead to topological quantum computation.   

Majorana Zero Modes in 1D Quantum Wires Without Long-Ranged Superconducting Order

We show that long-ranged superconducting order is not necessary to guarantee the existence of Majorana fermion zero modes at the ends of a quantum wire. We formulate a concrete model which applies, for instance, to a semiconducting quantum wire with strong spin-orbit coupling and Zeeman splitting coupled to a wire with algebraically-decaying superconducting fluctuations. We solve this model by bosonization and show that it supports Majorana fermion zero modes. We argue that a large class of models will also show the same phenomenon. We discuss the implications for experiments on spin-orbit coupled nanowires coated with superconducting film and for LaAlO3/SrTiO3 interfaces.   

Coulomb stability of the $\mathbf{4\pi}$-periodic Josephson effect of Majorana fermions

The Josephson energy of two superconducting islands containing Majorana fermions is a $4\pi$-periodic function of the superconducting phase difference. If the islands have a small capacitance, their ground state energy is governed by the competition of Josephson and charging energies. We calculate this ground state energy in a ring geometry, as a function of the flux $\Phi$ enclosed by the ring, and show that the dependence on the Aharonov-Bohm phase $2e\Phi/\hbar$ remains $4\pi$-periodic regardless of the ratio of charging and Josephson energies---provided that the entire ring is in a topologically nontrivial state. If part of the ring is topologically trivial, then the charging energy induces quantum phase slips that restore the usual $2\pi$-periodicity [B.\ van Heck, F.\ Hassler, A.\ R. Akhmerov, and C.\ W.\ J. Beenakker, Phys. Rev. B {\bf 84}, 180502(R) (2011)].   

Unconventional Josephson signatures of Majorana bound states

A junction between two topological superconductors containing a pair of Majorana fermions exhibits a `fractional' Josephson effect, $4\pi$ periodic in the superconductors' phase difference. An additional fractional Josephson effect, however, arises when the Majoranas are spatially separated by a superconducting barrier. This new term gives rise to a set of Shapiro steps which are essentially absent without Majorana modes and therefore provides a unique signature for these exotic states. Other new signatures associated with Majorana fermions will also be discussed.   

Signature of Majorana Fermions in Charge Transport in Semiconductor Nanowires

We investigate the charge transport in a semiconductor nanowire that is subject to a perpendicular magnetic field and in partial contact with an \textit{s}-wave superconductor. We find that Majorana fermions, existing at the interface between superconducting and normal sections of the nanowire within certain parameter region, can induce resonant Andreev reflection of electrons at the interface, which yields a zero energy peak in the electrical conductance of the nanowire. The width of the zero energy conductance peak for different experimental parameters is characterized. While the zero energy peak provides a signature for Majorana fermions in one dimensional nanowires, it disappears in a two-dimensional semiconductor thin film with the same experimental setup because of the existence of other edge states in two dimensions. The proposed charge transport experiment may provide a simple and experimentally feasible method for the detection of Majorana fermions in semiconductor nanowires.   

Searching for Majorana Zero-Energy Modes in Semiconductor Nanowires

Majorana fermions are proposed elementary particles with the unique property of being their own antiparticle, whose discovery remains elusive. Because of their non-Abelian statistics, Majorana fermions provide a promising opportunity to realize fault-tolerant topological quantum computation. Recently, semiconductor nanowires have been proposed as a possible platform for realizing Majorana physics in solid state systems. An s-wave superconductor inducing the proximity effect in a one-dimensional semiconductor nanowire would create chiral p-wave superconductivity in the nanowire; this superconductor would have Majorana modes as zero-energy excitations. We use nanofabrication techniques to create such nanowires out of MBE-grown two-dimensional electron gas formed in III-V semiconductor heterostructures. We present measurements which show the promise of this approach to creating and controlling Majorana excitations.   

Majorana fermions in superconducting helical magnets

In a variety of rare-earth based compounds singlet superconductivity coexists with helical magnetism. Here we demonstrate that surfaces of these system are expected to generically host a finite density of zero-energy Majorana modes. When confined to a wire geometry, a discrete number of Majorana modes can be isolated, in close analogy with the Rashba superconductors proposed recently as a framework for topological quantum computing. In contrast to the latter systems, however, the larger characteristic energy scales for superconductivity and magnetism, as well as the lack of need for fine-tuning, make helical magnetic superconducting compounds favorable for the observation and experimental investigation of Majorana fermions.   

Stability of Majorana fermions in proximity-coupled topological insulator nanowires

It has been shown previously [1] that a finite-length topological insulator nanowire, proximity-coupled to an ordinary bulk s-wave superconductor and subject to a longitudinal applied magnetic field, realizes a one-dimensional topological superconductor with an unpaired Majorana fermion localized at each end of the nanowire. Here we show that the unpaired Majorana fermions persist in this system for any value of the chemical potential inside the bulk band gap of order 300 meV in Bi$_2$Se$_3$, and, remarkably, also outside this gap in smaller domains, by computing the Majorana number. From this calculation, we also show that the unpaired Majorana fermions persist when the magnetic flux through the nanowire cross-section deviates significantly from half flux quantum. Lastly, we demonstrate that the unpaired Majorana fermions persist in strongly disordered wires with fluctuations in the on-site potential ranging in magnitude up to the size of the bulk band gap. These results suggest this solid-state system should exhibit the elusive Majorana particles under conditions accessible enough for their long sought-after experimental realization.\\[4pt] [1] A. Cook and M. Franz, Phys.\ Rev.\ B (in press, arXiv:1105.1787)   

Josephson current in finite-lenght nanowire SNS junctions with Majorana fermions

The dc Josephson effect (JE) through infinite-lenght junctions of one-dimensional topological superconductors exhibits an anomalous $4\pi$ periodic phase ($\phi$) dependence which originates from a parity-protected level crossing of zero-energy Majorana bound states (MBS) at $\phi=\pi$. This ``fractional'' JE provides an important experimental detection tool for MBS. In this talk, I will discuss the JE in more realistic SNS junctions of arbitrary transparency and when both the normal and the nanowire regions are of finite length, namely beyond the short-junction and infinite topological superconductor limits. In general, the spectrum of Andreev bound states can become rather intricate and dense as opposed to the infinite-lenght case. Moreover, the low-energy spectrum around $\phi=\pi$ shows always anticrossings, originated from hybridization of four MBS, which may preclude the experimental observation of the fractional JE. At finite bias voltages, Landau-Zener dynamics involving the MBS and quasi-continuum Andreev levels gives rise to a nontrivial ac Josephson current. Interestingly, the ac current phase diagram as a function of the Josephson frequency/normal transmission shows fractional JE regions which are tunable through bias/gate voltages.   

Detecting a Majorana-Fermion Zero Mode Using a Quantum Dot

We propose an setup for detecting a Majorana zero mode consisting of a spinless quantum dot coupled to the end of a p-wave superconducting nanowire [1]. The conductance through the dot is monitored by adding two external leads. We find that the Majorana bound state at the end of the wire strongly influences the conductance through the quantum dot: driving the wire through the topological phase transition causes a sharp jump in the conductance by a factor of 1/2. In the topological phase, the zero temperature peak value of the dot conductance (i.e. on resonance and symmetric coupling) is e$^2$/2h. In contrast, if the wire is in its trivial phase, the peak is e$^2$/h, or if a regular fermionic zero mode occurs, the conductance is 0. We also consider coupling the dot to both ends of the wire (two MBS), with a magnetic flux f through the loop. The conductance as a function of phase shows peaks at f/f0 = (2n+1)*pi which can be used to tune Flensberg's qubit system [PRL (2011)] to the energy degeneracy point. \\[4pt] [1] D. E. Liu and H. U. Baranger, PRB in press (2011); arXiv/1107.4338.   

Majorana chain coupled to a microwave cavity

We study the Majorana end-states in a one-dimensional Kitaev model in the presence of a microwave cavity. We analyze both the resonant and off-resonant coupling to the cavity for different cavity states. In the resonant regime, we find that the topology of the system can be modified depending on the number of photons in the cavity, while in the off-resonant regime (large detuning), the cavity could be used to detect the topological transition from a non-trivial to trivial state, being thus an optical alternative to the transport-based detection of the transition point. We also analyze the effects of the coupling to the cavity on the braiding of the emerging Majoranas.   

Majorana modes in time-reversal invariant s-wave topological superconductors

We present a time-reversal invariant $s$-wave superconductor supporting Majorana edge modes. The multi-band character of the model together with spin-orbit coupling are key to realizing such a topological superconductor. We characterize the topological phase diagram by using a partial Chern number sum, and show that the latter is physically related to the parity of the fermion number of the time-reversal invariant modes. By taking the self-consistency constraint on the $s$-wave pairing gap into account, we also establish the possibility of a direct topological superconductor-to-topological insulator quantum phase transition.   

Majorana Fermions in Disordered Quasi-One-Dimensional Topological Superconductors

Majorana fermions have long been predicted to emerge in certain quantum Hall states and other naturally occurring p-wave superconductors. However, these materials are quite delicate and consequently the experimental realization of Majorana fermions remains elusive. The possibility of engineering 1D networks of topological superconducting wires from conventional materials offers a promising alternative route to realize Majorana fermions and probe their predicted non-Abelian statistics. In practice, it is impossible to fabricate perfectly clean and strictly one-dimensional structures; how do these non-idealities affect the proposed Majorana states? This talk will show that Majorana end states are robust away from the strict 1D limit, so long as the sample width is not much larger than the superconducting coherence length. The effects of disorder are potentially more severe, as impurity scattering is generally pair-breaking and tends to suppress the gap protecting the Majorana modes. Finally, we propose new candidate materials and geometries that greatly simplify the experimental setup and mitigate the harmful effects of disorder.   

Session Q30: Focus Session: Superconducting Qubits: Architecture, Tunable, and Static Coupling

Coupling superconducting qubits and resonators

The performance of superconducting qubits has evolved rapidly in recent years, with coherence times now often measured in tens of microseconds. This makes superconducting qubits a promising candidate for a scalable quantum computing architecture and for modeling quantum systems. To realize this potential, consideration must be given to coupling multiple qubits to a system of microwave resonators in a way that balances coherence times, control and readout times, crosstalk, and space constraints. We compare three methods of coupling qubits to resonators: inductive coupling through a shared kinetic inductance with the resonator, capacitive coupling to a voltage antinode, and coupling to a three-dimensional superconducting cavity. We will also present designs and measurements of samples incorporating both inductively and capacitively coupled qubits on the same coplanar resonator. Lastly, we discuss a three-qubit/two-resonator system with one qubit bridging the two resonators that could serve as the building block of a large-scale architecture.   

Inductive coupling to the fluxonium qubit

Fluxonium is a highly anharmonic artificial atom, which utilizes an inductance formed by an array of large Josephson junctions to shunt the junction of a Cooper-pair box. The first excited state transition frequency is widely tunable with flux, and due to interactions of transitions to the second excited state with the readout cavity, a dispersive readout is possible over the entire five octave range. Previous fluxonium samples relied on a capacitive coupling to the readout cavity, but there is evidence that dielectric losses in these capacitors contributes significantly to relaxation [1]. We present a new method of coupling to the cavity through a mutual inductance, reducing relaxation through dielectric loss. \\[4pt] [1] V. E. Manucharyan et al., arXiv:1012.1928v1 (2010).   

A dc SQUID Phase Qubit with Controlled Coupling to the Microwave Line

We have designed and fabricated a Al/AlO$_{x}$/Al dc SQUID phase qubit on a sapphire substrate with a qubit junction area of 0.4 $\mu$m$^2$. The qubit junction is shunted with a 1 pF interdigitated capacitor, and is isolated from the bias leads by an LC filter and an inductive isolation network using a larger Josephson junction. Our previous device (A. Przybysz \textit{et al.}, IEEE Trans. on Appl. Supercond., 2011) with similar parameters had its relaxation time $T_{1}$ limited by coupling to the microwave line. To reduce this coupling, we adopted a coplanar stripline design and verified the coupling strength using finite element model microwave simulations. We will discuss our design, the microwave simulations, estimates for the overall coherence time due to losses and noise from various sources, the device fabrication process, and progress towards testing the device.   

Large tunable inductance of the decorated Josephson chain

We discuss the new design of a tunable superconductive inductance made from the decorated frustrated Josephson junction chains frustrated by magnetic field. We show that for the optimal choice of parameters the inductance of this chain varies in a very wide range as a function of the magnetic field. The resulting plasma frequency may exceed the value of quantum resistance, $\sqrt{L/C}\gg h/(2e)^2$ that characterizes superinductance. The important distinction of this design from the chain of dc-SQUIDs loops is the absence of phase slips at all magnetic fields. We present the results of the extensive numerical simulations that confirm these expectations.   

Driven dynamics of a qubit tunably coupled to a harmonic oscillator

We have investigated the driven dynamics of a superconducting flux qubit that is tunably coupled to a microwave resonator. We find that the qubit experiences an additional oscillating field mediated by off-resonant driving of the resonator, leading to unanticipated, strong modifications of the qubit Rabi frequency. Low-frequency noise in the coupling parameter translates to an effective noise in the amplitude of the drive field, causing a reduction of the coherence time during driven evolution. The noise can be mitigated with the rotary-echo pulse sequence, which, for driven systems, is analogous to the Hahn-echo sequence.   

Phase gate operation on a flux qubit via the readout SQUID line

Detuning a superconducting qubit from its rotating frame is one means to implement a phase gate operation. For superconducting flux qubits, this detuning can be realized by changing the magnetic flux threading the qubit loop, .e.g., by the mutual coupling from a nearby microwave antenna. In this work, we demonstrate an alternative approach: we implement a phase gate by pulsing a current through the readout DC SQUID. While the DC SQUID acts as a qubit flux sensor for readout, we in turn may use it as an actuator to impose the phase-gate flux shift. Using this pulsed current approach, we demonstrated Ramsey-type free-induction with more than 20 oscillation periods. We also studied the impact of the first phase gate on subsequent, sequential phase gates.   

Progress towards a metastable superconducting qubit

We will report on progress towards the demonstration of a metastable RF SQUID (MRFS) qubit, which has the potential to exhibit excited-state lifetimes many orders of magnitude longer than present-day superconducting qubits, while retaining long enough coherence times to allow gate error rates as low as $\sim 10^{-5}$. These properties result from the two main characteristics of the MRFS qubit: (i) its two lowest levels are essentially macroscopically distinct persistent-current states, which can be strongly decoupled from high-frequency electromagnetic fluctuations (in contrast to most superconducting qubits whose levels are approximately those of a nonlinear LC oscillator and are thus strongly coupled); and (ii) its extremely large inductance makes it only weakly sensitive to low-frequency magnetic flux noise.   

Quantum gates by qubit frequency modulation in circuit QED

Several types of two-qubit gates have been realized experimentally in circuit QED. These are based, for example, on tuning the pair of qubits in resonance with each other [Majer, Nature 449, 443-447 (2007)] or on a microwave pulse on one qubit at the transition frequency of a second qubit [Chow, Phys. Rev. Lett. 107, 080502 (2011)]. Another realization is based on a sequence of blue-sideband transitions generated by microwave pulses [Leek, Phys. Rev. B 79, 180511(R) (2009)]. Here, we propose a different approach relying on oscillations of the qubit frequency using a flux-bias line. We explain how frequency modulation leads to tunable qubit-resonator and qubit-qubit interactions. We also show how this form of quantum control leads to faster (first-order) sideband transitions and consider applications to two-qubit gates.   

Transmon qubit coupled to a quasi-lumped element resonator

We report on the design, fabrication and measurement of an Al/AlO$_{\mbox{x}}$/Al transmon qubit coupled to a quasi-lumped element superconducting resonator. Our resonator, which has a resonant frequency of $\approx 5.4\,$GHz, and a loaded quality factor $Q_l \approx 30,000$ is, in turn, coupled to a transmission line. The qubit is designed to have $E_J/E_c > 30$ to significantly decrease the sensitivity to low-frequency charge noise. The coupling of the qubit to the resonator is designed to be $g/2\pi> 100\, $MHz. We report and discuss preliminary spectroscopic measurements and coherence measurements of the qubit.   

Fast, coherent control of the tunable coupling qubit

We present results of time domain measurements on a tunable coupling qubit (TCQ) coupled to a superconducting coplanar waveguide resonator. The TCQ has the benefit of independently tunable qubit frequency and cavity-qubit coupling. We show that the TCQ's frequency and coupling can be dynamically controlled in tens of nanoseconds by using two on-chip flux control lines. Using this dynamic control, Rabi oscillations were measured at various coupling strengths showing that the coupling can be reduced by a factor greater than 1500. To measure qubit coherence at low coupling, the TCQ was tuned to a high coupling region, excited by a~synchronized~pi-pulse and then returned to the zero coupling region where the qubit state was measured. ~Coherence times of several microseconds were measured and are comparable to other superconducting qubits   

Transferring the state of a quantum register to a single oscillator: a simple circuit verses numerical optimization

We consider the problem of swapping a quantum state between a register of qubits and a single quantum oscillator. We design a mesoscopic quantum circuit to do this, using an off-resonant interaction, based on the concept of coherent feedback control. We consider an explicit realization of this circuit, and perform simulations of its performance. We then take a different approach, in which we couple the register directly to the resonator, including inter-qubit couplings and local controls, and use numerical optimization to search for a control protocol that will achieve the swap with very high fidelity. Our results show that the protocols found using numerical searches are superior in speed and fidelity to the manually-designed circuit. We also explore how the time and complexity of the protocols increases with the problem size.   

Gradiometric persistent current flux qubit with tunable tunnel coupling

The persistent current flux qubit is a Josephson junction based superconducting circuit exhibiting a strong anharmonicity in combination with excellent coherence times of more than 10\,$\mu$s. However, quantum coherence decreases drastically away from an optimal point and a controlled design of the transition frequency at this point is demanding with respect to fabrication stability. Here, we present the spectroscopic analysis of a gradiometric flux qubit, where the tunnel coupling can be tuned from a few hundreds of Megahertz to several Gigahertz.   

Large dispersive shift in superconducting flux qubit

We study dispersive readout in superconducting flux qubits which are capacitively coupled to a superconducting cavity with $\sim$ 10 GHz resonant frequency $f_r$. To discriminate the state of the qubit precisely, large magnitude of the dispersive shift $\chi$ is desirable. For the two-level system, $\chi$ is given by $g^2/\Delta$ where $g$ is the coupling strength and $\Delta$ is the detuning between the qubit and the cavity. For the multilevel system such as superconducting qubits, however, this formula is modified due to the contributions from higher levels [1]. It has been pointed out that if $f_r$ lies between 01 and 12 transition frequencies of the qubit ($f_{01}$ and $f_{12}$, respectively), $|\chi|$ becomes large because of constructive contributions from different levels [1]. Our flux qubit has $f_{01}=$ 5 GHz and $f_{12}=$ 15 GHz at the optimal flux bias, thus satisfying this condition. Moreover, because of the large anharmonicity ($|f_{12} - f_{01}|$) of the flux qubit, we can easily make $g$ as large as $\sim$ 100 MHz, while staying in the deep dispersive limit. Both of these enhance $|\chi|$ and we have obtained $\chi$ of 80 MHz at the optimal flux bias, which agrees well with the prediction by the energy band calculation. [1] J. Koch et al., PRA 76, 042319 (2007)   

Session Q31: Focus Session: Topological Insulators - Edge States

Electrical control of spin in topological insulators

All-electrical manipulation of electron spin in solids becomes a central issue of quantum information processing and quantum computing. The many previous proposals are based on spin-orbit interactions in semiconductors. Topological insulator, a strong spin-orbit coupling system, make it possible to control the spin transport electrically. Recent calculations proved that external electric fields can drive a HgTe quantum well from normal band insulator phase to topological insulator phase [1]. Since the topological edge states are robust against local perturbation, the controlling of edge states using local fields is a challenging task. We demonstrate that a p-n junction created electrically in HgTe quantum wells with inverted band structure exhibits interesting intraband and interband tunneling processes. We find a perfect intraband transmission for electrons injected perpendicularly to the interface of the p-n junction. The opacity and transparency of electrons through the p-n junction can be tuned by changing the incidence angle, the Fermi energy and the strength of the Rashba spin-orbit interaction (RSOI). The occurrence of a conductance plateau due to the formation of topological edge states in a quasi-one-dimensional p-n junction can be switched on and off by tuning the gate voltage. The spin orientation can be substantially rotated when the samples exhibit a moderately strong RSOI [2]. An electrical switching of the edge-state transport can also be realized using quantum point contacts in quantum spin Hall bars. The switch-on/off of the edge channel is caused by the finite size effect of the quantum point contact and therefore can be manipulated by tuning the voltage applied on the split gate [3,4]. The magnetic ions doped on the surface of 3D TI can be correlated through the helical electrons. The RKKY interaction mediated by the helical Dirac electrons consists of the Heisenberg-like, Ising-like, and Dzyaloshinskii-Moriya (DM)-like terms, which can be tuned by changing the gate voltage. It provides us a new way to control surface magnetism electrically. The gap opened by doped magnetic ions can lead to a short-range Bloembergen-Rowland interaction. The competition among the Heisenberg, Ising, and DM terms leads to rich spin configurations and an anomalous Hall effect on different lattices [4]. There are many proposals for quantum computation scheme are based on the spin in semiconductor quantum dots. Topological insulator quantum dots display a very different behavior with that of conventional semiconductor quantum dots [5]. In sharp contrast to conventional semiconductor quantum dots, the quantum states in the gap of the HgTe QD are fully spin-polarized and show ring-like density distributions near the boundary of the QD and optically dark. The persistent charge currents and magnetic moments, i.e., the Aharonov-Bohm effect, can be observed in such a QD structure. This feature offers us a practical way to detect these exotic ring-like edge states by using the SQUID technique. \\[0pt]Refs: [1] W. Yang, Kai Chang, and S. C. Zhang, Phys. Rev. Lett. 100, 056602 (2008); J. Li and Kai Chang, Appl. Phys. Lett. 95, 222110 (2009). [2] L. B. Zhang, Kai Chang, X. C. Xie, H. Buhmann and L. W. Molenkamp, New J. Phys. 12, 083058 (2010). [3] L. B. Zhang, F. Cheng, F. Zhai and Kai Chang, Phys. Rev. B 83 081402(R) (2011); Z. H. Wu, F. Zhai, F. M. Peeters, H. Q. Xu and Kai Chang, Phys, Rev. Lett. 106, 176802 (2011). [4] J. J. Zhu, D. X. Yao, S. C. Zhang, and Kai Chang, Phys. Rev. Lett. 106, 097201 (2011). [5] Kai Chang, and Wen-Kai Lou, Phys. Rev. Lett. 106, 206802 (2011).   

Conductance of the Quantum Spin Hall Edge in HgTe Quantum Wells

A two-dimensional electron system with band inversion due to spin-orbit interactions can support counterpropagating edge channels, each with one unit of conductance. Unlike the conventional quantum Hall effect, however, these channels can back scatter into each other in the presence of magnetic impurities (or other time-reversal breaking scattering sources). With topgates, we can create 1 um edges of these QSH states and characterize their transmission. In some regions, we are able to see the quantized conductance that is expected of the QSH effect. In other regions, we see a higher resistance corresponding to a nonzero amount of scattering in the channel.   

Inelastic electron backscattering in a generic helical edge channel

We calculate the low-temperature conductance of a generic one-dimensional helical liquid which exists at the edge of a two-dimensional topological insulator (quantum spin Hall insulator). In a generic case, the $S_z$ spin-symmetry is absent, which opens a possibility of single-particle inelastic electron backscattering. We show that although time-reversal invariance is preserved, inelastic backscattering gives rise to a temperature-dependent deviation from the quantized conductance, $\delta G \propto T^4$. In addition, $\delta G$ is sensitive to the position of the Fermi level in the gap of the insulator. We present an effective model for this type of helical liquid and determine its parameters explicitly from numerical solutions of microscopic models for two-dimensional topological insulators in the presence of Rashba spin-orbit coupling.   

Gate controlled Rotating Spin Wave and chiral FFLO Superconducting phases in Quantum Spin Hall edge

We explore the phases exhibited by an interacting quantum spin Hall edge state in the presence of finite chemical potential (applied gate voltage) and spin imbalance (applied magnetic field). We find that the helical nature of the edge state gives rise to orders that are expected to be absent in non-chiral one-dimensional electronic systems. For repulsive interactions, the ordered state has an oscillatory spin texture whose ordering wavevector is controlled by the chemical potential. We analyze the manner in which a magnetic impurity provides signatures of such oscillations. For attractive interactions, finite spin-imbalance, which acts to set up a finite current in unordered QSH edges, results in superconducting order that is characterized by FFLO-type oscillations.   

Phonon induced backscattering in helical edge states

A single pair of helical edge states as realized at the boundary of a quantum spin Hall insulator is known to be robust against elastic single particle backscattering as long as time reversal symmetry is preserved. However, there is no symmetry preventing inelastic backscattering as brought about by phonons in the presence of Rashba spin orbit coupling. In this work, we show that the quantized conductivity of a single channel of helical Dirac electrons is protected even against this inelastic mechanism to leading order. We further demonstrate that this result remains valid even when Coulomb interaction is included in the framework of a helical Tomonaga Luttinger liquid.   

Optically engineering the topological properties of helical edge states

Time-periodic perturbations can be used to engineer topological properties of matter by altering the Floquet band structure. This is demonstrated for the helical edge state of a spin Hall insulator in the presence of monochromatic circularly polarized light. We first demonstrate that the inherent spin structure of the edge state is influenced by the Zeeman coupling and not by the orbital effect. The photocurrent (and the magnetization along the edge) develops a finite, helicity dependent expectation value and turns from dissipationless to dissipative with increasing radiation frequency, signalling a change in the topological properties. The connection with Thouless' charge pumping and non-equilibrium Zitterbewegung is discussed, together with possible experiments. B. Dora, J. Cayssol, F. Simon, and R. Moessner, Optically engineering the topological properties of a spin Hall insulator, arXiv:1105.5963   

Fingerprints of a bidimensional topological insulator in Bismuth nanocontacts

We report on experimental and theoretical work of the electronic transport in Bismuth nanocontacts as created by repeated breaking and indentation using scanning tunneling microscopy techniques. The conductance exhibits a number of unusual features, not shared by normal metals, one of the most striking ones being the presence of plateaus at fractional values of the quantum of conductance at low temperatures. We understand this phenomenon on the basis of the formation of a bilayer of Bismuth (a predicted bidimensional topological insulator) which supports a maximum of a quantum of conductance as expected for its odd number of gapless edge modes. Theoretical transport results based on an atomistic tight-binding model with disorder and spin-orbit coupling permit us associate the fractional-valued plateaus to the final stages of the breaking of the bilayer.   

Spin Josephson effect at the quantum spin Hall edge

We study a spin Josephson effect in a ferromagnetic junction at the quantum spin Hall (QSH) edge. The helical nature of the QSH edge states has striking consequences for the transport properties of such a junction. We derive an expression for the spin current through the junction as a function of the change in magnetization, similar to the current-phase relation of a Josephson junction. We discuss the novel transport properties of the junction that result from fractionally charged excitations hosted by the QSH edge.   

Equality of certain bulk wave functions and edge correlations in $d=2$ and $d=3$

Ground state wavefunctions and gapless edge physics provide two complementary approaches to the study of quantum Hall liquids. Seminal work of Read and Moore establishes a connection between wavefunctions and 1+1 D Conformal Field Theories, which also describe edge states. Here we provide a transparent derivation of the edge correlation-wavefunction {\em equality} for certain topological superconductors - theories with edge states, where charge is not conserved. By studying the 2+1 D $p+ip$ superconductor in some detail, we show that the only necessary ingredient is an approximate Lorentz invariance. We are therefore able to extend the derivation to other dimensions, for example an analogous equality of bulk wavefunctions and edge correlations is derived for superfluid ${}^3He-B$ in $d=3$. A key realization is that ground state wavefunctions can be extracted by considering Euclidean partition functions with a time dependent chemical potential. We also demonstrate that the method works for interacting phases, by studying a ``fractional'' topological superconductor using the parton construction. This connection may help identify novel topological phases in various dimensions.   

Transport on the Surface of Weak Topological Insulators

Weak topological insulators have an even number of Dirac cones in their surface spectrum and are thought to be unstable to disorder, which leads to an insulating surface. Here we argue that the presence of disorder alone will not localize the surface states, rather, the presence of a time-reversal symmetric mass term is required for localization. Through numerical simulations, we show that in the absence of the mass term the surface always flow to a stable metallic phase and the conductivity obeys a one-parameter scaling relation, just as in the case of a strong topological insulator surface. With the inclusion of the mass, the transport properties of the surface of a weak topological insulator follow a two-parameter scaling form.   

Coherent transport of topological insulator surface states

Topological insulators (TIs) are a new state of matter recently predicted theoretically\footnote{C. L. Kane and E. J. Mele, Phys. Rev. Lett. 95, 226801 (2005).}$^,$\footnote{X.-L. Qi, T. L. Hughes, and S.-C. Zhang, Phys. Rev. B 78,195424 (2008).} and realized experimentally. In 3D they are characterized by the presence of gapless surface states which exhibit a linear dispersion, typical of Dirac fermions. Moreover, contrary to conventionnal materials, these Dirac cones occur in an odd number of Dirac fermions at the surface: ARPES experiments\footnote{Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, Nature Physics 5, 398 (2009).}$^,$\footnote{Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X.L.Qi,H.J.Zhang,D.H.Lu,X.Dai,Z.Fang,S.C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, Science 325, 178 (2009).} have found a single Dirac cone at the surface of Bi2Se3, Bi2Te3. This work focuses on the electronic transport properties calculations in the diffusive limite of a single Dirac cone. Specificities of the TI surface states, like the hexagonal warping coupling are taken into account.   

Spin polarized multi-terminal transport in helical edge states

We propose a three-terminal spin polarized scanning tunneling microscope setup for probing the helical nature of the edge states that appear in the quantum spin Hall system. We show that the three-terminal tunneling conductance depends on the magnetic anisotropy, i.e., the angle between the magnetization of the tip and the local orientation of the electron spin on the edge. We show that chiral injection of an electron into the helical Luttinger liquid is associated with fractionalization of the spin and charge of the injected electron. Finally, we show that the magnetic anisotropy of the probe also leads to Fabry-Perot like two-terminal resonances in charge transport.   

Session Q32: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides - Multiferroics and Magnetoelectrics

Skyrmions in Multiferroics

Magnetic skyrmion is a topologically stable particle-like object, which appears as nanometer-scale vortex-like spin texture in a chiral-lattice magnet. In metallic materials, electrons moving through skyrmion spin texture gain a nontrivial quantum Berry phase, which provides topological force to the underlying spin texture and enables the current-induced manipulation of magnetic skyrmion. Such electric controllability, in addition to the particle-like nature, is a promising advantage for potential spintronic device applications. In this talk, we report the experimental discovery of magnetoelectric skyrmion in an insulating chiral-lattice magnet Cu$_2$OSeO$_3$. We find that the skyrmion can magnetically induce electric polarization through the relativistic spin-orbit interaction, which implies possible manipulation of the skyrmion by external electric field without loss of joule heating. The present finding of multiferroic skyrmion may pave a new route toward the engineering of novel magnetoelectric devices with high energy efficiency.   

Dynamical matrix in magnetoelectrics

In ordinary dielectrics the dynamical matrix at the zone center is a nonanalytic function of degree zero in the wavevector {\bf q}. Its expression (for a crystal of arbitrary symmetry) is well known and is routinely implemented in first principle calculations. The nonanalytic behavior occurs in polar crystals and owes to the coupling of the macroscopic electric field {\bf E} to the lattice. In magnetoelectric crystals both electric and magnetic fields, {\bf E} and {\bf H}, are coupled to the lattice, formally on equal footing. I provide the general expression for the zone center dynamical matrix in a magnetoelectric, where the {\bf E} and {\bf H} couplings are accounted for in a symmetric way. As in the ordinary case, the dynamical matrix is a nonanalytic function of degree zero in {\bf q}, and is exact in the harmonic approximation. Besides the above major result, I will also discuss other related issues: (i) The Lyddane-Sachs-Teller relationship for MEs, where the fields {\bf E} and {\bf H} are (once more) dealt with in a symmetric way; (ii) The microscopic origin of the coupling of magnetic fields to the lattice, which may look counterintuitive; (iii) The relationship to first-principle implementations, where in the simplest cases {\bf E} and {\bf B} (not {\bf H}) are zero.   

Multiferroic behavior in Lu$_{2}$MnCoO$_{6}$

Lu$_{2}$MnCoO$_{6}$ is a new member of the multiferroics with coupling between net magnetization and net electric polarization. Similar to Ca$_{3}$MnCoO$_{6}$, an up-up-down-down order of the magnetic spins is found that breaks spatial-inversion symmetry and creates an electric polarization. Unlike Ca$_{3}$MnCoO$_{6}$, the Co and Mn ions are both in a S = 3/2 state, the ordering temperature is 42 K, and the magnetic field needed to suppress electric polarization is 2 T. We present an experimental study of the multiferroic properties and spin structure including neutron diffraction, electric polarization, magnetization, dielectric constant, and specific heat measurements.   

Structural and Magnetic Properties of Ln$_2$CoMnO$_6$ (Ln = Dy and La) Produced by Combustion Sinthesys

The lanthanum manganites have been intensively studied in recent years. These compounds present a wide variety of properties of great technological and scientific interest. The half-doped lanthanum manganite with Co in Mn site have ferroelectric and ferromagnetic properties with critical temperatures close to room temperature. The mechanisms responsible for magnetoelectric coupling in these materials are not yet understood. In this work we study the effect of Dy doping at La site in the structural and magnetic properties of lanthanum manganite half-doped with Co obtained by combustion method. The dark powder obtained was heat-treated in air and cooled slowly in the oven. The samples were characterized structurally by X-ray diffratometry with Rietveld refinement analysis. Magnetization measurements as a function of temperature and the magnetic field were carried out on the SQUID magnetometer in temperature interval of 5 - 300 K and in magnetic fields up to 7T. The results show an decreases of the magnetic transition temperature when we substitute the La by Dy.   

Emergence of a new order reconciling ferroelectric and antiferrodistortive instabilities in EuTiO$_{3}$

Control of magnetic moments with electric field or electric polarization with magnetic field can open new possibilies to develop future applications of low power sensors, data storages and spintronics. However, in general this magnetoelectric coupling is extremely small for device application. Although, a substantial change of the dielectric constant under magnetic field was observed in the EuTiO$_{3}$ system. This finding offers an insight into how the electric polarization couples with the magnetism through phonon modes to the spin of the Eu atoms. We present recent x-ray diffraction data on a single crystal EuTiO$_{3}$ providing the direct proof of antiferrodistortive (AFD) TiO$^{6}$ octahedral rotations correlated with the quantum paraelectric state. Forming an incommensurate AFD order mediates the competition between antiferroelectric and AFD order. We discuss the origin of magnetoelectric coupling based on the interplay of AFD order and antiferromagnetic interactions.   

Spin-phonon coupling in the rare-earth orthoferrite DyFeO$_3$

The rare-earth orthoferrite (RFeO$_3$) canted antiferromagnets are known to exhibit a wide array of magnetic properties, including spin reorinetation transitions and compensation points between the rare-earth and iron sublattices. Furthermore, strong magnetoelastic coupling has been observed to lead to field-induced multiferroism with a large dielectric polarization. Here we present an infrared optical study of DyFeO$_3$, focusing on the evolution of the phonon structure with temperature. Polarized single-crystal relfectance measurements are supplemented with magnetization and dielectric constant measurements to illuminate the role of spin-phonon coupling in the lattice dynamics.   

A first principles investigation of a hexagonal ferrite LuFeO$_3$

The multiferroic hexagonal manganites RMnO$_3$ (R=Dy-Lu,Y), are a fascinating class of materials that display an unusual, complex interplay between structural, polar and magnetic domains. For example, the electric polarization in these compounds are found to be a by-product of a trimerized (zone-boundary) lattice distortion, arising from the ionic size mismatch between R$^{+3}$ and Mn$^{+3}$ ions. As a direct consequence of this improper ferroelectric transition, the ferroelectric and structural trimer domains are locked; rotation of structural distortion at a structural domain not only flips the polarization, but also rotates the spins. The hexagonal ferrites RFeO$_3$ (R=Lu,Er-Tb) crystallize in the same polar structure as the manganite counterparts. However, unlike the \textbf{M}=0, non-collinear antiferromagnetism in manganites, the ferrites have recently been shown to display week ferromagnetic behaviour[1], the underlying microscopic mechanism of which so far is not understood. In the present study, using first principles density functional calculations, we investigate the structural and magnetic properties of LuFeO$_3$, one of the members of this ferrite series. \\[4pt] [1] A. R. Akbashev, A. S. Semisalova, N. S. Perov and A. R. Kaul, Appl. Phys. Lett \textbf{99}, 122502 (2011).   

Atomic Resolution Valence Mapping in LuFe2O4 in an Aberration Corrected STEM

LuFe2O4 is a multiferroic with the simultaneous existence of ferroelectricity and ferrimagnetism at the highest temperature of any known material. The improper ferroelectricity is attributed to charge ordering in the Fe-O layers, however, a direct measure of the Fe valence on individual columns in the crystal remains elusive. Scanning Transmission Electron Microscopy (STEM) in combination with Electron Energy Loss Spectroscopy (EELS) allows for spatially resolved, chemically sensitive investigation of oxide materials. We used a Nion 5th-order aberration corrected 100 keV dedicated STEM to collect spectroscopic images from a thin film of LuFe2O4 on MgAl2O4 to map the two-dimensional concentrations of every atomic species in the film. The Fe valence on individual columns was measured, however, no statistically significant modulation--as would be consistent with charge ordering--was observed. Finally, changes in the fine structure in the EELS O atoms in the Lu-O and Fe-O planes, was mapped in two-dimensions.   

Anisotropy in the magnetic and multiferroic properties of LuFe$_{2}$O$_{4-\delta }$ single crystals with varying oxygen stoichiometry

LuFe$_{2}$O$_{4}$ is a multiferroic, where the origin of the ferroelectricity is attributed to electron correlations and directly linked to the charge ordering of Fe$^{2+}$ and Fe$^{3+}$ in the lattice. The multiferroic properties of this system are known to be sensitive to the oxygen stoichiometry. Large single crystals of LuFe$_{2}$O$_{4-\delta}$ with varying oxygen stoichiometry have been produced by the floating zone technique. Detailed magnetic susceptibility, dielectric constant and polarization measurements have been carried out along specific crystallographic axes of the single crystals over a wide temperature range to study the anisotropic properties. The effect of altering the Fe$^{2+}$/ Fe$^{3+}$ stochiometry on the physical properties of LuFe$_{2}$O$_{4-d}$ is discussed.   

Charge dynamics in a frustrated charge ordered multiferroic system

Electronic ferroelectricity is known as phenomena where the electric polarization is caused by the electronic charge order without inversion symmetry. This is seen in some transition metal oxides, e.g. LuFe$_{2}$O$_{4}$, and organic salts. It is suggested from the theoretical work [1] that large charge fluctuation and frustration are responsible for the electric polarization. This charge fluctuation is expected to govern dynamical properties. Actually, the measurements of the low frequency dielectric dispersion and the optical conductivity indicate that the large charge fluctuation remains in charge ordered phase in LuFe$_{2}$O$_{4}$. Motivated by these experimental results, we study charge dynamics in charge ordered system on the layered triangular lattice. We adopt the V-t model where the inter-site electron transfers and the inter-site Coulomb interactions are taken into account. We analyze this model by utilizing the exact diagonalization method and focus on effects of frustration in the charge dynamics. In the 3-fold charge ordered phase associated with the electric polarization, the optical conductivity shows multiple-peak structure in a wide energy range. In finite temperature, the low frequency oscillator strength of the optical conductivity and the dynamical charge correlation functions in 3-fold charge ordered phase decrease slower than those in the non-polar 2-fold charge ordered phase. These results imply the strong charge fluctuation in the 3-fold charge ordered phase due to the geometrical frustration. [1] M. Naka et al. Phys. Rev. B. \textbf{77} 224441.   

Multiferroic M-type hexaferrites with room-temperature conical spin structure

Magnetic and magnetoelectric properties have been investigated for single crystals of Sc-doped M-type hexaferrites [1]. Magnetization and neutron diffraction studies have indicated that a longitudinal conical state is stabilized up to room temperature by tuning the Sc concentration. Magnetoelectric measurements have shown that electric polarization can be induced by applying a transverse magnetic field at lower temperatures, and that the spin helicity is nonvolatile and endurable up to near the transition temperature from conical to collinear state. In addition, the behavior of the polarization vector upon the reversal of magnetization varies with temperature, thereby allowing us to control the relation between spin helicity and magnetization vectors with magnetic field and temperature. This work was in part supported by FIRST program on \lq\lq Quantum Science on Strong Correlation\rq\rq \ from JSPS. \\[4pt] [1] Y. Tokunaga, Y. Kaneko, D. Okuyama, S. Ishiwata, T. Arima, S. Wakimoto, K. Kakurai, Y. Taguchi, and Y. Tokura, Phys. Rev. Lett. 105, 257201 (2010)   

The magnetoelectirc effect in the RAl$_{3}$(BO$_{3})_{4}$ (R=Tb, Ho, Er, and Tm)

We study the magnetoelectric (ME) effect of the rare earth aluminum borates, RAl$_{3}$(BO$_{3})_{4}$ (R=Tb, Ho, Er, and Tm). The magnetic, magnetoelectric, and magnetostrictive properties were investigated between 2K and 300K with different orientation of fields up to 70kOe. A giant magnetoelectric polarization, 3600 $\mu $C/m$^{2}$, is found in HoAl$_{3}$(BO$_{3})_{4}$ while a 70kOe transverse magnetic geometry field is applied. This value is significantly larger than that previously reported in all other bulk crystalline linear magnetoelectric or multiferroic materials. Furthermore, the ME polarization decreases with increasing magnetic anisotropy of the rare earth moment. The magnetostrictive measurements show that there is a strong coupling between the 4-f moments and the lattice. Our data further imply that the field-induced ionic displacements in a unit cell give rise to a change of structural symmetry from non-polar to polar symmetry.   

Polar Nanodomains and Giant Converse Magnetoelectric Effect in Charge-Ordered Fe$_{2}$OBO$_{3}$

Charge ordering (CO) is considered to be an important issue that leads to metal-insulator transitions in numerous materials and also shows possible correlations to many notable physical phenomena, such as colossal magnetoresistance, superconductivity and multiferroics. In recent investigations, oxyborate Fe$_{2}$OBO$_{3}$ has been found to show certain structural and physical features in connection with a continuous CO transition [1, 2]. By using\textit{ In-situ }TEM technique, we revealed that the charge-ordering transition characterized by an incommensurate modulation could evidently result in remarkable polar nanodomains at low temperatures. This kind of nanodomain could play a critical role in triggering a high dielectric constant and notable dielectric dispersion as observed in Fe$_{2}$OBO$_{3}$. Moreover, measurements of the magnetoelectric coupling under electrical field demonstrate the existence of giant electrically induced changes in magnetization around the magnetic transition [1, 2]. 1.Y. J. Song et al., Phys. Rev. B 81, 020101(R) (2010). 2.H. X. Yang et al., Phys. Rev. Lett. 106, (2011) 016406.   

Ferroelectric Phase Transition in Pb$_{5}$Cr$_{3}$F$_{19}$ and Coupling of Electric Polarization and Magnetization

The ferroelectric fluoride Pb$_{5}$Cr$_{3}$F$_{19}$ with ferroelectric/paraelectric phase transition at 545 K offers a possibility of multiferroic behavior. The paramagnetic Cr$^{3+}$ ion with electronic spin 3/2 has two inequivalent positions in the unit cell and is responsible for magnetic properties. These properties were measured with a SQUID magnetometer from 2 K to 630 K in addition to our earlier EPR measurements. At the ferroelctric/paraelectric phase transition the lattice parameters (c and a unit cell dimensions) experience relatively big changes leading to alteration of magnetic dipole-dipole and exchange interactions. The temperature dependence of magnetic susceptibility times temperature around the phase transitioin was analyzed following the usual free energy expansion. We obtained that a coupling between the electric polarization and the magnetization is quadratic. A magnetic anomaly was observed below 25 K.   

The origin and coupling mechanism of magnetoelectric effect in \textit{TM}Cl$_{2}$-4SC(NH$_{2})_{2}$ (\textit{TM} = Ni and Co)

Most research on multiferroics and magnetoelectric effects to date has focused on inorganic oxides. Metal organic frameworks (MOF) are a new field in which to search for ferroelectricity and explore new coupling mechanisms between electricity and magnetism. We will present the magnetic and electric properties of NiCl$_{2}$-4SC(NH$_{2})_{2}$, DTN, and CoCl$_{2}$-4SC(NH$_{2})_{2}$, DTC, compounds as a function of temperature, magnetic, and electric field. We gain insights into the coupling mechanism by observing that in DTN the electric polarization closely tracks the magnetic ordering whereas in DTC it does not. For DTN, all electrically polar thiourea, SC(NH$_{2})_{2}$, molecules are tilted in the same direction along the c-axis, breaking spatial inversion symmetry, whereas for DTC, two thiourea molecules are pointing up and the other two thiourea molecules are pointing down direction with respect to c-axis, perfectly canceling the net electrical polarization. Thus the magnetoelectric coupling mechanism is likely magnetostrictive adjustments of the thiourea molecule orientation in response to magnetic order.   

Session Q33: Focus Session: X-ray and Neutron Instruments and Measurement Science

Science Enabled by the Advanced Photon Source Upgrade

The Advanced Photon Source (APS) at Argonne National Laboratory is embarking on a major Upgrade that will significantly enhance capabilities for research using high brilliance, high energy synchrotron x-ray beams. The APS is a DOE Office of Science user facility that provides access to x-ray scattering, spectroscopy, and imaging instruments through an open, peer-reviewed proposal process. Currently 64 simultaneously operating beamlines are used by more than 4000 researchers each year across the full range of science and technology fields. The APS Upgrade project will provide major improvements to the x-ray sources as well as more than a dozen new or upgraded beamlines. Key areas of emphasis are using penetrating, high energy x-rays for atomic-scale studies of real materials in real time under real conditions, imaging of hierarchical structures on length scales from millimeters to nanometers, and ultrafast studies of chemical and physical processes on time scales down to picoseconds. I will illustrate the science enabled by the APS Upgrade using examples such as developing synthesis of new materials with outstanding properties and probing picosecond dynamics in energy conversion systems.   

Initial Results and Future Plans for the Soft X-ray Instrument for Materials at the Linac Coherent Light Source (LCLS)

For two years ultrafast high intensity x-ray pulses have been available at the Linac Coherent Light Source, the x-ray free electron laser at the SLAC National Accelerator Laboratory. The soft x-ray instrument (SXR) operates at an energy range from 480eV-2000eV and features a plane grating monochromator as well as a bendable refocusing mirror system. The measured performance of the instrument will be presented as well as the future direction for instrumentation development. \\[4pt] Acknowledgement: This research was carried out on the SXR Instrument at the Linac Coherent Light Source (LCLS), a division of SLAC National Accelerator Laboratory and an Office of Science user facility operated by Stanford University for the U.S. Department of Energy. The SXR Instrument is funded by a consortium whose membership includes the LCLS, Stanford University through the Stanford Institute for Materials Energy Sciences (SIMES), Lawrence Berkeley National Laboratory (LBNL), University of Hamburg through the BMBF priority program FSP 301, and the Center for Free Electron Laser Science (CFEL).   

Microfocusing options for sector 3 of the Advanced Photon Source upgrade project

Synchrotron radiation from third generation, high-brilliance rings is an ideal source for x-ray microbeams. The aim of this report is to describe a micofocusing scheme that combines both a toroidal mirror and a Kirkpatrick-Baez (KB) mirrors for upgrading the existing optical system for inelastic x-ray scattering experiments at sector 3 at the Advanced photon Source (APS). Shadow ray tracing simulations show that this combination can provide beam sizes of 4.5 $\mu $m (H) $\times $ 0.6 $\mu $m (V) (FWHM) at the end of the existing D-station (66 m from the source) with a transmission of up to 59 {\%} and a beam size of 3.7 $\mu $m (H) $\times $ 0.46 $\mu $m (V) (FWHM) at the front end of proposed E-station (68 m from the source) with a transmission of up to 57 {\%}. With this new setup, experiments that combine high pressure, low temperature and external magnetic field can be done.   

Advances in X-ray Raman spectroscopy at Stanford Synchrotron Radiation Lightsource

We present a state-of-the-art x-ray Raman spectroscopy end-station recently developed, installed, and operated at the Stanford Synchrotron Radiation Lightsource. The end-station consists of two multicrystal Johann type spectrometers arranged on a Rowland circle of 1m. The first one, positioned at the forward scattering angles (low-q), consists of 40 diced and spherically bended Si(110) crystals of 4" of diameter providing a large solid angle of detection as well as an overall energy resolution of about 270 meV at 6462.20 eV. The second spectrometer, consisting of 14 spherically bent Si(110) crystal analyzers, is positioned at the backward scattering angles (high-q) enabling the study of non-dipole transitions. These features, in particular the improved total resolution with a substantial increase in solid angle, positions the instrumentation as a unique alternative to soft x-ray absorption for difficult sample conditions and bulk sensitive measurements, which allows a systematic implementation of this photon-in/photon-out hard x-ray technique on emerging research of multidisciplinary scientific fields in energy-related science, physics, and material science. Preliminary results and prospects will be presented and discussed, in particular for applications in Energy Science.   

Facility Overview and Double-Focusing Thermal Triple-Axis Spectrometer at the NCNR

We will briefly overview the neutron scattering instrumentation at the NCNR, but will focus the talk on the capabilities of the new thermal triple-axis spectrometer is located at the BT-7 beam port [1]. This spectrometer takes full advantage of the large 165 mm diameter reactor beam to tailor the dual 20$\times $20 cm$^{2}$ double-focusing monochromator system to provide monochromatic fluxes exceeding 10$^{8}$ n/cm$^{2}$/s onto the sample. The two monochromators installed are PG(002) and Cu(220), which provide incident energies for 5 meV to above 500 meV. The computer controlled analyzer system offers six standard modes of operation, including a diffraction detector, a position-sensitive detector (PSD) in diffraction mode, horizontal energy focusing analyzer with detector, a \textbf{Q}-E mode employing a flat analyzer and PSD, a constant-E mode with the analyzer crystal system and PSD, and a conventional mode with a selection of S\"{o}ller collimators and detector. Additional configurations for specific measurement needs are also available. The capabilities and performance will be discussed and examples of published data presented. \\[4pt] [1] J. W. Lynn, Y. Chen, S. Chang, Y. Zhao, S. Chi, W. Ratcliff, II, B. G. Ueland, and R. W. Erwin, J. Research NIST 117 (in press).   

Advanced Thermal Neutron Detectors

With the advent of new high intensity spallation sources, there is a vital need for development of advanced position sensitive detectors. Using neutron conversion in helium 3, which yields a large signal with excellent background rejection capability, our research program focuses on improving the rate capability, resolution, efficiency and long term stability of detectors for neutron scattering studies. We have developed a suite of detectors using proportional chambers, the latest being an array of curved, multi-wire segments with interpolating cathode strip electrodes operating simultaneously and seamlessly in a single gas volume. With rate capability of nearly 1 million per sec, this instrument has significantly advanced the state-of-the-art for protein crystallography. To attain even higher count rates, a new concept based on operation in the ionization mode is being explored, in which direct ionization from a neutron conversion is collected with unity gain on one of many pads that form the anode plane. Each pad is implemented with charge sensitive electronics, using purpose-designed application specific integrated circuits. A prototype device with 48 by 48 pads has been successfully developed. Examples of measurements at major neutron user facilities will be presented.   

The wetting behavior of electrolytes at charged carbon electrode materials probed using neutron scattering

Breakthroughs in the performance of energy storage technologies come from efficient combinations of novel electrolytes and electrode materials. Knowledge of the structure of these materials under applied electric fields is necessary to better tailor them to our energy needs. Neutron scattering, as a structural probe to investigate the ordering of electrolytes at an interface, or the effects of confinement on an electrolyte in a nanoporous matrix, is well suited since the electrolytes commonly used contain hydrogen and the host matrix can often contain active sites that are difficult to discern without the use of contrast matching via isotopic substitution. We present small angle neutron scattering results, conducted at the EQ-SANS (ORNL) instrument and at the Low-Q Diffractometer (LANL), from in situ electrochemical measurements of a deuterated ionic liquid, and of aqueous electrolytes, in a mesoporous carbon membrane at different applied potentials over time. Recent neutron reflectometry measurements (LR, SNS) complement the observed behavior from SANS. We observe a higher electrolyte density near the electrode material surface, compared to without an applied potential. Furthermore, this high density region persists long after the applied potential is removed.   

Combined X-Ray and Neutron Powder Diffraction Studies of Nanoscale Ca$_{5-x}$Fe$_{x}$(PO$_{4})_{3}$OH Systems

Multi-substituted hydroxyapatite (HAp) with crystallite size 4-130 nm is the major mineral phase in physiological apatites. Substitutions at all ionic sites affect their physicochemical properties. Fe is one of the minor substitutions at the Ca sites of HAp. It is important because it reduces the solubility of HAp, functioning as a cavities preventive agent, whereas Fe overload leads to a decreased mechanical strength and osteoporosis. Powder x-ray and neutron diffraction methods as well as energy-filtered transmission electron microscopy were used to study the effect of Fe substitution on the crystal structure properties of the Ca$_{(5-x)}$Fe$_{x}$(PO$_{4})_{3}$OH systems. Single phase HAp is identified in systems with x $\le $ 0.1. Hematite is formed for higher x. Simultaneous Rietveld refinement of the x-ray and neutron diffraction patterns reveals an unexpected increase of the a-lattice constant. It is attributed to the increase of the Ca1-O3 and Ca2-O1 interatomic distances indicating a local lattice relaxation. Fe substitutes in both Ca1 and Ca2 sites with a preference to the Ca2 site and an occupancy up to 0.05 for x=0.3. Magnetic measurements reveal a transition from the diamagnetic state of the HAp to the paramagnetic of the Fe-doped systems.   

Profile retrieval using Spin-Echo Resolved Grazing Incidence Scattering combined with dynamical scattering theory

Spin-echo Resolved Grazing Incidence Scattering (SERGIS) is a novel neutron scattering technique that provides lateral and in-depth characterization of density correlations in thin films and at interfaces. The method can be used to study the self-assembly of materials in a periodic array of nano-channels such as a diffraction grating. Since scattering from such periodic structures is dominated by dynamical effects that are not accounted for in approximate scattering theories, we developed a dynamical theory (DT) model, based on a Parratt formalism, and tested it on SERGIS data collected from a set of nanostructured gratings with different profiles in various scattering geometries. The model shows good agreement with all the data sets obtained so far. We found that the SERGIS technique is very sensitive to slight variations in the scattering geometry and the sample profile and the DT calculations accurately reproduce this sensitivity. This is a very promising step in combining a neutron scattering technique with an exact theory to retrieve profile information of periodic samples with unknown structures and to probe the morphology of self-assemblies in periodic nano-confinements.   

Session Q34: Focus Session: Nano IV: Nanocatalysis

Cluster size effects on chemical and physical properties of model catalysts

Model catalysts are prepared by deposition of size- and energy-selected metal clusters on well characterized solid supports in an ultrahigh vacuum system. The system provides capabilities to probe the physical properties of the samples by X-ray and ultraviolet photoelectron spectroscopy (XPS, UPS), ion neutralization spectroscopy (INS), and low energy ion scattering (ISS). The chemical properties can be probed by a variety of pulsed, temperature-programmed, and constant temperature mass spectrometric methods, and resulting changes in physical properties from interactions with adsorbates are probed by XPS, UPS, INS, and or ISS. Recently, capabilities for in situ electrochemical characterization were added. Results from several systems will be presented, including gas-surface reactions over Pd/alumina and Pd/titania, and solution phase oxygen reduction over Pt/glassy carbon.   

CO Oxidation on Copper Oxide Cluster Ions

We investigated the reaction of CO and O$_2$ on size-selected copper cluster ions, Cu$_n^+$ ($n$=4--18) and Cu$_n^-$ ($n$=4--11), by use of a tandem mass-spectrometer equipped with octopole ion guides. A coadsorbing product, Cu$_n$O$_2$(CO)$^+$, was observed in the reaction of Cu$_n$O$_2^+$ with CO, and it was found that CO adsorbs onto Cu$_n$O$_2^+$ more efficiently than onto Cu$_n^+$ in $n \geq 9$. This shows the cooperative coadsorption of O$_2$ and CO. On the other hand, in the reaction of Cu$_n$O$_2^-$ with CO, a reduced product, Cu$_n$O$^-$, was obtained instead of the coadsorbing product, Cu$_n$O$_2$(CO)$^-$. In particular, Cu$_5$O$_2^-$ and Cu$_9$O$_2^-$ have relatively high efficiency for the production of Cu$_n$O$^-$. This result suggests the production of CO$_2$ by the oxidation of CO on Cu$_n$O$_2^-$. The DFT calculation indicates that the activation energy in the reaction of Cu$_5$O$_2$(CO)$^-$ $\rightarrow$ Cu$_5$O(CO$_2$)$^-$ is only 0.79 eV while that of the corresponding cation is 1.79 eV. The structure of Cu$_n^-$ is more flexible than that of Cu$_n^+$ probably because of its excess electron. It is concluded that the stabilization of the transition state and the decrease of the activation energy make the CO oxidation proceed on Cu$_n$O$_2^-$.   

Effective rate constants for nanostructured heterogeneous catalysts

There is currently a high level of interest in the use of nanostructured materials for catalysis. For instance, gold, which is largely inert in the bulk, can exhibit strong catalytic activity when in nanoparticle form. With precious metal catalysts such as Pt and Pd in high demand, the use of these materials in nanoparticle form can also substantially reduce costs by exposure of more surface area for the same volume of material. When reactants are plentiful, the effective activity of a nanoparticulate catalyst will increase roughly with its surface area. However, under diffusion-limited conditions, the reactant must diffuse to active sites on the catalyst, so a high surface area and a high density of active sites may bring diminishing returns if reactant is consumed faster than it arrives. Here we apply a mathematical homogenisation approach to derive simple expressions for the effective reactivity of a nanostructured catalyst under diffusion limited conditions that relate the intrinsic rate constants of the surfaces presented by the catalyst to an effective rate constant. When highly active catalytic sites, such as step edges or other defects are present, we show that distinct limiting cases emerge depending on the degree of overlap of the reactant depletion zone about each site. In gases, the size of this depletion zone is approximately the mean free path, so the effective reactivity will depend on the structure of the catalyst on that scale. We discuss implications for the optimal design of nanoparticle catalysts. \newline   

Towards a Molecular Level Understanding of CO and H$_{2}$ Adsorption and Dissociation on Cobalt Nanoparticles

The development of sustainable energy technologies, including the production of synthetic fuels, is of global importance. Fischer-Tropsch synthesis (FTS) has recently gained increased attention as it involves the formation of hydrocarbons via the catalytic conversion of syngas (CO and H$_{2})$, which can be derived from renewable sources. FTS is often performed using Co-based catalysts that are greatly affected by the adsorption state of reactants, as well as nanoparticle shape and size. Here we have used low-temperature scanning tunneling microscopy (LT-STM) to study the interaction of syngas with well-defined Co nanoparticles grown onto Cu {\{}111{\}}, an inert metal for FTS. Hydrogen adsorbs dissociatively on the Co surfaces, resulting in three unique coverage-dependent phases. We demonstrate that these phases can resolve crystal packing ambiguities of the underlying Co nanoparticles, a question that has been debated in the literature. Simultaneous exposure of the Co to H$_{2}$ and CO results in segregated islands of the adsorbates on the nanoparticle surface at 80 K, and we propose that atomic H blocks CO adsorption, causing the build-up of CO at the nanoparticle step edges. With increasing CO coverage, a two-dimensional phase compression of H by CO is observed, providing \textit{the first direct} visualization of this phenomenon in a catalytically relevant system. Our data suggest that FTS reactivity may be dominated by the interface length between the adsorbates and be subject to unforeseen kinetic restraints as a function of particle size.   

Cooperative Effects in the Oxidation of CO by Palladium Oxide Cations

It is shown that cooperative reactivity plays an important role in the oxidation of CO to CO$_{2}$ by palladium oxide cations. Comprehensive studies including guided-ion-beam mass spectrometry and theoretical investigations reveal the reaction products and profiles of PdO$_{2}^{+}$ and PdO$_{3}^{+}$ with CO through oxygen radical centers and dioxygen complexes bound to the Pd atom. We find that the O radical centers are more reactive than the dioxygen complexes, and experimental evidence of both direct and cooperative CO oxidation with the adsorption of two CO molecules are observed. The binding of multiple electron withdrawing CO molecules is found to increase the barrier heights for reactivity due to decreased binding of the secondary CO molecule, however reactivity is enhanced by the increase in kinetic energy available to hurdle the barrier. We examine the effect of oxygen sites, cooperative ligands, and spin including two-state reactivity.   

Design of nanocatalysts for improved selectivity and stability

Several examples from ongoing work in our laboratory on the use of self-assembly to prepare heterogeneous catalysts with novel architectures will be discussed in this presentation. In one case, catalysts consisting of dispersed platinum metal nanoparticles with narrow size distributions and well-defined shapes were prepared and tested for the selective promotion of carbon-carbon double-bond cis-trans isomerization reactions in olefins. It was shown that the selective formation of the cis isomer could be controlled by using tetrahedral particles with exposed (111) facets. In a second example, catalysts based on small platinum nanoparticles of well-defined sizes were made by using dendrimers as scaffolding structures. The organic framework in that case can provide new fuctionality, including chirality as a way to introduce enantioselectivity. The third example involves the control of metal nanoparticle sintering by covering those with a layer of mesoporous silica grown on top. The final case to be discussed is one where yolk@shell metal-semiconductor constructs are being developed for increase stability in oxidation and photocatalytic applications.   

Towards Catalysis by Gold Clusters: reaction cycles and poisons

Nanosized gold particles are good catalysts in a variety of oxidation reactions. These reactions, for which oxidation of CO to CO$_2$ serves as a paradigm, imply a transition in the total spin and therefore do not occur spontaneously in the gas phase. In the catalytic process, the catalyst clusters are exposed to an atmosphere of gas-phase O$_2$ and CO reactants at finite temperature and pressure. We have thus modeled free gold clusters in contact with an atmosphere composed of O$_2$ and CO by means of DFT calculations (PBE functional), and accounted for both temperature and pressure effects employing \textit{ab initio} atomistic thermodynamics. On the basis of this analysis, we could recognize the thermodynamic driving force of the catalytic CO oxidation process and single out the possible ($p,T$)-dependent reaction cycles and those paths leading to stable structures that poison the catalytic process. This as a useful (exploratory) theoretical step, before taking chemical reaction kinetics into consideration. In the proposed reaction paths, the total spin is conserved in each elementary step, and it is the adsorption of an incoming O$_2$ molecule that drives the catalyst cluster from the singlet to the triplet spin state, and \textit{vice versa}.   

Breaking Carbonyl Bonds in Formaldehyde via Complementary Active Sites

We had recently shown that the complementary active sites in homonuclear clusters may stimulate the breaking of polar bonds enabling an atomic level control of reactivity. However, such bond cleavage has only been observed in hydroxyl bonds. In this work, we present experimental and theoretical evidence that demonstrates that the stronger C=O carbonyl bond of formaldehyde is split by complementary active sites on size selective aluminum cluster anions. The resonance structure in which the carbonyl is reduced to a single bond is stabilized by the paired active sites establishing the potential use of these geometrically driven centers in devising precursors for synthesizing chemicals or radicals that might find use in production of fine chemicals.   

Morphological, electronic, and catalytic properties of Pt nanoclusters on defective graphene

The synthesis of well dispersed, size-controlled Pt nanoclusters on carbon supports is highly desirable since such clusters have been shown to possess enhanced catalytic activity and selectivity in a variety of chemical reactions. However, these nanoclusters interact rather weakly with defect-free carbon supports and can coarsen over time leading to loss of surface area and thence catalytic activity. Defects in carbon supports play an important role in enhancing Pt-carbon bonding, thereby reducing the propensity for cluster coalescence. Using a combination of density functional theory and empirical potential simulations, we examine the interaction of Pt nanoclusters with point defects in graphene. We focus on the role of the support defects in controlling the morphology, electronic structure, and CO-tolerance of Pt nanoparticles. Our results suggest possible avenues for controlling the dispersion and activity of Pt nanoclusters on carbon supports via defect engineering.   

Controlled Catalytic Properties of Platinum Clusters on Strained Graphene

We employed biaxially strained graphene as the supporting material for Pt clusters (Pt$_{x}$, x=1, 4 or 6) and studied the molecular adsorption behaviors of H$_{2}$, CO and OH on the cluster using ab initio calculations. It was shown that the applied strain enhances binding of the Pt cluster on the graphene, which lowers the average energy of Pt d electron (d-band center). The binding energies of H$_{2}$, CO and OH on Pt$_{1}$/graphene are strongly correlated with the d-band center modulated by the graphene strain. The calculations with small Pt clusters (Pt$_{4}$ and Pt$_{6}$) also show that the d-band center is a substantial factor for the catalytic activity of the Ptx/graphene system. We also found that the stability of the Pt clusters was enhanced by applying the strain on the graphene support.   

Composition-Dependent Size and Shape Changes of Pt-Rh Alloy Nanoparticles on $\alpha$-Al$_2$O$_3$(0001) during CO Oxidation Reactions

Pt-Rh nanoparticles are widely used in chemical industry and in automotive exhaust control where they catalyze among other reactions the oxidation of CO. Major attention has in recent years been paid to the study of alloy nanoparticles with the aim to identify systems that allow to control the catalyst selectivity and to enhance its activity and lifetime [1]. Sintering is regarded as one of the major causes of catalyst deactivation and it is of utmost scientific and economic interest to find ways to prevent it. Here we present concentration-dependent size and shape changes of epitaxial Pt-Rh alloy nanoparticles on $\alpha$-Al$_2$O$_3$(0001) substrates observed in-situ during CO oxidation at near atmospheric pressures. The experiments were carried out in a flow-reactor at the high energy beamline ID15A (ESRF) by means of grazing incidence x-ray diffraction (E=78.8 keV), x-ray reflectivity measurements and in-situ mass-spectrometry [2]. During the experiments the O$_2$ pressure ranged between 0 and 14 mbar while the temperature and CO pressure were kept at 550 K and 20 mbar, respectively. Our results demonstrate that a higher Rh concentration reduces sintering significantly.\\[4pt] [1] J.Y. Park et al., Nano Lett. 8 673 (2008)\\[0pt] [2] R. v. Rijn et al., Rev. Sci. Instr. 81 014101 (2010)   

Session Q35: Focus Session: DFT VI: New Functional Developments

Some thoughs about old and new density functionals

The only theoretical approximation that lies at the heart of DFT appears is the (in)famous exchange-correlation functional. It is therefore not surprising that this quantity has been extensively studied, and that more than 150 different approximations have been put forward in the past 50 years. In this talk I will show some results concerning different families of functionals. The first concerns hybrid functionals, and in particular the role of the mixing parameter. This is commonly assumed to be fixed at a value around 0.2-0.3. However, by noting the similarities between the hybrid functionals and screened Hartree-Fock and ultimately GW theories, we can relate this parameter to the screening properties of the system. In this way we can build a recipe that allows for a considerable improvement on the results obtained by traditional hybrid functionals for solids. As a second topic, I will discuss if it is possible to completely get rid of the Slater integrals present in both Hartree-Fock, hybrid functionals or OEP approaches, and anyway get a proper description of the exchange in terms of reduced densities. I will pay particular attention to the new meta-GGA functionals for the exchange potentials, like, e.g., the Becke-Johnson potential and its more recent variations, like the Tran and Blaha or the Rasanen, Pittalis, and Proetto functionals.   

Self-interaction corrected Kohn--Sham potentials

Exchange-correlation potentials derived from conventional density-functional approximations fail to exhibit the slow Coulombic decay---a problem that is related to the self-interaction error in the potential. We show how the self-interaction error of standard semilocal approximations can be effectively reduced by employing modified electron densities to construct the corresponding Kohn--Sham potentials. Using this correction scheme in the framework of adiabatic time-dependent density-functional theory we obtain significantly improved electronic excitation energies, especially for Rydberg states.   

Density-on-wave-function mapping beyond the Hohenberg-Kohn theorem

Density-functional theory is based on the Hohenberg-Kohn theorem, establishing a one-on-one mapping between ground-state densities and wave functions. That theorem does not, however, make a direct statement on whether two wave functions that are in some sense close are mapped on two densities that are also close, and vice versa. In this work, a metric is defined that allows to quantify the meaning of ``close'' in the preceding sentence. This metric stratifies Hilbert space into concentric spheres on which maximum and minimum distances between states can be defined and geometrically interpreted. Numerical calculations for the Helium atom, Hooke's atom and a lattice Hamiltonian show that the mapping between densities and ground states, which is highly complex and nonlocal in the coordinate description, in metric space becomes a monotonic and nearly linear mapping of vicinities onto vicinities. In this sense, the density-on-wave-function mapping is not only simpler than expected; it is as simple as it could be. \\[4pt] I. D'Amico, J. P. Coe, V. V. Fran\c{c}a, and K. Capelle, Phys. Rev. Lett. 106, 050401 (2011) and Phys. Rev. Lett. 107, 188902 (2011). See also E. Artacho, Phys. Rev. Lett. 107, 188901 (2011).   

Finding density functionals with machine learning

Using standard methods from machine learning, we introduce a novel technique for density functional approximation. We use kernel ridge regression with a Gaussian kernel to approximate the non-interacting kinetic energy of 1-dimensional multi-electron systems. With fewer than 100 training densities, we can achieve mean absolute errors of less than 1 kcal/mol on new densities. We determine densities for which our new functional will fail or perform well. Finally, we use principle component analysis to extract accurate functional derivatives from our functional, enabling an orbital-free minimization of the total energy to find a self-consistent density. This empirical method has two parameters, set via cross-validation, and requires no human intuition. In principle, this general technique can be extended to multi-dimensional systems, and can be used to approximate exchange-correlation density functionals.   

New Density Functionals with Broad Applicability in Chemistry (SOGGA11, SOGGA11-X, M11, M11-L) and Approaches to Open-Shell DFT

The accuracy of density functional theory for practical applications is determined by the quality of the necessarily approximate exchange-correlation functional (``density functional'') being used, and the goal of functional development in chemical physics is to obtain a functional that is accurate for a broad range of chemistry and physics. In our work we consider molecular structures and solid-state lattice constants and band gaps, but we emphasize energetics for main-group and transition-metal chemistry, including thermochemistry and barrier heights, noncovalent interaction energies, and excitation energies. This lecture will discuss four new density functionals, each optimized to give the best across-the-board performance for a broad range of chemistry in their class of functional: SOGGA11, a generalized gradient approximation (GGA); SOGGA11-X, a global hybrid GGA; M11: a range-separated hybrid meta-GGA, and M11-L, a meta-GGA. SOGGA11 and M11-L are local functionals, and SOGGA11-X and M11 include some nonlocal Hartree--Fock exchange. To the extent that time permits, I may also discuss recent progress in the treatment of open-shell systems by density functional theory, including time-dependent DFT, open-shell SCF, and noncollinear DFT. This invited lecture is based on collaborative research carried out with Roberto Peverati, Sijie Luo, Ke Yang, Boris Averkiev, Yan Zhao, and Rosendo Valero.   

Self-Interaction Free and Analytic Treatment of the Coulomb Energy in Kohn-Sham Density Functional Theory

We have developed a new treatment of the LDA functional in Kohn-Sham density functional theory which is expressed in terms of the pair density of a non-interacting system of particles, thus avoiding from the outset self-interaction effects. The pair density is expressed explicitly in terms of the density using a orthonormal and complete basis expressed as a functional of the density. This allows its functional differentiation with respect to the density and therefore the determination of the self-interaction free Coulomb potential by analytic means. The method is illustrated with numerical results for the atom series.   

Electronic structure via potential functional approximations

The universal functional of Hohenberg and Kohn is given as a coupling-constant integral over the density as a functional of the potential [1]. Conditions are derived under which potential-functional approximations are variational. Construction via this method and imposition of these conditions are shown to greatly improve the accuracy of the non-interacting kinetic energy needed for orbital-free Kohn-Sham calculations. This result provides a direct route to a self-consistent, orbital-free theory for the electronic structure of matter within the Kohn-Sham framework. It solely requires an approximation to the non-interacting density as a functional of the potential, which, so far, has been derived for simple systems [2,3]. \\[4pt] [1] A. Cangi, D. Lee, P. Elliott, K. Burke, E. K. U. Gross, Phys. Rev. Lett. 106, 236404, (2011).\\[0pt] [2] A. Cangi, D. Lee, P. Elliott, K. Burke, Phys. Rev. B 81, 235128, (2010).\\[0pt] [3] P. Elliott, D. Lee, A. Cangi, K. Burke, Phys. Rev. Lett. 100, 256406, (2008).   

Self-Consistent Random Phase Approximation

We report self-consistent Random Phase Approximation (RPA) calculations within the Density Functional Theory. The calculations are performed by the direct minimization scheme for the optimized effective potential method developed by Yang et al. [1]. We show results for the dissociation curve of H$_{2}^{+}$, H$_{2}$ and LiH with the RPA, where the exchange correlation kernel has been set to zero. For H$_{2}^{+}$ and H$_{2}$ we also show results for RPAX, where the exact exchange kernel has been included. The RPA, in general, over-correlates. At intermediate distances a maximum is obtained that lies above the exact energy. This is known from non-self-consistent calculations and is still present in the self-consistent results. The RPAX energies are higher than the RPA energies. At equilibrium distance they accurately reproduce the exact total energy. In the dissociation limit they improve upon RPA, but are still too low. For H$_{2}^{+}$ the RPAX correlation energy is zero. Consequently, RPAX gives the exact dissociation curve. We also present the local potentials. They indicate that a peak at the bond midpoint builds up with increasing bond distance. This is expected for the exact KS potential.\\[4pt] [1] W. Yang, and Q. Wu, \emph{Phys. Rev. Lett.}, {\bf 89}, 143002 (2002)   

On the Hohenberg-Kohn and Levy-Lieb Constrained Search Proofs of Density Functional Theory

In HK, a 1-1 relationship between the density $\rho ({\bf{r}})$ and the potential $v({\bf{r}})$ is established. (The relationship between $v({\bf{r}})$ and the ground state $\Psi$ is 1-1.) The proof, valid for $v$-representable densities, shows $\rho({\bf{r}})$ to be a basic variable. The LL proof is independent of $v({\bf{r}})$, and is valid for $N$-representable densities. In,\footnote{Pan and Sahni, IJQC 110, 2833 (2010)} we have proved that in an external magnetic field ${\bf{B}}({\bf{r}})=\mathbf{\nabla} \times {\bf{A}}({\bf{r}})$, there is a 1-1 relationship between $\{\rho({\bf{r}}), {\bf{j}} ({\bf{r}})\}$, with ${\bf{j}}({\bf{r}})$ the physical current density, and the potentials $\{v({\bf{r}}), {\bf{A}}({\bf{r}})\}$. (The relationship between $\{v({\bf{r}}), {\bf{A}}({\bf{r}})\}$ and $\Psi$ is \emph{many-to-one}.) This proves that $\{\rho({\bf{r}}), {\bf{j}}({\bf{r}})\}$ are the basic variables. The LL proof independent of $\{v({\bf{r}}), {\bf{A}}({\bf{r}})\}$ follows readily. However, such a proof also follows if $\{\rho({\bf{r}}), {\bf{j}}_{p}({\bf{r}})\}$, with ${\bf{j}}_{p}({\bf{r}})$ the paramagnetic current density, are considered the basic variables. As such knowledge of the basic variables as determined via HK is a pre-requisite to any LL type proof.   

Efficient van der Waals energy calculations via a continuum mechanics approach

Recent developments in continuum mechanics (CM) [Tao \emph{et al}, PRL{\bf 103},086401] enable the calculation of density response functions from groundstate properties only. Using the direct Random Phase Approximation (dRPA) we develop this CM approach into a third-rung van der Waals energy functional, which we dub the CM-dRPA. The functional requires as input the groundstate Kohn-Sham potential $V^{\rm{KS}}(\vec{r})$, density $n^0(\vec{r})$ and a kinetic stress tensor ${\rm{T}}^0(\vec{r})$ defined via $T^0_{\mu\nu}=Re\sum_{i\rm{ occ}} \psi_{i,\mu}^*\psi_{i,\nu} - n^0_{,\mu,\nu}/4$ where $\psi_i$ is an orbital. We present efficient algorithmic schemes for its evaluation in bulk and molecular systems using the full eigen-solutions of the bare CM equation and a second, simpler evaluation to find the interacting eigenvalues. These eigen-solutions are then used to calculate the correlation energy via a simple summation. The CM-dRPA is \emph{significantly} faster than a full dRPA calculation in systems with many electrons. We then apply the CM-dRPA functional to metallic, slab-like 2D-homogeneous jellium systems and periodic solids, with good results for vdW dispersion. In the metallic case most efficient vdW functionals would fail qualitatively.   

Session Q36: Water and Ice

Ionic force field optimization and modified ion-pair mixing rules

We propose an optimization scheme to obtain good ionic force fields for classical simulations of salt solutions, also of biological relevance. Our work is based on Molecular Dynamics simulations with explicit (SPC/E) water for different halide and alkali ions forming salt solutions at finite ion concentration. The force field derivation technique we propose is based on a simultaneous optimization of single-ion and ion-pair properties and the determination of the cation-anion interaction parameters (traditionally given by the mixing rules). From the finite-concentration simulations, thermodynamic properties of the salt solutions are derived, using the Kirkwood-Buff theory of solutions, and compared to relevant experimental data. For the rather size-symmetric salt solutions involving bromide and chloride ions, this scheme using the standard mixing rules works fine. For the iodide and fluoride solutions, corresponding to the largest and smallest anion we have considered, a rescaling of the mixing rules was necessary. In this respect, we have introduced scaling factors for the cation-anion Lennard-Jones interaction that quantify deviations from the standard mixing rules. We discuss the efficiency and complications of the proposed ionic force field optimization scheme.   

Effects of Applied Electric Field on the Dynamics of Nano-Confined Water

We present quasi-elastic neutron scattering measurements of the proton diffusion in water confined in silica nanopores (FSM), with average pore diameters of 16 {\AA} and 39 {\AA}. The measurements were performed on the high resolution backscattering silicon spectrometer (BaSiS) at the Spallation Neutron Source (SNS). From the data, we determine the self diffusion constants, and the translational and rotational relaxation times, as a function of temperature from 300 K down to 200 K. We observe a significant slowing down of the proton diffusion as the temperature is lowered, and a remarkable effect of confinement of the translational motion. Recent results on the effects of applied electrical field on these dynamical processes will be reported.   

Competing Nuclear Quantum Effects and van der Waals Interactions in Water

Water plays a central role in many scientific disciplines, and a number of studies have been performed to understand its properties. However, providing an accurate ab initio description is a significant challenge, and because of this, many of water's properties remain elusive. In particular, the description of hydrogen bonding and the importance of van der Waals (vdW) interactions and nuclear quantum effects are still matters of debate. Recent computational advancements have been made that allow for the accurate and efficient modeling of such effects. We present results from path integral molecular dynamics simulations based on density functional theory employing exchange and correlation functionals capable of accounting for vdW interactions (so-called vdW-DF, vdW-DF2, and optB88-vdW). We demonstrate that, contrary to expectation, the interaction between nuclear quantum effects and vdW interactions hardens the structure of water. These results suggest that ad hoc methods to account for these effects, such as temperature rescaling of simulations employing classical nuclei, are insufficient to describe water, and that fully ab initio calculations must be performed. We discuss the implications of these results for understanding the local structure and hydrogen bonding in water.   

BSE/GW calculations of liquid and solid H$_2$O

We have calculated both the UV/VIS and Oxygen K-edge x-ray spectra of model ice and water systems within many-body perturbation theory using state-of-the-art Bethe-Salpeter equation (BSE) and GW self-energy approximations [1], as implemented in the valence- and core-excitation codes OCEAN and AI2NBSE [2]. While the various phases of crystalline ice have well-characterized structures, the local environment and fluctuations of liquid water remain subjects of debate. Due in part to limitations of previous theoretical models, the interpretation of experimental probes has been controversial. We find that the BSE approach, which provides an accurate treatment of core-hole interactions, is vital for a quantitative agreement between experiment and theory. Likewise the effects of self-energy corrections within the GW approximation are needed to explain the observed band-stretching and damping of the spectra. Prospects for further improvements are briefly discussed. \\[4pt] [1] J. Vinson, J. J. Kas, F. D. Vila, J. J. Rehr, and E. L. Shirley, arXiv:1010.0025 (2011).\\[0pt] [2] J. Vinson et al., Phys. Rev. B 83, 115106 (2011); H. M. Lawler et al., Phys. Rev. B 78, 205108 (2008).   

Effect of hydrogen bond cooperativity on the phase behavior of water

Four scenarios have been proposed for the low--temperature phase behavior of liquid water, each predicting different thermodynamics. The physical mechanism which leads to each is debated. Moreover, it is still unclear which of the scenarios best describes water, as there is no definitive experimental test. Here we address both open issues by analyzing a microscopic cell model within a mean--field limit. We show that a common physical mechanism underlies each of the four scenarios, and that two key physical quantities determine which of the four scenarios describes water: (i) the strength of the directional component of the hydrogen bond and (ii) the strength of the cooperative component of the hydrogen bond. The four scenarios may be mapped in the space of these two quantities. Using estimates from experimental data for H bond properties, the model predicts that the low-temperature phase diagram of water exhibits a liquid--liquid critical point at positive pressure.   

Structure and dynamics of the liquid water-ZnO$(10\bar{1}0)$ interface from first principles

Liquid water-metal oxide interfaces are of fundamental and technological interest. In this context, the water-ZnO$(10\bar{1}0)$ interface is an extensively studied system, which is also relevant for instance to the field of heterogeneous catalysis and photocatalysis. Yet, whether or not water dissociates at this surface at coverages exceeding one monolayer is still a matter of debate. Likewise questions about proton transfer to the surface, water diffusion and rearrangement within the hydrogen-bonded network remain unanswered. Here we report the first density functional theory (DFT) molecular dynamics study of a liquid water film on ZnO$(10\bar{1}0)$ and of water at monolayer coverages. The water structure obtained for the first layer in the liquid simulation differs quite significantly from that at monolayer coverage. Hydrogen bonding between the first layer and the water overlayer plays a crucial role in the stabilisation of the new adsorption structure. Rapid proton transfer and rattling within the hydrogen bonding network at the interface is observed and analysed in detail. On the whole, this study provides considerable new insight into water structure and dynamics and proton transfer at ZnO$(10\bar{1}0)$ and in the field of liquid water-metal oxides interfaces in general.   

Density fluctuations and dielectric constant of water in low and high density liquid states

The hypothesis of a liquid-liquid critical point (LLCP) in the phase diagram of water, though first published many years ago, still remains the subject of a heated debate. According to this hypothesis there exists a critical point near $T \approx 244$ K, and $P \approx 215$ MPa, located at the end of a coexistence line between a high density liquid (HDL) and a low density liquid state (LDL). The LLCP lies below the homogenous nucleation temperature of water and it has so far remained inaccessible to experiments. We study a model of water exhibiting a liquid-liquid phase transition (that is a liquid interacting through the ST2 potential) and investigate the properties of dipolar fluctuations as a function of density, in the HDL and LDL. We find an interesting correlation between the macroscopic dielectric constants and the densities of the two liquids in the vicinity of the critical point, and we discuss possible implications for measurements close to the region where the LLCP may be located.   

The role of quantum nuclear effects in hydrogen bonded crystals and their calculated NMR shielding constants

Because of its ubiquity in nature the hydrogen atom plays a very important role in computational materials science. As the lightest element, hydrogen nuclei are also the most strongly affected by quantum nuclear effects (QNEs). The path integral (PI) formalism provides a rigorous approach to obtain equilibrium quantum static properties, but PI simulations in conjunction with electronic structure calculations are rarely used due to high computational requirements. This contribution will discuss ab initio PI simulations aimed at elucidating the role of QNEs in hydrogen bonded crystals and how these impact upon experimental observables such as nuclear magnetic resonance (NMR) shielding constants and chemical shifts. We find that ab initio PI simulations improve the agreement with experimental chemical shifts compared to simulations with classical nuclei and that the influence of QNEs is very sensitive to the strength of the hydrogen bonds in the crystal.   

Selective mode analysis of nuclear quantum effects for liquid water using non-Markovian thermostats

Simulating nuclear quantum effects in liquid water using both DFT and force fields has been an active area of research in recent years. Recently, Ceriotti et. al [1] introduced a comprehensive framework to use a custom-tailored Langevin equation with correlated-noise in the context of molecular-dynamics simulations. One of the interesting applications of these thermostats is that, such a framework can be used to selectively damp normal modes whose frequency falls within a prescribed range. In this work we study how the flexible force field models respond to the selective mode thermostating using the delta-like memory kernels. We apply this delta thermostat to the molecular dynamics of TIP4P/F water force field [2], a model explicitly fitted with the lack of zero point ionic vibrations. We address the question of whether thermostating each mode to its zero point temperature is enough to generate the nuclear quantum effects in water and similar systems. This work also provides a way to identify the dominant modes for which the quantum effects are important. [1] M. Ceriotti, G. Bussi, and M. Parrinello, Phys. Rev. Lett. 103, 030603 (2009). [2] S. Habershon, T. E. Markland, and D. E. Manolopoulos, J. Chem. Phys 131, 024501 (2009 ).   

Anomalous nuclear quantum effects in ice

The lattice parameters of light (H$_2$O) and heavy (D$_2$O) Ih ice at 10 K differ by 0.09\%.$[1]$ The larger lattice constant is that of the heavier isotope. This isotope shift with anomalous sign is linked to the zero point point energy of phonons in ice. To determine the origin of this anomaly, we use \textit{ab initio} density functional theory to compute the free energy of ice within the quasiharmonic approximation. As expected, the frozen lattice constant at T = 0 K is smaller than the quantum lattice constant, independent of the isotopic substitution. We find that, the heavy isotope D gives more zero point expansion than H, whereas the heavy isotope $^{18}$O gives normal zero point expansion, i.e smaller than $^{16}$O. Relative to the the classical result, the net effect of quantum nuclei (H and O) on volume has the conventional (positive) sign at T = 0 but it becomes negative above 70 K, indicating that it may be also relevant for liquid water. These results are not reproduced by state of art polarizable empirical potentials.$[2]$ [1] B. K. R\"{o}ttger \textit{et. al.}, Acta Cryst. B {\bf 50}, 644-648 (1994). [2] C. P. Herrero and R. Ram\'{i}rez, J. Chem. Phys. {\bf 134}, 094510 (2011).   

Mechanism of sessile water droplet evaporation

The energy transport mechanisms during the evaporation of sessile water droplets have been investigated. Steady-state evaporation experiments were conducted on substrates of Cu, Au(111) and PDMS. The buoyancy-driven convection was suppressed by maintaining the droplets' base temperature just less than 4$^{\circ}$C while evaporation cooled the liquid-vapor interface to lower temperatures. The temperature fields were measured in solid (only in Au(111) experiments), liquid and vapor phases. On all three substrates, the energy balance at the liquid-vapor interface showed that thermocapillary convection transported the major portion of the energy required for the evaporation. It transported up to 98\% for Cu, up to 87\% for Au(111) and up to 72\% for PDMS. The role of thermocapillary convection is dominant close to three-phase contact line where most of the evaporation occurs. The experiment on Au (111) showed that of the energy supplied by the solid substrate, only a small portion is transported perpendicular to the solid-liquid interface to the bulk liquid phase. A much larger proportion is conducted through the adsorbed layer at the solid-liquid interface to the three-phase contact line where it is distributed by thermocapillary convection over the liquid-vapor interface and consumed by the phase change process.   

Theory and Simulation of Droplet Wetting on Patterned Surfaces

Liquid droplets can have multiple wetting modes on physically patterned surfaces, each corresponding to a (meta)stable state. For example, in the Cassie mode, the droplet resides on top of the pattern, while in the Wenzel mode, the droplet penetrates into the pattern. In this work, we study the wetting of patterned surfaces on two different length scales: on the nano-scale using molecular dynamics (MD) and on the macro-scale by minimizing free-energy expressions for various droplet wetting modes. We find that surface topography, size, and initial position of the droplet strongly affect the wetting states and contact angles. In the small Bond-number (small droplet) regime, the surface topography can be scaled by the droplet size, such that the preferred wetting modes and contact angles become independent of droplet size for surfaces with the same scaled topography. MD simulations and theory are in good agreement for small Bond numbers. For moderate to large Bond numbers, gravity plays an important role and MD simulations cannot accurately describe wetting. We create wetting phase diagrams and find that our predictions are in good agreement with experiment. The resulting wetting phase diagrams may serve as a guideline in creating surfaces with desired wettability.   

Freezing of Water next to Solid Surfaces Probed Using Sum-Frequency Generation Spectroscopy

The control of ice formation next to solid surfaces is important in many technological applications such as de-icing for aircrafts and generation of power using wind turbines. We have studied the water-ice transition next to sapphire surface to understand the freezing transition and nucleation of ice. The infrared-visible sum frequency generation spectroscopy is sensitive to the structure and orientation of water molecules next to the solid interface and provides direct information on transition kinetics at the interface. The differences in the nucleation kinetics will be discussed for water in contact with hydrophilic and hydrophobic surfaces.   

Charging and transmission of low energy particles through Amorphous Solid Water films

The interaction of charged particles with condensed water films has drawn significant attention in recent years due to its importance in biological and atmospheric processes. We have studied low energy electrons (3-25 eV) and positive argon ions (55 eV) charging and transmission effects while striking Amorphous Solid Water (ASW) films, 240-1080 ML thick, deposited on ruthenium single crystal substrate, utilizing contact potential difference (CPD) measurements. Charging by both species has shown a plate capacitor-like behaviour. L-defects energetically located just below the conduction band of ice, are likely to stabilize them. The incoming electrons kinetic energy dictates the maximal CPD by retardation of any further electrons from adding up to the already accumulated charges. Electron transmission measurements (0.5-1.5 microamps) have shown that the maximal and stable CPD values were obtained only following a relatively slow change that has developed within the ASW structure. Upon film stabilization, the spontaneous discharge was measured over a period of up to three hours. UV laser photo-emission study of the charged films has suggested that the negative charges tend to reside primarily at the ASW-vacuum interface, in good agreement with a study of charged water nano-clusters.   

Session Q37: Focus Session: Students, Physics and Innovation

Physicists and Economic Growth: Preparing the Next Generation

For many years it has been recognized that many physicists are ``hidden'' -- deep in the industrial world or holding positions not named ``physicist.'' In parallel with this phenomenon is the recognition that many new and innovative product ideas are, in fact, generated by physicists. There are many more ideas that could be brought to market to the benefit of both society and the inventor, but physicists don't often see themselves as the innovators and inventors that they actually are. A number of education programs have arisen to try to address this issue and to engender a greater entrepreneurial spirit in the scientific community. The \textit{ScienceWorks} program at Carthage College was one of the first to do so, and has for nearly twenty years prepared undergraduate science majors to understand and practice innovation and value creation. Other programs, such as professional masters degrees, also serve to bridge the technical and business universes. As it is no doubt easier to teach a scientist the world of business than it is to teach a businessperson the world of physics, providing educational experiences in innovation and commercialization to physics students can have tremendous economic impact, and will also better prepare them for whatever career direction they may ultimately pursue, even if it is the traditional tenure-track university position. This talk will discuss education programs that have been effective at preparing physics students for the professional work environment, and some of the positive outcomes that have resulted. Also discussed will be the variety of opportunities and resources that exist for faculty and students to develop the skills, knowledge and abilities to recognize and successfully commercialize innovations.   

Teaching Innovation Through Undergraduate Research

A three-year investigation into the use of ongoing research programs to incubate innovative behavior among undergraduates is underway. Inspired by the 2005 report, Rising Above the Gathering Storm, this investigation embraces the claim that more innovation in the US should help arrest the current slippage in US competitiveness. Believing that the development of approaches to teach innovation is timely, physicists at Lawrence University are employing a five-step strategy that spans ten summer weeks to boost innovative attitudes and behavior among physics majors. We are also attempting to inculcate fifteen character traits associated with successful innovators. Recent progress in this investigation will be discussed.   

The Innovation Hyperlab - Linking Student Innovation at University and Pre-College Levels

We have created a laboratory environment to support collaboration between university and pre-college students on innovation and entrepreneurship projects. Called the ``Innovation Hyperlab,'' this facility is located in a K-12 complex called VistaPEAK schools in Aurora, Colorado. The lab is supported by four elements: a research-grade technical infrastructure of supplies and equipment for technical prototyping, a developing curriculum of ``learning modules on demand'' for rapid assimilation of technical skills, mentors from universities / medical schools / industry, and innovation projects stimulated by connections with the regional community. A current focus of projects is on medical technology development, linking tenth graders with university undergraduate research students and coordinated with the University of Colorado Denver's medical school. The Innovation Hyperlab is a work in progress and we will describe challenges that arise in connecting such a collaboration with traditional curriculum at both the university and pre-college levels.   

The Physics Entrepreneurship Program - 11 Years of Teaching and Practicing Innovation and Entrepreneurship to Graduate Students and Beyond

The Physics Entrepreneurship Program (PEP) at Case Western Reserve University is a MS in Physics, Entrepreneurship Track that teaches physics, business, and innovation. PEP admitted its first class in 2000 with the original goal of empowering physicists to be successful entrepreneurs. Since Y2K, much has happened in the world's economies and markets, and we have shifted our goals to include a strong innovation component. For instance, our metrics have changed from ``companies created'' to ``capital raised by our students'' (i.e., grants and investment in innovation), which allows our students to participate in an apprentice-type relationship with a more experienced entrepreneur before venturing out on their own (which could take many years before they are ready). We will describe the program, how we teach innovation, student and alumni activities and how difficult it is to operate a sustainable graduate program in this arena.   

The Story of a Typical Atypical Graduate of the Physics Entrepreneurship Program at Case Western Reserve University

An entrepreneurial perspective to life can lead to wearing a myriad of hats. Long gone is the stereotypical start-up role. Entrepreneurs now hold physics degrees and procure innovation when called upon. ~An alumni of the Physics Entrepreneurship Program, Adele ~Luta has spent the last 5 years at NASA developing an innovative approach to spacesuit sizing. Previously, she founded Eleda International consulting firm and is currently working with Adjuvat Biosciences, on a proprietary treatment pancreatic cancer.   

Developing affordable multi-touch technologies for use in physics

Physics is one of many areas which has the ability to benefit from a number of different teaching styles and sophisticated instructional tools due to it having both theoretical and practical applications which can be explored. The purpose of this research is to develop affordable large scale multi-touch interfaces which can be used within and outside of the classroom as both an instruction technology and a computer supported collaborative learning tool. Not only can this technology be implemented at university levels, but also at the K-12 level of education. Pedagogical research indicates that kinesthetic learning is a fundamental, powerful, and ubiquitous learning style [1]. Through the use of these types of multi-touch tools and teaching methods which incorporate them, the classroom can be enriched to allow for better comprehension and retention of information. This is due in part to a wider range of learning styles, such as kinesthetic learning, which are being catered to within the classroom. \\[4pt] [1] Wieman, C.E, Perkins, K.K., Adams, W.K., ``Oersted Medal Lecture 2007: Interactive Simulations for teaching physics: What works, what doesn't and why,'' \textit{American Journal of Physics}. \textbf{76 }393-99.   

Wolfram technologies as an integrated scalable platform for interactive learning

We rely on technology profoundly with the prospect of even greater integration in the future. Well known challenges in education are a technology-inadequate curriculum and many software platforms that are difficult to scale or interconnect. We'll review an integrated technology, much of it free, that addresses these issues for individuals and small schools as well as for universities. Topics include: Mathematica, a programming environment that offers a diverse range of functionality; natural language programming for getting started quickly and accessing data from Wolfram$\vert $Alpha; quick and easy construction of interactive courseware and scientific applications; partnering with publishers to create interactive e-textbooks; course assistant apps for mobile platforms; the computable document format (CDF); teacher-student and student-student collaboration on interactive projects and web publishing at the Wolfram Demonstrations site.   

Promoting Conceptual Coherence in Quantum Learning through Computational Models

In order to explain phenomena at the quantum level, scientists use multiple representations in verbal, pictorial, mathematical, and computational forms. Conceptual coherence among these multiple representations is used as an analytical framework to describe student learning trajectories in quantum physics. A series of internet-based curriculum modules are designed to address topics in quantum mechanics, semiconductor physics, and nano-scale engineering applications. In these modules, students are engaged in inquiry-based activities situated in a highly interactive computational modeling environment. This study was conducted in an introductory level solid state physics course. Based on in-depth interviews with 13 students, methods for identifying conceptual coherence as a function of students' level of understanding are presented. Pre-post test comparisons of 20 students in the course indicate a statistically significant improvement in students' conceptual coherence of understanding quantum phenomena before and after the course, Effect Size = 1.29 SD. Additional analyses indicate that students who responded to the modules more coherently improved their conceptual coherence to a greater extent than those who did less to the modules after controlling for their course grades.   

Session Q39: Focus Session: Materials and Functional Structures for Biological Interfaces - Micro and Nanofluidics

Integration of Materials and Functions in Microfluidic Devices

The physical and chemical properties of a surface determine how that surface interacts with its surrounding environment. Despite the large number of potential schemes feasible for surface modification, the covalent attachment of polymers remains the most promising approach to tailor important properties of lab-on-chip (LOC) devices such as adhesion, wettability and biocompatibility. This presentation deals with ``surface related'' issues that must be addressed in the development of LOC systems. An innovative approach that allows the attachment of polymer molecules to surfaces of different composition such as glass, silicon and polymer materials will be presented. Examples of interfaces modified by ``smart coatings'' able to give an appropriate and predictable response to outside conditions and decorated with biologically relevant biomolecules will be discussed.   

Dynamic micromolds to fabricate multi-layered hydrogel microstructures

Hydrogel microstructures can be used to mimic living systems and create drug carriers. Living materials can be encapsulated within multi-layered microgels to replicate native tissues. Furthermore, multiple drugs can be immobilized within different layers of microgels to create multifunctional drug carriers. Photolithography is a commonly used method to create these multi-layered microgels, but it is not applicable to non-photocrosslinkable materials. Also, conventional micromolding methods do not allow creating multi-layered microgels due to the static environment of the microstructures. Herein, we created dynamic micromolds by exploiting the thermoresponsiveness of poly(N-isopropylacrylamide). These micromolds allowed sequential molding of microgels at different temperatures. Different cell types were spatially immobilized in different layers of microgels to replicate native tissue complexity. Furthermore, fluorescent microbeads were spatially immobilized within different microgel layers to show a concept of drug carriers which could encapsulate various drugs. These dynamic micromolds could be potentially useful in creating multi-layered hydrogel microstructures in order to mimic biological systems and fabricate multifunctional drug carriers.   

Implementation of a Peltier-based cooling device for localized deep cortical deactivation during in vivo object recognition testing

While the application of local cortical cooling has recently become a focus of neurological research, extended localized deactivation deep within brain structures is still unexplored. Using a wirelessly controlled thermoelectric (Peltier) device and water-based heat sink, we have achieved inactivating temperatures ($<$20 C) at greater depths ($>$8 mm) than previously reported. After implanting the device into Long Evans rats' basolateral amygdala (BLA), an inhibitory brain center that controls anxiety and fear, we ran an open field test during which anxiety-driven behavioral tendencies were observed to decrease during cooling, thus confirming the device's effect on behavior. Our device will next be implanted in the rats' temporal association cortex (TeA) and recordings from our signal-tracing multichannel microelectrodes will measure and compare activated and deactivated neuronal activity so as to isolate and study the TeA signals responsible for object recognition. Having already achieved a top performing computational face-recognition system, the lab will utilize this TeA activity data to generalize its computational efforts of face recognition to achieve general object recognition.   

Droplet Microfluidics for Artificial Lipid Bilayers

Droplet interface bilayer is a versatile approach that allows formation of artificial lipid bilayer membrane at the interface of two lipid monolayer coated aqueous droplets in a lipid filled oil medium. Versatility exists in the form of voltage control of DIB area, ability of forming networks of DIBs, volume control of droplets and lipid-oil, and ease of reformation. Significant effect of voltage on the area and capacitance of DIB as well as DIB networks are characterized using simultaneous optical and electrical recordings. Mechanisms behind voltage-induced effects on DIBs are investigated. Photo induced effect on the DIB membrane porosity is obtained by incorporating UVC-sensitive photo-polymerizable lipids in DIB. Photo-induced effects can be extended for in-vitro studies of triggered release of encapsulated contents across membranes. A droplet based low voltage digital microfluidic platform is developed to automate DIB formation, which could potentially be used for forming arrays of lipid bilayer membranes.   

Density fluctuations in nanochannel-confined DNA

The dynamic behavior of a polymer chain in dense solution is typically described within the framework of reptation, which assumes that polymers primarily move along tubes formed by other chains. We have studied the dynamic density fluctuations of single DNA molecules confined to nanofabricated channels that mimic reptation tubes, and found that the classical harmonic spring model yields a satisfactory description. In particular, we have recovered the expected dispersion relationship. By looking at fluctuation amplitudes, we have also found that the description demands a minimum spring length approximately equal to the size of self-avoiding DeGennes blobs.   

Extension and Diffusion of DNA in Nanochannels

Nanochannels are an ideal platform for studying the basic physics of confined polymers, using DNA as the model polymer. While the scaling laws for strong (Odijk) and weak (de Gennes) confinement were established decades ago, recent experiments have illuminated the complex physics arising between these limiting cases. We will first present Monte Carlo simulation data on the extension of DNA in nanochannels. Our results provide clear evidence for the existence of two transition regimes between the Odijk and de Gennes regimes, thereby resolving the apparent contradiction between these scaling theories and the corresponding experiments by Austin and coworkers. We will then present results for the diffusivity of DNA in nanochannels and explain their connection to the different regimes of extension. By using Monte Carlo sampling of the Kirkwood diffusivity and a numerical solution for the confined Green's function, we have calculated the diffusivity for DNA contour lengths ranging over three orders of magnitude and nanochannel sizes over two orders of magnitude. By using a DNA model that accurately reproduces the free solution radius of gyration and diffusivity over a range of molecular weights, we can directly connect the simulation data and experiments.   

DNA conformation and dynamics in quasi-2D and -1D confinement

We investigate the structure and correlation length of DNA molecules in sub-100nm quasi-2D slits and 1D square channels. In strong slit confinement, the segmental correlation length of DNA molecules separates into two components -- in the confined and unconfined dimensions. In the confined dimension, the segmental correlation length is controlled by the slit height. In the unconfined dimension, the segmental correlation length increases as the slit height decreases. In the nano-channel, segmental correlation length increases beyond the chain contour length as channel height decreases below channel persistence length. We generalize how this affects the entropic elasticity of confined DNA molecules and how it affects chain thermodynamic properties.   

Mapping the yeast genome by melting in nanofluidic devices

Optical mapping of DNA provides large-scale genomic information that can be used to assemble contigs from next-generation sequencing, and to detect re-arrangements between single cells. A recent optical mapping technique called denaturation mapping has the unique advantage of using physical principles rather than the action of enzymes to probe genomic structure. The absence of reagents or reaction steps makes denaturation mapping simpler than other protocols. Denaturation mapping uses fluorescence microscopy to image the pattern of partial melting along a DNA molecule extended in a channel of cross-section $\sim$100nm at the heart of a nanofluidic device. We successfully aligned melting maps from single DNA molecules to a theoretical map of the yeast genome (11.6Mbp) to identify their location. By aligning hundreds of molecules we assembled a consensus melting map of the yeast genome with 95\% coverage.   

Spatially Varying Nanoconfinement as a Probe of Polymer Physics

Complex nanofluidic systems have the capability to unveil a rich landscape of new polymer physics. One-dimensional channels and two-dimensional slits have been used for precise measurements of persistence length and to verify scaling laws. Recently, devices with spatially varying confinement have been used to gain further control over single molecule polymer conformation. We use a system consisting of a nanofluidic slit embedded with a lattice of pits acting as entropic traps. Single DNA polymers in this system self-organize into discrete conformational states. We have shown that this system can be used to define stable DNA configurations at equilibrium and to fine-tune diffusion to a local minimum corresponding to stable conformational states. Measurements of mean occupancy with varying device parameters can be fit to theory, giving information about the confinement free energy of DNA in a nanoslit (a subject of controversy) and the strength of excluded volume interactions. Measurements of the excluded volume interaction provide information about the strength of intersegmental repulsive electrostatic interactions, quantified by the notion of effective width. The scaling of width with respect to salt concentration is observed in single DNA molecules for the first time.   

The Nanofluidic Staircase: A Brownian Motor for Polymer Characterization and Transport

A coarse-grained molecular dynamics simulation is used to study the motion of a polymer chain in a nanofluidic staircase (Stavis et al., Nanotechnology, 20(16), 2009), a device which consists of a collection of nanoslits of increasing depth arranged in step-like fashion in a fluidic channel. The slit depths span the Odijk ($H [Preview Abstract]

Geometrically induced polarization and alignment of cells on nanopillar arrays

Topological features at the nano and microscale can trigger mammalian cell growth and differentiation. In this work, we describe geometrical tuning of ordered arrays of nanopillars and micropillars that elicit specialized morphologies in adherent cells. Systematic analysis of the effects of the pillar radius, height, and spacing reveals that stem cells assume either flattened, polarized, or stellate morphologies in direct response to interpillar spacing. Notably, on patterns of pitch near a critical spacing (dcrit = 2 ?m for C3H10T1/2 cells), cells exhibit rounding of the cell body, pronounced polarization, and extension of narrow axon-like cell projections aligned with the square or hexagonal lattice of the NP array. This morphology persists for various stem cell lines and primary mesenchymal stem cells. The neuron-like morphological characteristics suggest that NP arrays can be utilized in tissue engineering applications that require directed axon growth. The ability of nano and micropillars to support various morphogenetic trends will allow rational design of scaffolds that may be useful for stem cell lineage specification, formation of patterned neural networks, and enhancement of implant integration with adjoining tissue.   

Session Q40: Focus Session: Systems Biology and Biochemical Networks III

Fold-change detection and scalar symmetry of sensory input fields

Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold-changes in input, and not on absolute changes. We show that FCD is necessary and sufficient for sensory search to depend only on the spatial profile of the input, and not on its amplitude. Such amplitude scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling systems. We present a wide class of mechanisms that have FCD, including certain nonlinear feedback and feedforward loops. In addition, we find that bacterial chemotaxis displays feedback within the present class, and has indeed recently been shown to exhibit FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study thus suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input fields.   

Network architectural conditions for prominent and robust stochastic oscillations

Understanding relationship between noisy dynamics and biological network architecture is a fundamentally important question, particularly in order to elucidate how cells encode and process information. We analytically and numerically investigate general network architectural conditions that are necessary to generate stochastic amplified and coherent oscillations. We enumerate all possible topologies of coupled negative feedbacks in the underlying biochemical networks with three components, negative feedback loops, and mass action kinetics. Using the linear noise approximation to analytically obtain the time-dependent solution of the master equation and derive the algebraic expression of power spectra, we find that (a) all networks with coupled negative feedbacks are capable of generating stochastic amplified and coherent oscillations; (b) networks with a single negative feedback are better stochastic amplified and coherent oscillators than those with multiple coupled negative feedbacks; (c) multiple timescale difference among the kinetic rate constants is required for stochastic amplified and coherent oscillations.   

Properties of gene expression including the non-functional binding of transcription factors to DNA

Many eukaryotic transcription factors bind to DNA sequences with a remarkable lack of specificity. This suggests that non-functional binding between transcription factors and DNA might not have the detrimental effect on regulation one would naively assume results from competition for binding. In fact, if binding to DNA protects transcription factors from degradation, the number and binding affinity of these 'decoy' binding sites should have no influence on the copy number of transcription factors available for regulation. We calculate the influence of adding decoy binding sites on several important aspects of gene expression including the noise, the time to reach steady state, and bimodal switch rates. Analyzing these effects could shed some light on how a gene functions in the 'dressed' environment of a genomic background.   

Single promoters as regulatory network motifs

At eukaryotic promoters, chromatin can influence the relationship between a gene's expression and transcription factor (TF) activity. This additional complexity might allow single promoters to exhibit dynamical behavior commonly attributed to regulatory motifs involving multiple genes. We investigate the role of promoter chromatin architecture in the kinetics of gene activation using a previously described set of promoter variants based on the phosphate-regulated PHO5 promoter in S. cerevisiae. Accurate quantitative measurement of transcription activation kinetics is facilitated by a controllable and observable TF input to a promoter of interest leading to an observable expression output in single cells. We find the particular architecture of these promoters can result in a significant delay in activation, filtering of noisy TF signals, and a memory of previous activation -- dynamical behaviors reminiscent of a feed-forward loop but only requiring a single promoter. We suggest this is a consequence of chromatin transactions at the promoter, likely passing through a long-lived ``primed'' state between its inactive and competent states. Finally, we show our experimental setup can be generalized as a ``gene oscilloscope'' to probe the kinetics of heterologous promoter architectures.   

Towards a principled way of making kinetic models from data

Kinetic model extraction from noisy data is the basic route to mechanistic insight in biology. I will show how the tools of Maximum Caliber (the dynamical analog of Maximum Entropy) can be used to infer -and not fit- models in a way which is driven by the structure and limitations of the data. For instance, the typical output of an experiment in systems biology is the stochastic expression of one reporter gene. Master equations used to model the regulatory process underlying the stochastic gene expression require knowledge of a circuit topology and rates. However rates and topology are often fit as these are rarely all independently determinable from the limited data. Our goal is to build a kinetic model from the data available with no adjustable parameter using the tools of Maximum Caliber. We apply our method to infer the statistics of rare stochastic switching events in the genetic toggle switch from fluctuations on shorter measurable timescales. In addition, we discuss how these tools can be used to infer kinetic models from real single molecule data drawn from anomalous folding kinetics of phosphoglycerate kinase and RNA hairpin zipping-unzipping time traces.   

Reaction kinetics in the cell membrane: confining domains lead to reaction bursts

Our goal is to reveal the effects of confining domains such as those observed in cell membranes on the kinetics of reversible reactions in two-dimensions. During the last two decades, single molecule tracking experiments showed that proteins and lipids are temporarily confined in the compartments of a meshwork induced by the actin cytoskeleton, while diffusing laterally in the plasma membrane. It has been clearly demonstrated that the presence of these compartments significantly hinders the diffusion of membrane molecules. Nevertheless, how confinement affects the interaction between membrane molecules and the regulation of signaling has still not been clarified. Using Monte Carlo simulations and the mathematical theory of diffusion, we showed that the presence of compartments leads to reaction bursts, during which the number of reactions an individual molecule experiences rises sharply, but briefly. Surprisingly, we found that the mean reaction rate does not depend on whether compartments exist or not. However, our results show that the variance of the rate depends strongly on the presence of confinement effects, which turns out to be an indicator of a profound change in the temporal pattern of reaction events: bursts of reactions instead of constant but low yield.   

Inference of Mechanical Network Parameters in Epithelial Tissue Development

Mechanical stress in cells has been linked to biochemical networks that influence cell structure and function. Yet direct \emph{in vivo} measurements of mechanical forces in epithelial tissues remain a serious experimental challenge. I will present an alternative approach based on a computational analysis of high resolution images of epithelial tissues. Assuming that epithelial cell layers are close to mechanical equilibrium, we use the observed geometry of the two dimensional cell array to infer interfacial tensions and intracellular pressures. I will present applications of this mechanical parameter inference algorithm in the context of several developmental processes involving epithelial cell layers.   

Regulatory dynamics and stability in discrete and continuous models

Biological processes such as cell deviation, cell differentiation and so on are regulated dynamics. These dynamics are often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to another class of models, Boolean dynamics, which are dealing with larger systems, higher complexity and less computational details. Here we study the reaction of discrete and continuous dynamics to perturbations. When asking if a gene-regulatory system reproduces a prescribed trajectory despite noise, large perturbations are to be considered in the case of low copy numbers of regulatory molecules and bursty stochastic response. Small perturbations, however, are more appropriate when modelling systems with large copy numbers and an integrative response to filter out bursts. In Boolean networks, the dynamics has been called unstable if flip perturbations lead to damage spreading. We find that this stability classification strongly differs from the stability properties of the original continuous dynamics under small perturbations of the state vector. In particular, random networks of nodes with large sensitivity yield stable dynamics under small perturbations and chaotic regime disappears.   

Polarization and molecular information transmission in the cell

During chemotaxis, pseudopodia are extended at the leading edge and retracted at the back of the cell. Efficient chemotaxis is the result of a refined interplay between signaling modules to transmit and integrate spatial information such as PtdIns(3,4,5)P3. The localization of PtdIns(3,4,5)P3 is expected to depend on the distributions or activities of PI3Ks, PTEN, and 5-phosphatases. The spatial signals spread relatively slowly so that high local concentrations of PIP3 in the plasma membrane appear in patches. These gradients induce localization of PIP3 and PTEN to the front and back of the cell, respectively. To simulate this polarization process that involves the action of seven reaction-channels inside the cell we carried out extensive stochastic simulations using Gilliespie algorithm. The simulations were done on a square cell with ten thousand sites $(100\times100)$ emulating a square cell with side $10\>\mu m$ long. We found that there are localized patches of PIP3 at the active receptors and segregation of PTEN on the opposite side of the cell. When we block the reaction-channel, $PTEN + PIP3 \rightarrow PIP2$ that involves the production of PIP2 we obtained a five-fold increase in the concentration of PIP3. This finding appears to be consistent with the o   

Energy Flow in Neuronal Systems

We will present results from a computational model designed to investigate the physical underpinnings of neuronal systems. Most neuronal models assume that the ionic flow across neuronal membranes is to small to effect the ionic composition inside and outside of cells. However neurons exhibiting high levels of activity can produce ionic redistributions large enough to cause significant changes to cellular excitability. Furthermore, physically-accurate neuronal models must obey conservation of mass and energy. Energy is injected into these cells through the consumption of atp, stored in electrochemical gradients, and dissipated through ionic flow down these gradients. Our model incorporates essential biological mechanisms required to reproduce this energy flow and storage. We will discuss the advantages and limitations of this dynamic system in the context of neuronal function.   

Rhythm-Induced Spike-Timing Patterns Characterized by 1D Firing Map

A basic problem in neuroscience is to understand how the dynamic mechanisms that govern the responses of nerve cells to stimuli, which are both non-linear and noisy, still produce reliable collective activity. We study patterning in the responses of neurons subjected to periodic rhythms. These patterns are governed by simple, low-dimensional mathematical structures independent of modeling detail. We show both theoretically and in whole-cell recordings that the 1D map generated from successive spike times is such a construct. As expected, the stable periodic points of this 1D map cause a neuron's entrainment or phase-locking to a periodic rhythm. But our work has also revealed a complementary and unexpected patterning in the spike-timing of un-entrained neurons in the form of repeated sequences of reliable spike-phase advances, which cannot be characterized simply as a noisy perturbation near the stable periodic points of the noise-free return map. This new patterning appears to require both noise and a sufficiently steep return map.   

The Effects of Intrinsic Noise on an Inhomogeneous Lattice of Chemical Oscillators

Intrinsic or demographic noise has been shown to play an important role in the dynamics of a variety of systems including biochemical reactions within cells, predator-prey populations, and oscillatory chemical reaction systems, and is known to give rise to oscillations and pattern formation well outside the parameter range predicted by standard mean-field analysis. Motivated by an experimental model of cells and tissues where the cells are represented by chemical reagents isolated in emulsion droplets, we study the stochastic Brusselator, a simple activator-inhibitor chemical reaction model. Our work extends the results of recent studies on the zero and one dimensional system to the case of a non-uniform one dimensional lattice using a combination of analytical techniques and Monte Carlo simulations.   

Session Q41: Biofluids

Fool's Gold Footprinting: microfluidic probing of nucleic acids

We describe a microfluidic device containing a mineral matrix capable of rapidly generating hydroxyl radicals that enables high-resolution structural studies of nucleic acids. Hydroxyl radicals cleave the solvent accessible backbone of DNA and RNA; the cleavage products can be detected with as fine as single nucleotide resolution. Protection from hydroxyl radical cleavage (footprinting) can identify sites of protein binding or the presence of tertiary structure. Here we report preparation of micron sized particles of iron sulfide (pyrite) and fabrication of a microfluidic prototype that together generate enough hydroxyl radicals within 20 ms to cleave DNA sufficiently for a footprinting analysis to be conducted. This prototype enables the development of high-throughput and/or rapid reaction devices with which to probe nucleic acid folding dynamics and ligand binding.   

Dislocation dynamics and bacterial growth

Recent experiments have revealed remarkable phenomena in the growth mechanisms of rod-shaped bacteria: proteins associated with the cell wall growth move at constant velocity in circles oriented approximately along the cell circumference (Garner et al., Science 2011, Dom\'inguez-Escobar et al., Science 2011, Deng et al., PNAS 2011). We view these dislocations in the partially ordered peptidoglycan structure, and study theoretically the dynamics of these interacting dislocations on the surface of a cylinder. The physics of the nucleation of these dislocations and the resulting dynamics within the model show surprising effects arising from the cylindrical geometry, which are predicted to have important implications on the growth mechanism. We also discuss how long range elastic interactions affect the dynamics of the fraction of active dislocations in the environment.   

Signal Relay During Cell Migration

We developed a signal relay model to quantify the effect of intercellular communication in presence of an external signal, during the motion of groups of Dictyostelium discoideum cells. A key parameter is the ratio of amplitude of the cAMP (cyclic adenosine monophosphate) a signaling chemical secreted from individual cells versus the external cAMP field, which defines a time scale. Another time scale is set by the degradation rate of the cAMP. In our simulations, the competition between these two time scales results rich dynamics including uniform motion, as well as streaming and clustering instabilities. The simulations are compared to experiments for a wide range of different external signal strengths for both cells that secrete cAMP and a mutant which cannot relay cAMP. Under different strength of external linear cAMP gradient, the wild type cells form streams and exhibit clustering due to the intercellular signaling through individual cAMP secretion. In contrast, cells lacking signal relay move relatively straight. We find that the model captures both independent motion and the formation of aggregates when cells relay the signal.   

Intracellular Transport in Beta Cells - from Anti-Corellated to Active

The intracellular transport along micro-tubules is the main focus of this research. We study the transport of insulin granules inside Beta cells. By developing new technique for the analysis of single 2D trajectories we observe a transition in the transport behavior from anti-correlated to active as a function of time. We further use the observed effect in order to discriminate between possible scenarios of active transport through disordered media as models of efficient intracellular transport.   

Acoustic streaming in the cochlea under compressive bone conduction excitation

This work examines the acoustic streaming in the cochlea. A model will be developed to examine the steady flow over a flexible boundary that is induced by compressive excitation of the cochlear capsule. A stokeslet based analysis of oscillatory flows was used to model fluid motion. The influence of evanescent modes on the pressure field is considered as the limit of the aspect ratio epsilon approaches zero. We will show a uniformly valid solution in space.   

Subtle exchange model of flow depended on the blood cell shape to enhance the micro-circulation in capillary

In general the exchange of gases or other material in capillary system is conceptualized by the diffusion effect. But in this model, we investigate a micro-flow pattern by simulation and computation on a micro-exchange model in which the blood cell is a considered factor, especially on its shape. It shows that the cell benefits the circulation while it is moving in the capillary. In the study, the flow detail near the cell surface is mathematically analyzed, such that the Navier-Stokes equations are applied and the viscous factor is also briefly considered. For having a driven force to the motion of micro-circulation, a breathing mode is suggested to approximately compute on the flow rate in the blood capillary during the transfer of cell. The rate is also used to estimate the enhancement to the circulation in additional to the outcome of diffusion. Moreover in the research, the shape change of capillary wall under pressure influence is another element in the beginning calculation for the effect in the assistance to cell motion.   

Modeling fluid diffusion in cerebral white matter with random walks in complex environments

Recent studies with diffusion MRI have shown new aspects of geometric order in the brain, including complex path coherence within the cerebral cortex, and organization of cerebral white matter and connectivity across multiple scales. The main assumption of these studies is that water molecules diffuse along myelin~sheaths of neuron axons in the white matter and thus the anisotropy of their diffusion tensor observed by MRI can provide information about the direction of the axons connecting different parts of the brain. We model the diffusion of particles confined in the space of between the bundles of cylindrical obstacles representing fibrous structures of various orientations. We have investigated the directional properties of the diffusion, by studying the angular distribution of the end point of the random walks as a function of their length, to understand the scale over which the distribution randomizes.~We will show evidence of qualitative change in the behavior of the diffusion for different volume fractions of obstacles. Comparisons with three-dimensional MRI images will be illustrated.   

Adhesion of a Cylindrical Bacterium in the Presence of DLVO Potential

A single cigar shape bacterium attaches to a rigid substrate (e.g. sand surface). In the presence of electrostatic double layers and van der Waals attraction according to the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, the bacterium glycoprotein shell deforms and may settle in either the primary or secondary energy minimum depending on whether it has sufficient energy to overcome the repulsive energy barrier. The adhesion-detachment mechanics is derived using a computational approach, and the followings are obtained: (i) relation between the applied load and contact area with the substrate, (ii) deformed profile at equilibrium, (iii) mechanical stress distribution in the shell, (iv) critical compressive load to force the shell going from secondary energy minimum to primary, and (v) ``pull-off'' forces to detach the shell from substrate. The model leads to better understanding of bacteria adhesion-aggregation-transportation, and has significant relevance to environmental and medical sciences.   

Hydrodynamic behavior of tumor cells in a confined model microvessel

An important step in cancer metastasis is the hydrodynamic transport of circulating tumor cells (CTCs) through microvasculature. In vivo imaging studies in mice models show episodes of confined motion and trapping of tumor cells at microvessel bifurcations, suggesting that hydrodynamic phenomena are important processes regulating CTC dissemination. Our goal is to use microfluidics to understand the interplay between tumor cell rheology, confinement and fluid forces that may help to identify physical factors determining CTC transport. We use leukemia cells as model CTCs and mimic the in vivo setting by investigating their motion in a confined microchannel with an integrated microfluidic manometer to measure time variations in the excess pressure drop during cell motion. Using image analysis, variations in excess pressure drop, cell shape and cell velocity are simultaneously quantified. We find that the throughput of the technique is high enough (~ 100 cells/min) to assess tumor cell heterogeneity. Therefore, in addition to measuring the hydrodynamic response of tumor cells in confined channels, our results indicate that the microfluidic manometer device could be used for rapid mechanical phenotyping of tumor cells.   

Flow and rupture of vesicles in narrow channels

Small lipid bilayer vesicles, also known as liposomes, are used for drug delivery systems in vasculature. Consequently how they deform and when they become unstable and rupture (lose their inner contents) under capillary flow is of great interest. In addition vesicles with a filling fraction of 0.6 can be considered as a simple mechanical model of red blood cells. We use coarse-grained molecular dynamics (CGMD) simulations with explicit solvent to study lipid bilayer vesicles in 3D capillary flow with filling fractions of 1.0 and 0.6. The shapes of the vesicles obtained in these simulations compare well to other experimental and theoretical studies. Using CGMD allows the study of rupture. This is in contrast to the majority of other approaches which model the bilayer as a purely elastic surface and only allow the investigation of deformation. We look at the stress profiles of these vesicles as measured by the area expansion per lipid along the membrane, and determine the location and pressure of rupture for a given confinement ratio (diameter of the vesicle divided by diameter of the channel). We also discuss the subsequent loss of inner fluid content.   

Simulations of cardiovascular blood flow accounting for time dependent deformational forces

Cardiovascular disease is currently the leading cause of death in the United States, and early detection is critical. Despite advances in imaging technology, 50\% of these deaths occur suddenly and with no prior symptoms. The development and progression of coronary diseases such as atherosclerosis has been linked to prolonged areas of low endothelial shear stress (ESS); however, there is currently no way to measure ESS in vivo. We will present a patient specific fluid simulation that applies the Lattice Boltzmann equation to model the blood flow in the coronary arteries whose geometries are derived from computed tomography angiography data. Using large-scale supercomputers up to 294,912 processors, we can model a full heartbeat at the resolution of the red blood cells. We are investigating the time dependent deformational forces exerted on the arterial flows from the movement of the heart. The change in arterial curvature that occurs over a heartbeat has been shown to have significant impact on flow velocity and macroscopic quantities like shear stress. We will discuss a method for accounting for these resulting forces by casting them into a kinetic formalism via a Gauss-Hermite projection and their impact on ESS while maintaining the static geomtry obtained from CTA data.   

Using vortex corelines to analyze the hemodynamics of patient specific cerebral aneurysm models

We construct one-dimensional sets known as vortex corelines for computational fluid dynamic (CFD) simulations of blood flow in patient specific cerebral aneurysm models. These sets identify centers of swirling blood flow that may play an important role in the biological mechanisms causing aneurysm growth, rupture, and thrombosis. We highlight three specific applications in which vortex corelines are used to assess flow complexity and stability in cerebral aneurysms, validate numerical models against PIV-based experimental data, and analyze the effects of flow diverting devices used to treat intracranial aneurysms.   

Picoliter droplet-based digital peptide nucleic acid clamp PCR and dielectric sorting for low abundant K-ras mutations

Colorectal cancer (CRC) remains the second leading cause of cancer-related mortality in the US, and the 5-year survival of metastatic CRC (mCRC) is less than 10{\%}. Although monoclonal antibodies against epidermal growth factor receptor (EGFR) provide incremental improvements in survival, approximately 40{\%} of mCRC patients with activating KRAS mutations won't benefit from this therapy. Peptide nucleic acid (PNA), a synthetic non-extendable oligonucleotides, can bind strongly to completely complementary wild-type KRAS by Watson-Crick base pairing and suppress its amplification during PCR, while any mutant allele will show unhindered amplification. The method is particularly suitable for the simultaneously detection of several adjoining mutant sites, just as mutations of codons 12 and 13 of KRAS gene where there are totally 12 possible mutation types. In this work, we describe the development and validation of this method, based on the droplet-based digital PCR. Using a microfluidic system, single target DNA molecule is compartmentalized in microdroplets together with PNA specific for wild-type KRAS, thermocycled and the fluorescence of each droplet was detected, followed by sorting and sequencing. It enables the precise determination of all possible mutant KRAS simultaneously, and the precise quantification of a single mutated KRAS in excess background unmutated KRAS.   

Liquid solution delivery through the pulled nanopipette combined with QTF-AFM system

Nanopipette is a versatile fluidic tool for biochemical analysis, controlled liquid delivery in bio-nanotechnology. However, most of the researches have been performed in solution based system, thus it is challenge to study nanofluidic properties of the liquid solution delivery through the nanopipette in ambient conditions. In this work, we demonstrated the liquid ejection, dispersion, and subsequent deposition of the nanoparticles via a 30 nm aperture pipette based on the quartz tuning fork -- atomic force microscope (QTF-AFM) combined nanopipette system.   

Session Q42: Focus Session: Stochastic Population Dynamics II - Games and Spatial Dynamics

Bacterial Games

Microbial laboratory communities have become model systems for studying the complex interplay between evolutionary selection forces, stochastic fluctuations, and spatial organization. Two fundamental questions that challenge our understanding of evolution and ecology are the origin of cooperation and biodiversity. Both are ubiquitous phenomena yet conspicuously difficult to explain since the fitness of an individual or the whole community depends in an intricate way on a plethora of factors, such as spatial distribution and mobility of individuals, secretion and detection of signaling molecules, toxin secretion leading to inter-strain competition and changes in environmental conditions. We discuss two possible solutions to these questions employing concepts from evolutionary game theory, nonlinear dynamics, and the theory of stochastic processes. Our work provides insights into some minimal requirements for the evolution of cooperation and biodiversity in simple microbial communities. It further makes predictions to be tested by new microbial experiments.   

Evolutionary dynamics of range expansions with curved fronts and inflationary directed percolation

We compare the evolutionary dynamics of populations expanding into a new territory with flat and curved fronts. When actively reproducing individuals confined to a thin, uniform population front experience deleterious mutations, the evolutionary dynamics fall into the directed percolation (DP) universality class. At the DP phase transition, the selective advantage of the fit individuals balances the deleterious mutation rate. Curvature in the front changes the dynamics: Sectors of the population become causally disconnected after a time $t_* = R_0/v$, where $R_0$ is the initial radius of the population and $v$ is the radial front propagation speed. The reproducing population size increases, creating an inflationary effect that prevents the loss of fit individuals due to sector boundary diffusion and sector interactions. We develop a generalization of the Domany-Kinzel model on amorphous, isotropic lattices to simulate radial expansions. We find scaling functions characterizing the effects of inflation at criticality. We also discuss analytic results for two-point correlation functions and survival probabilities in the two limiting cases of no mutations (compact DP)and no selection.   

Competition and cooperation in one-dimensional stepping stone models

Mutualism and cooperation are major biological forces sustaining ecosystems and enabling complex evolutionary adaptations. Although spatial degrees of freedom and number fluctuations often significantly affect evolutionary dynamics, their effects on mutualism are not fully understood. We show that, even when mutualism confers a distinct selective advantage, it persists only in populations with high density and frequent migrations. When these parameters are reduced, number fluctuations lead to the local extinctions of one of the species, segregating the species in space and decreasing the size of regions where cooperation occurs. The segregated and mutualistic states are separated by a second order nonequilibrium phase transition. Generically, this transition is in the universality class of directed percolation (DP), but the phase diagram is strongly influenced by an exceptional symmetric directed percolation (DP2) transition. This influence is manifested in a strong increase in the resilience to number fluctuations of symmetric mutualism, when organisms benefit equally from interacting.   

Range expansion of mutualists

The expansion of a species into new territory is often strongly influenced by the presence of other species. This effect is particularly striking for the case of mutualistic species that enhance each other's proliferation. Examples range from major events in evolutionary history, such as the spread and diversification of flowering plants due to their mutualism with pollen-dispersing insects, to modern examples like the surface colonisation of multi-species microbial biofilms. Here, we investigate the spread of cross-feeding strains of the budding yeast \textit{Saccharomyces cerevisiae} on an agar surface as a model system for expanding mutualists. Depending on the degree of mutualism, the two strains form distinctive spatial patterns during their range expansion. This change in spatial patterns can be understood as a phase transition within a stepping stone model generalized to two mutualistic species.   

Cooperation, cheating, and collapse in microbial populations

Natural populations can suffer catastrophic collapse in response to small changes in environmental conditions, and recovery after such a collapse can be exceedingly difficult. We have used laboratory yeast populations to study proposed early warning signals of impending extinction. Yeast cooperatively breakdown the sugar sucrose, meaning that there is a minimum number of cells required to sustain the population. We have demonstrated experimentally that the fluctuations in the population size increase in magnitude and become slower as the population approaches collapse. The cooperative nature of yeast growth on sucrose suggests that the population may be susceptible to cheater cells, which do not contribute to the public good and instead merely take advantage of the cooperative cells. We have confirmed this possibility experimentally by using a cheater yeast strain that lacks the gene encoding the cooperative behavior [1]. However, recent results in the lab demonstrate that the presence of a bacterial competitor may drive cooperation within the yeast population.\\[4pt] [1] Gore et al, \textit{Nature} \textbf{459}, 253 -- 256 (2009)   

Evolution of cooperation in microbial biofilms - A stochastic model for the growth and survival of bacterial mats

Cooperative behavior is essential for microbial biofilms. The structure and composition of a biofilm change over time and thereby influence the evolution of cooperation within the system. In turn, the level of cooperation affects the growth dynamics of the biofilm. Here, we investigate this coupling for an experimentally well-defined situation in which mutants of the Pseudomonas fluorescens strain form a mat at the liquid-air interface by the production of an extra-cellular matrix [1]. We model the occurrence of cooperation in this bacterial population by taking into account the formation of the mat. The presence of cooperators enhances the growth of the mat, but at the same time cheaters can infiltrate the population and put the viability of the mat at risk. We find that the survival time of the mat crucially depends on its initial dynamics which is subject to demographic fluctuations [2]. More generally, our work provides conceptual insights into the requirements and mechanisms for the evolution of cooperation.\\ $[1]$ P. Rainey et al., Nature 425, 72 (2003).\\ $[2]$ A. Melbinger et al., PRL 105, 178101 (2010).   

Bacterial Cheating Limits the Evolution of Antibiotic Resistance

The emergence of antibiotic resistance in bacteria is a significant health concern. Bacteria can gain resistance to the antibiotic ampicillin by acquiring a plasmid carrying the gene beta-lactamase, which inactivates the antibiotic. This inactivation may represent a cooperative behavior, as the entire bacterial population benefits from removal of the antibiotic. The presence of a cooperative mechanism of resistance suggests that a cheater strain - which does not contribute to breaking down the antibiotic - may be able to take advantage of resistant cells. We find experimentally that a ``sensitive'' bacterial strain lacking the plasmid conferring resistance can invade a population of resistant bacteria, even in antibiotic concentrations that should kill the sensitive strain. We use a simple model in conjunction with difference equations to explain the observed population dynamics as a function of cell density and antibiotic concentration. Our experimental difference equations resemble the logistic map, raising the possibility of oscillations or even chaotic dynamics.   

Does fast migration imply well-mixing?

A popular assumption in population dynamics is that the population is well mixed, i.e., a spatial character of the interactions between the individuals can be neglected. A common justification of this assumption is that the rate of migration between the local possibly well-mixed population-dynamics domains is much larger than the rates of interactions within a domain. We consider a system of local well-mixed domains of varying carrying capacity. In the limit of infinite migration rate we calculate the stationary probability distribution of the total population and find that generally it is not equivalent to the stationary probability distribution of a single well-mixed domain with a large carrying capacity. This proves that fast migration does not generally justify the well-mixed population assumption.   

Turing patterns and a stochastic individual-based model for predator-prey systems

Reaction-diffusion theory has played a very important role in the study of pattern formations in biology. However, a group of individuals is described by a single state variable representing population density in reaction-diffusion models and interaction between individuals can be included only phenomenologically. Recently, we have seamlessly combined individual-based models with elements of reaction-diffusion theory. To include animal migration in the scheme, we have adopted a relationship between the diffusion and the random numbers generated according to a two-dimensional bivariate normal distribution. Thus, we have observed the transition of population patterns from an extinction mode, a stable mode, or an oscillatory mode to the chaotic mode as the population growth rate increases. We show our phase diagram of predator-prey systems and discuss the microscopic mechanism for the stable lattice formation in detail.   

Session Q43: Invited Session: Techniques to Study Dynamic Cellular Processes One Molecule at a Time (Including Delbruck Award Lecture)

Max Delbruck Prize in Biological Physics Lecture: Single-molecule protein folding and transition paths

The transition path is the tiny fraction of an equilibrium molecular trajectory when a transition occurs by crossing the free energy barrier between two states. It is a uniquely single-molecule property, and has not yet been observed experimentally for any system in the condensed phase. The importance of the transition path in protein folding is that it contains all of the mechanistic information on how a protein folds. As a major step toward observing transition paths, we have determined the average transition-path time for a fast and a slow-folding protein from a photon-by-photon analysis of fluorescence trajectories in single-molecule FRET experiments. While the folding rate coefficients differ by 10,000-fold, surprisingly, the transition-path times differ by less than 5-fold, showing that a successful barrier crossing event takes almost the same time for a fast- and a slow-folding protein, i.e. almost the same time to fold when it actually happens.   

ATP-induced helicase slippage reveals highly coordinated subunits

Helicases are vital enzymes that carry out strand separation of duplex nucleic acids during replication, repair and recombination. T7 helicase, a model hexameric motor, has been observed to use dTTP, but not ATP, to unwind dsDNA as it translocates along ssDNA. Whether and how different subunits of the helicase coordinate their chemo-mechanical activities and DNA binding during translocation is still under debate. Here we address this question using a single-molecule approach to monitor helicase unwinding. We found that T7 helicase does in fact unwind dsDNA in the presence of ATP and that the unwinding rate is even faster than that with dTTP. However, unwinding was repeatedly interrupted by sudden slippage events, ultimately preventing unwinding over a substantial distance. This behaviour was greatly reduced with the supplement of a small amount of dTTP. These findings presented an opportunity to use nucleotide mixtures to investigate helicase subunit coordination. Our results support a model where nearly all subunits coordinate their chemo-mechanical activities and DNA binding. Such subunit coordination may be general to many ring-shaped helicases and reveals a potential mechanism for regulation of DNA unwinding during replication.   

Unraveling the motion of single-stranded DNA binding proteins on DNA using force and fluorescence spectroscopy

Single-stranded DNA binding (SSB) proteins bind to and control the accessibility of single stranded (ss) DNA generated as a transient intermediate during a variety of cellular processes. For subsequent DNA processing, however, such a tightly wrapped, high-affinity protein--DNA complex still needs to be removed or repositioned quickly for unhindered action of other proteins. Here we show, using single-molecule two- and three-colour fluorescence resonance energy transfer, that SSB can spontaneously migrate along ssDNA. Diffusional migration of SSB helps in the local displacement of SSB by an elongating RecA filament. SSB diffusion also melts short DNA hairpins transiently and stimulates RecA filament elongation on DNA with secondary structure. This observation of diffusional movement of a protein on ssDNA introduces a new model for how an SSB protein can be redistributed, while remaining tightly bound to ssDNA during recombination and repair processes. In addition, using an optomechanical tool combining single-molecule fluorescence and force methods, we probed how proteins with such a large binding site size ($\sim $ 65 nucleotides) can migrate rapidly on DNA and how protein-protein interactions and tension may modulate the motion. We observed force-induced progressive unravelling of ssDNA from the SSB surface between 1 and 6 pN, followed by SSB dissociation at $\sim $10 pN, and obtained experimental evidence of a reptation mechanism for protein movement along DNA wherein a protein slides via DNA bulge formation and propagation. SSB diffusion persists even when bound with RecO, and at forces under which the fully wrapped state is perturbed, suggesting that even in crowded cellular conditions SSB can act as a sliding platform to recruit and carry its interacting proteins for use in DNA replication, recombination and repair.   

Beholding the subcellular world in your PALM: nanometer resolution optical measurements of protein assemblies in cells

Key to understanding a protein's biological function is the accurate determination of its spatial distribution inside a cell. Although fluorescent protein markers enable specific targeting with molecular precision, much of this utility is lost when the resultant fusions are imaged with conventional, diffraction-limited optics. In response, several imaging modalities that rely on the stochastic activation and bleaching of single molecules, and that are capable of resolution 10x below the diffraction limit (250 nm for visible wavelengths), have emerged. This talk will cover superresolution imaging of biological structures using photoactivated localization microscopy (PALM). In addition to covering the theory, we will also discuss the use of the technique in understanding biological phenomena on the nanoscale, including the organization of bacterial chemoreceptors, the movement of actin in neuronal spines, and the stratification of focal adhesions.   

Single-molecule conductance measurements of biomolecule translocation across biomimetic nuclear pores

After a brief overview of our recent work on solid-state nanopores, I will present single-molecule transport data across biomimetic nanopores that contain the key regulating parts of the nuclear pore complex (NPC). The mechanism for the remarkable selectivity of NPCs has remained unclear in a large part due to difficulties in designing experiments that can probe the transport at the relevant length and time scales. Building and measuring on biomimetic NPCs provides new opportunities to address this long-standing problem. covalently tether the natively unfolded Phe-Gly rich domains (FG-domains) of human nuclear binding proteins to a solid-state nanopore (a 10-100 nm sized hole in a SiN membrane). Ionic current measurements provide a probe to monitor single molecules that traverse the pore. Translocation events are observed for transport receptors (Imp$\beta )$, whereas transport of passive molecules (BSA) is found to be blocked. Interestingly, a single type of nuclear pore proteins appears already sufficient to form a selective barrier for transport. A translocation time of about 2.5 ms is measured for Imp$\beta $. This time is found to be similar for transport across Nup153 and Nup98 coated pores, although the observed ionic conductance differs between these two types of pores. We compare two simple models for the pore conductance and find, for both Nups, that the data fits best to a model with an open central channel and a condensed layer along the outer circumference of the pore. reproducing the key features of the NPC, our biomimetic approach opens the way to study a wide variety of nucleo-cytoplasmic transport processes at the single-molecule level in vitro.   

Session Q44: Focus Session: Interparticle Interactions in Polymer Nanocomposites - Transport and Dynamics

Multiscale structure, interfacial cohesion, adsorbed layers, miscibility and properties in dense polymer-particle mixtures

A major goal in polymer nanocomposite research is to understand and predict how the chemical and physical nature of individual polymers and nanoparticles, and thermodynamic state (temperature, composition, solvent dilution, filler loading), determine bulk assembly, miscibility and properties. Microscopic PRISM theory provides a route to this goal for equilibrium disordered mixtures. A major prediction is that by manipulating the net polymer-particle interfacial attraction, miscibility is realizable via the formation of thin thermodynamically stable adsorbed layers, which, however, are destroyed by entropic depletion and bridging attraction effects if interface cohesion is too weak or strong, respectively. This and related issues are quantitatively explored for miscible mixtures of hydrocarbon polymers, silica nanospheres, and solvent using x-ray scattering, neutron scattering and rheology. Under melt conditions, quantitative agreement between theory and silica scattering experiments is achieved under both steric stabilization and weak depletion conditions. Using contrast matching neutron scattering to characterize the collective structure factors of polymers, particles and their interface, the existence and size of adsorbed polymer layers, and their consequences on microstructure, is determined. Failure of the incompressible RPA, accuracy of PRISM theory, the nm thickness of adsorbed layers, and qualitative sensitivity of the bulk modulus to interfacial cohesion and particle size are demonstrated for concentrated PEO-silica-ethanol nanocomposites. Temperature-dependent complexity is discovered when water is the solvent, and nonequilibrium effects emerge for adsorbing entangled polymers that strongly impact structure. By varying polymer chemistry, the effect of polymer-particle attraction on the intrinsic viscosity is explored with striking non-classical effects observed. This work was performed in collaboration with S.Y.Kim, L.M.Hall, C.Zukoski and B.Anderson.   

Organically Modified Nanoclay-Reinforced Rigid Polyurethane Films

The nanodispersion of vermiculite in polyurethanes was investigated to produce organoclay-reinforced rigid gas barrier films. Reducing gas transport can improve the insulation performance of closed cell polyurethane foam. In a previous study, the dispersion of vermiculite in polyurethanes without organic modification was not sufficient due to the non-uniform dispersion morphology. When vermiculite was modified by cation exchange with long-chain quaternary ammonium cations, the dispersion in methylene diphenyl diisocyanate (MDI) was significantly improved. Dispersion was improved by combining high intensity dispersive mixing with efficient distributive mixing. Polymerization conditions were also optimized in order to provide a high state of nanodispersion in the polyurethane nanocomposite. The dispersions were characterized using rheological, microscopic and scattering/diffraction techniques. The final nanocomposites showed enhancement of mechanical properties and reduction in permeability to carbon dioxide at low clay concentration (around 2 wt percent).   

Shear viscosity of polymer nanocomposites from NEMD simulations

Polymer nanocomposites (PNC) are preferred for a variety of applications since they offer excellent thermal, electrical, and mechanical properties. The viscosity of PNC is primarily a strong function of filler size. For micron-sized fillers, the shear viscosity increases with filler volume fraction following the well-known Einstein relationship. However as the particle size approaches the nanoscale, the viscosity is found to either increase or decrease depending on the strength of interactions between the particle and polymer. In this study, the shear viscosity of an entangled polymer melt of N=400 beads of diameter $\sigma $ with and without fillers is estimated using NEMD simulations. The diameter of the nanoparticles (1-10$\sigma )$ and volume fraction (0.05-0.3) are varied for shear rate from 10$^{-2}$ to 10$^{-6 }\tau ^{-1}$. The viscosity of PNC decreases when compared to pure melt for nanoparticles of size 1$\sigma $ and recovers to the value of a pure melt when the size approaches 10$\sigma $, provided all the interactions are neutral. It thus appears that the increase in viscosity embodied in the Einstein relationship only manifests itself for large nanoparticle size $>$10$\sigma $.   

Towards the Next Generation of Polymer Nanocomposites: More Rigid, Lighter Weight, Yet Easier to Process

Polymer nanocomposites are attractive for their lightness in weight and excellent mechanical reinforcement. Current nanocomposites incorporate high aspect ratios fillers such as clays, carbon nanotubes (CNT), and graphenes. Exfoliation of clay, for example, is essential to obtain maximum mechanical reinforcement, yet this results in a 2 to 4 order of magnitude melt viscosity increase. This high viscosity leads to a reduction in the production rate and/or increased processing cost, which is undesirable. In order to obtain reduced melt viscosity without sacrificing the advantages of current nanocomposites, we prepared poly(styrene) (PS) nanocomposites by inclusion of various spherical nanoparticles using a technique that ensures good dispersion. Tensile tests demonstrated enhanced tensile modulus in the glassy state while a reduced melt viscosity was observed. The results show that nanoparticle geometry is extremely important and nanoscale effects can lead to the next generation of polymer nanocomposites.   

A Comparative Study of Interfacial Slip in Polymer Blends with Nanoparticles and Diblock Copolymer Compatibilizers

The interfacial region in polymer blends has been identified as a low viscosity region in which considerable slip can occur when the blend is subjected to shear forces. Here we use Molecular Dynamics simulations to establish and compare the roles that added nanoparticle fillers and diblock copolymers play in modifying the interfacial rheology. By choosing conditions under which the fillers and diblocks are localized, either in the two phases or at the interface, we can look at the interplay between their strengthening capabilities and the change in the interfacial slip behavior. We examine particle size, attraction between the particle and the polymer component, and the amount of filler in the material and compared this to systems including diblock copolymers at the same volume fraction. Our studies are performed, for a variety of shear values, both above and below the point at which the filler particles form a transient network in the blend.   

The Effect of Elongational Flow on the Placement and Orientation of Nanorods in Polymer: Modeling and Experiments

Nanorods are often incorporated into a polymer to enhance its functionality. Gaining control over the placement of nanorods in polymer is important to improve the desired nanocomposite material property and for application like solar cell. First, we used coarse-grained molecular dynamics (CGMD) simulation to quantitatively examine the effect of elongational flow on the placement of model nanorods in homopolymer matrix. We have investigated how flow strength, concentration, interaction, and aspect ratio of nanorods affect its placement in homopolymer. As an analogous experiment, we have electrospun polyvinyl alcohol (PVA) in water with Au nanorods. The experimental result showed dispersion and alignment of Au nanorods, as predicted by the simulation. We also demonstrated selective placement of nanorods along the outer layer of fiber by co-axially electrospinning PVA/Au nanorods and pure PVA as shell and core, respectively. The material properties of the PVA/Au nanocomposite fiber are tested to show its potential application such as electromagnetic interference (EMI) shielding. The good agreements between simulation and experiment suggest that CGMD simulation can be used as a predictive tool for controlling nanorod placement in a polymer under extensional flow.   

Directed Self-Assembly of Nanoparticles via Flexible-Blade Flow Coating

We present a facile, non-lithographic, one-step method termed flexible-blade flow coating to direct the assembly of quantum dots. This versatile technique exploits the phenomenon known as the ``coffee ring effect'' coupled with confined convective flow and controlled stick-slip motion to fabricate ribbons and fabrics with a broad range of length scales of nearly any material. We achieve nanostripe dimensions of width below 300 nm, thickness of a single nanoparticle ($\sim$8 nm), and continuous length exceeding 5 cm. This multi-length scale control is facilitated by the use of a flexible blade, which allows capillary forces to self-regulate the uniformity of convective flow processes. We exploit solvent mixture dynamics and nanoparticle chemistry to enhance intra-assembly particle packing, leading to novel assembly properties including conductivity and free-standing mechanical flexibility and strength. This simple technique and the use of novel materials open up a new paradigm for integration of nanoscale patterns over large areas for various applications.   

Properties of Macroscopic Nanoparticle Assemblies Fabricated by Flexible Blade Flow Coating

Nanoparticle assemblies have gained much interest for their potential in electronic, photonic, optical, chemical, and biological applications. Although one of the greatest challenges is the controlled positioning of nanoscale components into the desired multi-length scale structures, understanding the properties of nanoparticle assemblies has also remained elusive. We have developed a technique termed flexible blade flow coating to direct the assembly of nanoparticles into ribbons and fabrics with a broad range of length scales. Ribbons and fabrics constructed with photoreactive quantum dots are crosslinked by UV irradiation affording long, flexible and robust structures that allow for subsequent liftoff from the substrate by dissolution of a sacrificial underlayer. The structural integrity of freely floating fabrics and extremely high aspect ratio ribbons are observed through fluorescence microscopy. Physical properties of these assemblies are explored with varying dimensions and ligand chemistry. We find that nanoparticle ribbons and fabrics possess unique properties in comparison to continuous polymer thin films, such as spherical wrapping and two-dimensional flexibility.   

Reversible Shear-Flow-Induced Polymer and Colloid Aggregates

Using hydrodynamic simulations and a coarse-grained interaction model, we show that self-associating polymer and colloid mixtures can form reversible flow-induced aggregates in shear flow. We find that when increasing shear rates, the mixtures go through four distinct conformations from no aggregation to dense aggregates. The different conformations are verified by analyzing their radial distribution functions, g(r), as well as by visual inspection. Furthermore, we find that the formation of the aggregates is reversible. That is, the shear-induced aggregates disappear when we decrease the shear rates, and reappear when we increase the shear rates again.   

Impact of Carbon Nanoparticle Shape on Polymer Dynamics in Nanocomposites

In forming quality nanocomposites of carbon-based nanoparticles (CNPs) in a polymer matrix, achieving and maintaining a high degree of dispersion is a crucial problem. One method to attain well-dispersed CNP nanocomposites is to incorporate non-covalent interactions between the CNP and matrix, which also impacts the dynamics of the polymer chain. In this work, T2 NMR relaxometry (T2 NMR) examines the effect on polymer chain dynamics of incorporating CNPs into polystyrene-co-acrylonitrile (SAN) random copolymer matrices. In SAN-CNP composites, the segmental-chain dynamics can be influenced by the non-covalent interactions formed with the nanoparticle (interacting), but are also influenced by the CNP steric bulk alone (non-interacting). The use of T2 NMR allows for the examination of the influence of the extent of non-covalent interactions on this segmental chain level. This segmental level view also allows for the distinction between relaxation dynamics of the interacting and non-interacting regimes. Current data indicates that increased acrylonitrile content in the copolymer results in increased non-covalent interactions and overall slowing of chain dynamics.   

Modifying Fragility and Length Scales of Polymer Glass Formation with Nanoparticles

We investigate the effects of nanoparticles on glass formation in a model polymer melt by molecular dynamics simulations. The addition of nanoparticles allows us to change the glass transition temperature $T_g$, the fragility of glass formation, and both static and dynamical length scales in a controlled fashion. We contrast the length scales of static density changes with the length scale over which nanoparticles perturb the dynamics, as well as the length scale of cooperative string-like motion. Using the Adam-Gibbs approach, we show how the changes of fragility can be interpreted as a measure of the scale of cooperative string-like motion. We contrast the behavior along isobaric and isochoric paths to $T_g$, and find that changes along an isobaric path (most relevant experimentally) are much smaller than those along an isochoric path.   

Glass transition temperature of polymer nano-composites with polymer and filler interactions

We systematically studied versatile coarse-grained model (bead spring model) to describe filled polymer nano-composites for coarse-grained (Kremer-Grest model) molecular dynamics simulations. This model consists of long polymers, crosslink, and fillers. We used the hollow structure as the filler to describe rigid spherical fillers with small computing costs. Our filler model consists of surface particles of icosahedra fullerene structure C320 and a repulsive force from the center of the filler is applied to the surface particles in order to make a sphere and rigid. The filler's diameter is 12 times of beads of the polymers. As the first test of our model, we study temperature dependence of volumes of periodic boundary conditions under constant pressures through NPT constant Andersen algorithm. It is found that Glass transition temperature (Tg) decrease with increasing filler's volume fraction for the case of repulsive interaction between polymer and fillers and Tg weakly increase for attractive interaction.   

Payne effect in model nanocomposite the role of polymer confinement

Payne effect is a non-linearity observed in polymer nanocomposites at small strain amplitudes, abiove the bulk glass transition temperature. The origin is the non-linear mechanical response of the polymer located near the solid fillers. However the exact nature of the mechanical response is still the object of debate. We have developed since ten years model nano-composite systems consisting in monodisperse spherical particles dispersed in an elastomer matrix. Thanks to NMR and Neutrons scattering, we have been able to determine precisely the amount of polymer confined between pairs of particles and with a modified dynamics. From that we have deduced that the Payne effect clearly originates in two mechanisms: i) around each particle, a glass transition temperature gradient ii) around this first layer, a modified topology of the polymer --originating itself in the glassiness of the polymer very near the particles. Hence, we are able to build a master curve for the Payne effect amplitude versus the number of particles connected to their neighbors by these two layers, that gathers measurements at various temperatures, volume fractions and frequencies.   

Session Q45: Elastomers and Gels

Can a Rheological Experiment Distinguish Between a Gel and a Soft Glass? If yes, which Experiment?

Generic rheological differences between gels and soft glasses appear most pronounced in the \textit{immediate approach of the liquid-to-solid transition from the liquid side}. Two model systems of known linear viscoelasticitywere chosen to exemplify the two material classes: a crosslinking PDMS represents gelation and a concentrated, aqueous suspension represents the soft glass transition. The longest relaxation time and the zero shear viscosity diverge for both materials, which look very similar in this way. However, the relaxation time spectrum and its expression as complex modulus, with components G' and G'', provide a clear distinction between gelation and the soft glass transition. While the long-time component of the relaxation time spectrum follows a powerlaw in time for both, log $H\sim n$ log $t$, their powerlaw exponent $n $is of different sign: negative $n$ for the critical gel (material at the gel point) (Chambon et al. Polym Bull 13:499--503, 1885; Winter et al. J Rheology 30:367--382, 1986; Chambon et al. J Rheol 31:683--697, 1987) and positive $n$ for the soft glass (Siebenb\"{u}rger et al. J Rheology 53:707-720, 2009; Winter et al. Rheol Acta 48:747--753). The powerlaw spectrum is cut off by the diverging, longest relaxation time (called ``alpha relaxation time'' for the soft glass) in the approach of the liquid-to-solid transition. In summary, relaxation data provide a clear distinction between these two classes of materials.   

Effects of crosslinker concentration and chemical disorder on the nonlinear mechanics of thermoreversibly associating networks

We present simulation studies of thermoreversibly associating polymer networks that relate dramatic differences in nonlinear mechanics (e.\ g.\ creep and fracture) to differences in crosslinker placement and consequent differences in the equilibrium structure and quiescent dynamics of these systems. Our results illustrate how the greater structural and dynamical heterogeneity in systems possessing randomly placed crosslinkers leads to higher mobility, increased creep compliance and decreased fracture toughness in comparison to systems with uniformly spaced crosslinkers. Further quiescent-dynamical slowdown and mechanical property enhancement may be obtained through well-defined but nonuniform placement of crosslinkers. The variation of properties with crosslinker concentration $c$ and parent chain length $N$ is also investigated. Increasing characteristic chemical distances between crosslinkers decreases effects arising from network ``loops,'' the prevalence of which is closely associated with chemical order. At fixed $c$, while differences associated with chemical (dis)order decrease with increasing $N$, they remain dramatic in the $N \sim N_e$ regime which is often used in practical applications.   

Mechanically induced oscillations in Belousov-Zhabotinsky gels

Belousov-Zhabotinsky (BZ) gels are a unique class of stimuli-responsive materials that exhibit periodic changes in both color and size due to the self-oscillating kinetics of the BZ reduction-oxidation reaction. Such oscillations last for several hours, ending when a steady-state is reached in which the chemical reactants have been depleted. Here, we demonstrate that a depleted, non-oscillating BZ gel can be mechanically resuscitated, extending the oscillatory functionality of the material. These results represent the first experimental demonstration of mechanically induced oscillations in N-isopropylacrylamide-Ru(bpy)$_{3}$ gels. We characterize this phenomenon by quantifying the critical stress required to trigger oscillations, and the dependence of period and amplitude for triggered oscillations as a function of malonic acid concentration. Lastly, we demonstrate sensor applications comprising arrays of discrete BZ gel discs in which individual gels oscillate in color upon compression and have the capacity to transmit chemical signals away from the deformation site.   

Nonlinear Elasticity of Entangled Polymer Networks

We develop a microscopic model for elasticity of entangled polymer networks. The classical models of rubber elasticity (affine network and phantom network models) take into account only the effect of cross-links, but not the entanglements between polymer chains. For uniaxial deformation, the entanglement effects can be characterized by the dependence of Mooney ratio on network deformation. Constrained network models (such as constrained-junction and diffused-constraint models), tube models (such as Edwards' tube and nonaffine tube models) as well as phenomenological models (such as Mooney- Rivlin model) have been proposed to capture the experimentally observed dependence of Mooney ratio on network deformation. One of the latest efforts in the field is the slip-tube model, in which the entanglements are represented by slip-rings that can glide along the network chains but elastically constrained in space. The model we study improves over the original slip-tube model by taking into account harmonic interactions along the chain between such slip-links. We analytically and numerically solve the new microscopic model and present our results in comparisons with experimental and simulation data for both uniaxial and biaxial deformation.   

Coarse grain modeling of the high-rate stress-strain behavior for select model Poly[urethane urea] (PUU) elastomers

Microphase-separated PUU, which consists of 4,4'-dicyclohexylmethane diisocyanate, diethyltoluenediamine and poly[tetramethylene oxide](PTMO), exhibits versatile mechanical properties making them an excellent choice for potential applications in the form of films, adhesives, coatings and matrix materials for composites. To elucidate the effects of composition, including the hard segment content {\&} molecular weight of PTMO, on rate-dependent mechanical deformation in the high strain-rate regime ($>>$ 10$^{5}$/s) the stress-strain behavior for PUU at various rates are calculated for four model systems using a coarse-grain model. Pair interactions between topologically non-connected particles are described by the standard truncated Lennard-Jones (LJ) pair potential, where bonded particles interact according to the standard FENE/LJ potential. An angle harmonic potential is also used to enforce the rigidity of the hard segments, and the system is evolved using molecular dynamics. Stress-strain curves are calculated at various strain-rates and qualitatively agree with experimental results when extrapolated to higher rate. Further analysis of the morphology is also performed to characterize the morphology and discern its connection to the calculated mechanical properties.   

Swelling Behavior of Crosslinked Rubber: Does the Peak in Dilational Modulus Exist?

Previous work\footnote{G.B. McKenna and J.M. Crissman.J. Polym. Sci., Part B: Polym. Phys. 35, 817 (1997).} has shown that when handled properly, Frenkel\footnote{J. Frenkel, Acta Phys. USSR, 9, 235 (1938); Rubber Chem. Technol., 13, 264 (1940).}-Flory-Rehner\footnote{P. J. Flory and J. J. Rehner, Jr., J. Chem. Phys.,11, 521 (1943).}(FFR) theory is an excellent model to explain swelling behavior with the exception of failing to describe the peak of the swelling activity parameter S, or dilational modulus. This peak was first observed by Gee et al.\footnote{G. Gee, J. B. M. Herbert, and R. C. Roberts, Polymer, 6, 541 (1965).} and has eluded explanations. In the present work, we explored the importance of fitting procedure to the isopiestic data on the presence of the peak of S. We found the peak in S disappears when using a FFR model based fit instead of the empirical or polynomial fits used previously. We take model material parameters and show that adding less than 1{\%} random error to the theoretical curves can lead to the peak in S. Our findings suggest strongly that the ``peak'' in S is due to experimental errors that are amplified by the fitting method.   

Microphase Separation and Dynamics of Elastomeric Polyureas

Polyureas, consisting of alternating polyether soft segments and urea-containing hard segments, are of interest for shock and other energy absorbing applications. The properties of these materials are strongly influenced by microphase separation of the hard and soft segments, which is rather incomplete. Bulk- and solution-polymerized polyureas based on oligomeric polytetramethylene oxide and methylene diphenyl diisocyanate were investigated, and the role of PTMO molecular weight was identified. The morphology was characterized using atomic force microscopy and quantitative degrees of phase separation were determined from small-angle X-ray scattering. Dielectric relaxation spectroscopy and dynamic mechanical analysis were used to probe the dynamics. Particular attention was paid to the segmental dynamics of the soft phase, which has been proposed to be a major contributor to shock energy absorption in these materials.   

Opening and Closing of Nanocavities under Stress in Soft Nanocomposites: A Real Time Small Angle X-ray Scattering (SAXS) Observation

Cavitation occurring at the nanometer length scale has been recently demonstrated conclusively in rubbers$^{1}$. Real time SAXS with synchrotron radiation is employed to probe the structure changes in carbon black filled styrene-butadiene rubber (SBR) under uniaxial tension. The scattering invariant Q($\lambda )$, where $\lambda $ is the extension ratio, increases sharply, which we attribute to void formation, above a critical true stress ($\sim $25 MPa) that is roughly independent of both filler content and crosslinking density. During step-cycle tests Q decreases on unloading to Q$_{0}$, its value before any testing, and does not increase again until $\lambda $ exceeds the maximum previous $\lambda =\lambda _{max}$, showing that the voids close upon unloading and only reappear upon reloading when $\lambda \quad > \quad \lambda _{max}$ (Mullins effect). We attribute the increase of the scattering invariant once $\lambda $ exceeds $\lambda _{max}$ to the creation of new voids rather than to the reopening of old ones. The scattering of the voids in the region q $<$ 0.1 nm$^{-1}$ can be separated from that of the carbon black particles and provides information on average void size and shape.   

Reversible shape memory

An ``Achilles' heel'' of shape memory materials is that shape transformations triggered by an external stimulus are usually irreversible. Here we present a new concept of reversible transitions between two well-defined shapes by controlling hierarchic crystallization of a dual-network elastomer. The reversibility was demonstrated for different types of shape transformations including rod bending, winding of a helical coil, and widening an aperture. The distinct feature of the reversible shape alterations is that both counter-shapes are infinitely stable at a temperature of exploitation. Shape reversibility is highly desirable property in many practical applications such as non-surgical removal of a previously inserted catheter and handfree wrapping up of an earlier unraveled solar sail on a space shuttle.   

Inscribing dynamical patterns within heterogeneous self-oscillating gels.

Grafting the ruthenium catalyst to the network of swollen chemo-responsive polymer gel creates a new class of materials, which exhibit the autonomous, coupled chemical and mechanical oscillations induced by the ongoing Belousov-Zhabotinsky (BZ) reaction. The mechanical oscillations occur due to the hydrating effect of the oxidized Ru that causes the gel to swell and de-swell repeatedly. It was predicted previously that compartmentalization of BZ gels in a nonresponsive gel matrix would enable a researcher to create gel-based devices with the functionality inscribed by the configuration of the Ru-containing patches. Recently, the heterogeneous gels were fabricated that encompass the disk-shaped BZ patches. It was demonstrated experimentally for the first time that the direction of propagation of the chemo-mechanical waves in an array of the BZ patches can be controlled by varying the ruthenium content and size of the patches. Here, we present the results of computational modeling of such heterogeneous self-oscillating gels. We discuss how the catalyst concentration, patch size, and inter- patch distance affect the synchronization of oscillations in the neighboring BZ gels, and how the synchronization effects can be utilized to control the dynamical behavior of the entire system.   

Swelling instabilities in patterned, microscale gels

Hydrogels facilitate reconfigurable structures with response integrated at the material level. Response is engendered by a competing mechanism: the elasticity of the network ounterbalances expansion by the solvent. If the strength of expansion can be controlled by an environmental cue, the hydrogel can be adjusted in situ. The equilibrium state occurs when the osmotic stress exerted by the solvent in the gel equals the osmotic pressure of the solvent outside the gel. For a free structure, the equilibrium state corresponds to homogenous swelling. If a free surface of the gel is mechanically constrained, however, the dimensions available for the relief of the osmotic stress are reduced, resulting in non-uniform or inhomogeneous swelling. In this study, we demonstrate how mechanical constraints impose differential gel swelling and buckling in patterned gels. Depending on the initial geometry of the constrained gel, three general modes of swelling-induced deformation can be observed: lateral differential swelling, bulk sinusoidal buckling, and surface wrinkling. Through confocal microscopy and 3D image rendering, the mechanics of swelling has been evaluated in the context of linear elasticity theory.   

Thermoresponsive hydrogels from ABC triblock terpolymers

We have prepared novel thermoreversible ABC hydrogels from poly(ethylene-alt-propylene)-b-poly(ethylene oxide)-b-poly(N-isopropylacrylamide) (PEP-PEO-PNIPAm) triblock terpolymers. The terpolymers form micelles in water at low temperatures with hydrophobic PEP cores surrounded by hydrophilic PEO-PNIPAm coronas, and these micelles subsequently associate to form a hydrogel upon heating above the lower critical solution temperature (LCST) of PNIPAm. The separation of micellization and gelation leads to the formation of a two-compartment network with exclusively bridging conformations for the PEO midblocks. Therefore, gelation can be achieved at a much lower concentration, with better mechanical properties and a sharper sol-gel transition, when compared with ABA triblock copolymer hydrogels from PNIPAm-PEO-PNIPAm. The results highlight the intricate nanostructures and new properties available from ABC terpolymer hydrogels.   

Single Quantum Dot Tracking in Heterogeneous Polyacrylamide Hydrogels

Structural heterogeneity within polymer gels plays an important role in determining their material properties, yet is difficult to characterize by established methods. Single particle tracking measurements can provide highly localized information on the diffusion dynamics of tracer particles, and therefore on the material properties of the medium. We use tailored core-shell quantum dots (QDs) with hydrophilic ligands to characterize polyacrylamide hydrogels with varying crosslink density. We find that QDs show sub-diffusive behavior and non-Gaussian displacement distributions, consistent with prior reports on diffusive behavior in other heterogeneous media. We also consider the distribution of particle caging times, which is dictated by the potential energy barriers to escape pores, and therefore provides insight into structural heterogeneity. Specifically, we find that gels with a higher density of crosslinks yield broader distributions of caging times, indicating greater heterogeneity of these networks.   

Modeling Photo-Reconfiguration and Directed Motion of Spirobenzopyran- Containing Polymer Gels

We develop a computational model to simulate the behavior of photo-responsive polymer gels that contain spirobenzopyran (SP) chromophores. Using this model, we design three-dimensional samples with dynamically reconfigurable morphologies and photo-induced motility. In the dark, the SP moieties assume an open ring conformation and are hydrophilic; under illumination with blue light, the chromophores assume a closed ring conformation and are hydrophobic. This collapse of the gels is caused by the decrease in hydration due to conformational changes and not by a light-induced heating of the polymer network. We demonstrate that these gels can be effectively patterned remotely and reversibly with light by illuminating the sample through photomasks. We also show that by introducing variations in crosslink density within the gels during their preparation, as well as introducing temperature gradients, we have additional means of guiding the dynamic behavior of these versatile, responsive systems. Furthermore, we demonstrate that one can use a mobile light source to move multiple gel pieces to a specific location. The results point to a novel method for controlling the self-organization of soft, reconfigurable materials.   

Gelation of Copolymers Photo-crosslinked by Pendent Benzophenones

Copolymers containing pendent benzophenone (BP) groups provide a simple and powerful route to crosslinkable polymer films. While the solution state photo-chemistry of BP is well established, and crosslinking of polymers blended with BP has been studied in detail, the process of crosslinking by covalently attached BP has received comparatively little attention. We have prepared copolymers of BP with several different monomers, and studied gelation as a function of BP content and degree of photochemical conversion. Understanding the influence of polymer chemistry on crosslinking efficiency allows the appropriate choice of materials for nanostructured photo-crosslinkable polymer films and reactive polymer blends.   

Session Q46: Invited Session: Quantum Information Processing in Diamond

Single spins in diamond: scalable quantum registers and nanoscale sensors

Ability to detect single atoms is a key element of several key technologies of including quantum information processing, communications as well as nanoscale imaging and sensing. Usually single atom control techniques are limited to low temperature operation. In this talk we will show that single spins associated with nitrogen-vacancy defects diamond (NV centers) can be used as nanoscale magnetic field sensor allowing detecting magnetic moment associated with single electrons under ambient conditions. We also show that coupled arrays of spins can be used as building blocks for scalable quantum registers.   

Towards large-scale quantum computing using spins and photons on a chip

Nitrogen-vacancy (NV) centers in diamond are attractive candidates for quantum bits for quantum information processing. Theoretically it should be possible to build large-scale quantum optical networks with the NV-diamond system. We report HP Labs' recent results toward coupling chip-based optical cavities to negatively charged NV centers in two systems: all diamond micro-ring cavities coupled to native NV centers and GaP micro-ring cavities coupled to near surface centers formed by implantation and annealing. In both systems we observe an enhancement of the spontaneous emission rate into the NV zero-phonon line. Additionally we will discuss recent results in engineering the optical properties of near-surface NV centers suitable for photonic coupling.   

Probing the motion of a mechanical resonator via coherent coupling to a single spin qubit

Mechanical systems can be inuenced by a wide variety of extremely small forces, ranging from gravitational to optical, electrical, and magnetic. If the mechanical resonator is scaled down to nanometer-scale dimensions, these couplings can be harnessed to monitor and control individual quantum systems. In this talk, I will describe experiments in which the coherent evolution of a single electronic spin associated with a Nitrogen Vacancy (NV) center in diamond is coupled to the motion of a magnetized mechanical resonator. Specifically, we have used coherent manipulation of the NV spin to sense the resonator's Brownian motion under ambient conditions. Potential applications of th is technique include the detection of the zero-point uctuations of a mechanical resonator, the realization of strong spin-phonon coupling at a single quantum level, and the implementation of quantum spin transducers.   

Preparation, single-shot readout and long-distance coupling of solid-state quantum registers

A key challenge in quantum science is to robustly control and to couple long-lived quantum states in solids. In this talk, we report on our latest advances towards realizing long-distance quantum networks with spins in diamond. First, we demonstrate preparation and single-shot measurement of a quantum register containing up to four quantum bits [1]. Projective readout of the electron spin of a single NV center in diamond is achieved by resonant optical excitation. In combination with hyperfine-mediated quantum gates, this readout enables us to prepare and measure the state of multiple nuclear spin qubits with high fidelity. We show compatibility with qubit control by demonstrating initialization, coherent manipulation, and single-shot readout in a single experiment on a two-qubit register, using techniques suitable for extension to larger registers. Second, we observe quantum interference of photons emitted by two spatially separated NV centers [2]. By using electrical tuning of the optical transition frequencies, we are able to observe such interference even for initially dissimilar centers, indicating a viable path for scaling towards a multi-node diamond-based quantum network. We will present these results, along with our most recent data, and discuss the prospects of realizing quantum networks with NV centers in diamond in the near future. \\[4pt] [1] Nature 477, 574 (2011) \\[0pt] [2] arXiv 1110.3329   

Electrical tuning of single-photon emission in diamond devices

For quantum information applications, nitrogen-vacancy (NV) centers in diamond combine many of the advantages of atomic systems (optical access, millisecond spin-coherence times) with the engineering flexibility of solid-state devices. Recent demonstrations of coherent coupling between photons and individual NV-center spins [1,2] provide a route to integrating NV-center qubits within photonic networks and for on-demand generation of entangled single-spin/single-photon pairs. Such applications require the ability to tune the NV-center zero-phonon optical transitions, to compensate for natural sample inhomogeneities which perturb the electronic orbital states. Here we demonstrate the ability to electrically control the orbitals of individual NV centers by applying voltages to micron-scale surface gates [3]. Surprisingly, the local electric field experienced by an NV center is significantly enhanced by a photoinduced space charge resulting from photoionization of deep donor impurities within the diamond, even in high-purity single-crystal material ($<5$~ppb nitrogen content). Since the photoinduced electric fields are reproducible as a function of gate voltage and are predominantly directed perpendicular to the diamond surface, we can harness them to obtain three-dimensional control of the local electric field vector with surface gates alone. To demonstrate this technique, we tune the excited-state orbital doublet of a strained NV center to degeneracy, as required for some spin-photon entanglement protocols [2], and then adjust the optical transition frequency, showing that we can tune multiple NV centers to have the same degenerate transition energy. This method should enable the coherent coupling of multiple NV center spins to indistinguishable photons within a scalable photonic network. \\ \\ {[1]} B.~B.~Buckley, G.~D.~Fuchs, L.~C.~Bassett, and D.~D.~Awschalom, \emph{Science} \textbf{330}, 1212 (2010).\\ {[2]} E.~Togan \emph{et al.}, \emph{Nature} \textbf{466}, 730 (2010).\\ {[3]} L.~C.~Bassett, F.~J.~Heremans, C.~G.~Yale, B.~B.~Buckley, and D.~D.~Awschalom, \emph{Phys.~Rev.~Lett.} (in press).   

Session Q47: Focus Session: DNA-Coated Colloid Particles

Heterogeneous 3D Assembly of DNA-encoded Quantum Dots and Gold Nanoparticles

We report the heterogeneous assembly of quantum dots (QDs) and gold nanoparticles (AuNPs) into three-dimensional (3D) superlattices by means of DNA encoding. CdSe/ZnS core-shell QDs were functionalized with stranded (ss) DNA to obtain a stable aqueous dispersion of QD-DNA conjugates, which maintains the optical properties of the original QDs. By introducing AuNPs modified by complementary ssDNA, QD-AuNP aggregates were assembled. Using synchrotron-based small angel X-ray scattering, we found that QD-AuNP assemblies form a body center cubic (BCC) lattice, while each nanoparticle type, QD and AuNP, are positioned in a simple cubic (SC) manner. Distance-dependent optical property of QDs in heterogeneous superlattices was studied by time-resolved fluorescence spectroscopy. The potential applications of the above optically-active nanosystems will also be discussed.   

Self-Assembly of Octopus Nanoparticles into Pre-Programmed Finite Clusters

The precise control of the spatial arrangement of nanoparticles (NP) is often required to take full advantage of their novel optical and electronic properties. NPs have been shown to self-assemble into crystalline structures using either patchy surface regions or complementary DNA strands to direct the assembly. Due to a lack of specificity of the interactions these methods lead to only a limited number of structures. An emerging approach is to bind ssDNA at specific sites on the particle surface making so-called octopus NPs. Using octopus NPs we investigate the inverse problem of the self-assembly of finite clusters. That is, for a given target cluster (e.g., arranging the NPs on the vertices of a dodecahedron) what are the minimum number of complementary DNA strands needed for the robust self-assembly of the cluster from an initially homogeneous NP solution? Based on the results of Brownian dynamics simulations we have compiled a set of design rules for various target clusters including cubes, pyramids, dodecahedrons and truncated icosahedrons. Our approach leads to control over the kinetic pathway and has demonstrated nearly perfect yield of the target.   

DNA-induced 2D-to-1D Phase Transition of Nanoparticle Assemblies at Liquid-Vapor Interface

We have investigated the structure formation and development for two-dimensional assembly of DNA functionalized nanoparticles at liquid-vapor interface. The adsorption of negatively charged DNA-coated particle to the interface was triggered by a positively charged lipid layer. A normal and in-plane structure of the nanoparticle monolayer were probed using in-situ surface scattering methods, x-ray reflectivity and grazing incidence small angle x-ray scattering. We observed the formation of the hexagonally closed packed (HCP) 2D lattice of nanoparticles due to a combination of electrostatic surface-to-particle attraction and interparticle repulsion. Upon an onset of DNA hybridization between particles the phase transition from HCP order to 1D crystalline structure was observed. The control on the interparticle spacing and monolayer confinement were also examined by changing a salt concentration. Our studies demonstrate novel mechanism for transition from ordered 2D to ordered 1D structure due to the domination of DNA-induced attraction over an electrostatic repulsion and open a route for nano-structure manipulations at the interfaces.   

Structural Diversity of DNA-Coated Particle Assemblies

Custom designed nanoparticles (NP) or colloids with specific recognition offer the possibility to control the phase behavior and structure of particle assemblies for a range of applications. One approach to realize these new materials is by attaching DNA to a core particle; the hybridization of double-stranded DNA between particles results in the spontaneous assembly of higher-order structures. Control of the assembled state can be achieved by adjusting several parameters, including sequence selectivity, DNA link orientation, DNA length and flexibility, and the balance between the length of links and non-specific repulsive interactions. I will discuss the results of a coarse-grained molecular model for DNA-linked nanoparticles that helps to rationalize experimental findings and demonstrate new routes to control the assembled structure. We examine how the number and orientation of strands affects the structure, phase behavior, and dynamics. We show that it is possible to realize unusual phase diagrams with many thermodynamically distinct phases, both amorphous and crystal. We further examine the parameters that control the pathways of assembly, which are critical to avoid kinetic bottlenecks. Finally, we discuss strategies to create highly anisoptropic structures using both isotropic and anisotropic core units.   

DNA Mediated Nanoparticle Crystallization: Characterizing How Equilibrium is Reached

DNA programmed self-assembly is becoming one of the most powerful tools for designing nanoparticle crystals due to the exquisite control over lattice size and structure achievable. While in recent years the inventory of crystalline structures accessible through DNA programming has grown, our understanding of the dynamical processes that lead to crystallization is still limited. Using MD we simulate the nucleation and growth of DNA programmed nanoparticle crystallization and characterize the different processes that determine the relaxation times leading to equilibrium. In particular, we classify the topological defects and the processes leading to their annihilation. Implications for experiments as well as for achieving single crystals are also discussed.   

Packing of DNA-assembled Nanocubes and Nanooctahedra

Nanoparticle shape has a profound effect on assembly behavior. However, the contribution of surface-attached molecules can significantly modulate the packing of nanoscale objects, inducing phases markedly different from the known packing rules of macroscopic objects. Our studies uncover the phase behavior of nanocubes and nanooctahedron assembled by DNA-mediated interactions into three-dimensional structures, which were probed in-situ by small angle x-ray scattering. We observed that the packing of these nanoscale anisotropic objects depends strongly on the details of the DNA linkages. Using electron microscopy and optical spectroscopy, we elucidate the factors that drive assembly and dictate the spatial organization of the nano-objects. The relationship between particle shape and the mechanism of phase formation for nanocubes has been also investigated.   

Making DNA competitive: a new strategy to improve the self-assembly properties of DNA-coated particles

We present a new approach to widen the normally very narrow temperature window for equilibrium self-assembly (e.g. crystallization) of DNA-coated particles. Using Monte Carlo simulations, we first show that not only enthalpic but also entropic effects - due to the multi-bond character of the DNA-mediated interactions - play an important role in the overall binding properties of the particles. We then outline a new strategy that exploits the competition between different types of inter-particle DNA linkages to achieve a temperature-dependent switching of the dominant bond type. Depending on the length ratio of the DNA constructs, the bond switching is either energetically driven or controlled by a combinatorial entropy gain, which arises from the large number of possible binding partners for each DNA strand. Importantly, the resulting particle interaction is less strongly temperature dependent than in ``conventional'' systems with only one bond type, thus enhancing the experimental control over self-assembly. Finally, we will also show that in general stable gas-liquid separation is expected to occur only for particles smaller than a few tens of nanometers, which suggests that nanoparticles and micrometer-sized colloids will follow different routes to crystallization.   

DNA Regulated Clusters: Structure and Self-limiting Assembly

We have investigated the structural details of nanoparticle clusters assembled by flexible DNA linkers in dimer clusters using electron microscopy, in-situ x-ray scattering and optical methods. The observed dependence of interparticle distance on a DNA length significantly deviates from the predictions for single chain linkages and previous measurements for superlattices. The observed effect is attributed to a large solid angle of interparticle contact, in agreement with computational results. Our studies further reveal the non-monotonic decrease of interparticle distance for the longer linkers; that suggests nanoparticles confinement by hybridized linkers from opposite particles' hemispheres. The effect is accompanied by inhibited development of nanoclusters and results in a self-limited cluster assembly. The mechanism of dimer formation was investigated in details using the optical methods.   

Kinetics of the Association of DNA Coated Colloids

The self-assembly of DNA coated colloidal particles opens a door to complex colloidal architecture. To understand how particles aggregate due to DNA hybridization between particles is the key to program colloidal aggregation. In this study, we investigate theoretically and experimentally the aggregation time of micron scale particles as a function of DNA coverage and the ion concentration $I$. Our particles coated with streptavidin can attach $\sim$70,000 biotinlated DNA molecules, which have a double strand with 49 base pairs and an 11 base sticky end. At $I$ = 60 mM , particles 100\% fully covered with DNA show an aggregation time of $\tau$ = 6 minutes. For 10\% DNA covered particles at $I$ = 35 mM, $\tau$ = 57 hours. A simple model based on the reaction limited aggregation and electrical repulsion for DNA hybridization is developed and tested. These experiments and the model also allow us to use the microscopic colloidal aggregation to measure nanoscopic hybridization rates.   

Phase Behavior and Magnetic Response of DNA-mediated Gold and Iron Oxide Nanoparticle Assemblies

Gold nanoparticles (NPs) have long been long served as model systems to study phase behavior of DNA-assisted NP assemblies. Incorporation of different types of nano-objects into DNA-NP systems opens attractive possibilities for the material design. Furthermore, it also allows enriching a self-assembly behavior by an introduction of non-specific yet controllable interparticle interactions. Herein, we report the DNA-mediated assembly of a heterogeneous system comprising gold and superparamagnetic iron oxide (IO) NPs. We systematically studied the phase diagram of the assembled systems by varying a system's composition, DNA design and environmental conditions. Our studies show that by controlling a balance between non-specific and DNA-recognition interactions via system design the assembled phase can be switched between a face-centered cubic (fcc) structure of a IO assembly and a superlattice formed by Au-IO core-shells clusters. We also observed that structure of assemblies is responsive to the magnetic field.   

Modeling of DNA-Directed Colloidal Self-Assembly and Crystallization

A series of design rules have recently been developed for using gold nanoparticles conjugated with a dense layer of double stranded DNA chains to assemble a wide variety of nanoparticle superlattice structures [1]. Key design parameters for obtaining different structures in a binary system were shown to be the ratio of the hydrodynamic radii of the DNA-conjugated particles, the ratio of the number of DNA strands per particle, and the self- or non-self-complementary nature of the DNA sequences guiding the assembly process. Guided by those experiments, we have built a coarse grained model that faithfully mimics relative design parameters in the experimental system. Working with nanoparticles in the size range from 8nm to 15nm, overall DNA-nanoparticle hydrodynamic radii of 10nm to 30nm, and the number of DNA strands per particle between 30 and 100, we have developed a simulation method that confirms that these design rules can be used to assemble a variety of different crystal structures. In particular, we have identified FCC, BCC, CsCl, $AlB_2$ and $Cr_3Si$ structures. With these data, we have constructed a detailed phase diagram that closely corresponds to the experimentally obtained phase diagram developed in ref. [1]. [1] R. J. Macfarlane, B. Lee, M. R. Jones, N. Harris, G.   

DNA coated rods: pure Biological materials for self assembly studies

We will present a way of coating Fd virus, a model of colloidal liquid crystal, with DNA. The DNA coating provides new interesting tunable properties to control the liquid crystalline behavior.   

Linear DNA-linked colloidal chains: a model to visualize polymer dynamics

We present the development of synthetic materials consisting of chains of DNA-linked paramagnetic colloids that have rigidity and length specificity. These chains have demonstrated capability for folding and self-assembly. This is classic bead-spring-bead model can be a model system to visualize polymer dynamics. Here, I will describe the formation mechanism and stability of these DNA-linked magnetic particle chains. I will also describe a model that describes the total energy landscape that describes the inter-particle interactions and provides a workable theory toward the optimization of experimental parameters in synthesizing more stable and reliable colloidal assemblies. In addition to stability, we will also present the use of a colloidal worm-like chain (WLC) model system to describe chain dynamics. We measure bending rigidity by monitoring the thermal fluctuations of the chains. We show that the persistence length of the chains can be tuned from 1 to 50 mm (L/LP = 0.002 - 0.1), by changing the length of the DNA used to link adjacent particles from 75 to 15 bases. We also will show that the bending relaxation dynamics of these chains, which match well with theoretical predictions, further supporting the validity of using these colloidal chains as models for semiflexible polymer systems in both equilibrium and dynamic studies.   

Session Q48: Polymer Blends and Crystallization

How Pure Components Control Polymer Blend Miscibility

We present insight into some intriguing relationships revealed by our recent studies of polymer mixture miscibility. Applying our simple lattice-based equation of state, we discuss some of the patterns observed over a sample of experimental blends. We focus on the question of how much key information can one determine from a knowledge of just the pure components only, and further, on the role of separate enthalpic and entropic contributions to the miscibility behavior. One interesting correlation connects the value of the difference in pure component energetic parameters with that of the mixed segment interactions, suggesting new possibilities for predictive modeling. We also show how in some cases these two parameter groupings act as separate controls determining the entropy and enthalpy of mixing. Also discussed are the different patterns exhibited for UCST-type and LCST-type blends, these being revealed in some cases by simple examination of the underlying microscopic parameters.   

Tailoring Co-continuous Nanostructured Morphologies in Polymer Blends

We describe a simple approach to prepare thin films of polymer mixtures with co-continuous morphologies having characteristic length scales down to tens of nanometers based on spinodal phase separation. The degree of immiscibility between polystyrene (PS) and poly(2-vinylpyridine) (P2VP) is tuned by incorporating styrene monomers into the P2VP backbone to yield a random copolymer, thereby tailoring the nonfavorable interactions between the two components. The size scale of the co-continuous morphology is controlled by varying the molecular weights of the components and the film thickness. This strategy is shown to be robust in that the process involves a simple solution-casting; the co-continuity of the morphology occurs provided the solvent dissolves both components; and the co-continuous morphology is insensitive to the substrate surface chemistry. Porous membranes with continuous channels and gradient co-continuous structures can also be generated from the phase separated blend films.   

Structure and elasticity of crosslinked polymer blends

We consider a blend of mutually incompatible homopolymer species, A and B, that are randomly crosslinked to form a network. In such a network there is a competition between the repulsion of the A and B polymers (which favors the demixing of the two species) and the crosslinking (which prohibits complete demixing) [1,2].~ We treat the system by means of a model of flexible polymers, which are permanently crosslinked (with statistics modeled by the Deam-Edwards distribution) and have species-dependent excluded-volume interactions [3].~ As expected, the model shows that at sufficiently low temperatures the demixing tendency drives microphase separation, with a characteristic scale set by the network localization length.~ It also shows that if the system is strained after crosslinking, correspondingly anisotropic microdomains are generated in the pattern of A-B polymer concentration fluctuations trapped in by the network and, furthermore, allows the impact of microphase separation on the elastic properties of the network to be determined.\\[4pt] [1] P.G. de Gennes, J. Phys. (Paris) Lett., 40 (1979) L-69. \newline [2] D.J. Read, M.G. Brereton and T.C.B. McLeish, J. Phys. II, 5 (1995) 1679. \newline [3] C. Wald et al., Europhys. Lett. 70, 843--849 (2005); J. Chem. Phys. 124, 214905 (2006).   

Assessing the Strength Enhancement of Heterogeneous Networks of Miscible Blends of 1,2-Polybutadiene and Polyisoprene

At typical crosslink densities of elastomers, failure properties vary inversely with mechanical stiffness, so that compounding entails a compromise between stiffness and strength. Our approach to circumvent this conventional limitation is by forming networks of two polymers that: (i) are thermodynamically miscible, so that the chemical composition is uniform on the nm level; and (ii) have markedly different reactivities for network formation. The resulting elastomer consists of one highly crosslinked component and one that is lightly or uncrosslinked. This disparity in crosslinking causes their respective contributions to the network mechanical response to differ diametrically. Earlier results showed some success with this approach for thermally vulcanized blends of 1,2-polybutadiene and polyisoprene, taking advantage of their differing reactivities to sulfur. In this work we explore networks of this miscible blend formed via UV irradiation with a photoinitiator. The vinyl group in 1,2-polybutadiene has a much greater photo-reactivity than the double bond in polyisoprene, resulting in a disparity in respective degrees of crosslinking, while the thermodynamic miscibility is retained. Mechanical properties of the radiation crosslinked blend are compared to conventional networks.   

Compatibilization of polymer blends with star polymers containing a gamma-cyclodextrin core and polystyrene arms

Cyclodextrins (CDs) are cyclic starch molecules having a hollow central cavity which can be threaded by a polymer to form an inclusion compound. This characteristic is exploited in a new type of compatibilizer: a star polymer with a gamma-CD (g-CD) core and polystyrene (PS) arms (CD-star). The mechanism of compatibilization involves threading of the CD core by a second polymer and solubilization of the threading polymer into a PS matrix by the PS star arms. In principle, the same CD-star polymer can be used to compatibilize blends of several different polymers with PS, provided that the second polymer is able to thread the CD core. We have taken the first step toward demonstrating the generality of this approach by producing compatibilized blends of PS with poly(dimethyl siloxane) (PDMS) or poly(methyl methacrylate) (PMMA) using the same CD-star polymer. Thin spun-cast films of these blends exhibit a nanoscale level of mixing, while spun-cast films of the same blends without CD-star exhibit large-scale phase separation. The number of CD-star molecules that must be threaded onto the polymer chain to achieve compatibilization is larger for PMMA than for PDMS.   

Theory of Hydrogen-Bonding in Diblock Copolymer/Homopolymer Blends

The phase behavior and physical properties of hydrogen-bonding diblock copolymer/ homopolymer (AB/C) blends are examined using self-consistent field theory. We consider two methods for modeling the formation of hydrogen bonds between polymer chains. The first using a large negative (attractive) interaction parameter and the second using polymer-polymer complexation. Despite the success of the first model in describing the phase behavior of the system, it fails to correctly predict the change in lamella spacing induced by addition of homopolymer chains, previously shown in many experiments. Using polymer-polymer complexation we were able to qualitatively show the order-order phase transitions and decrease in lamella spacing for the case of strong hydrogen bonding. Our analysis of both methods show that hydrogen bonding of polymer chains should be described by polymer-polymer complexation.   

Effect of mid-block on the morphology and properties of PDLA-softblock-PDLA/PLLA Blends

A novel method to overcome the brittleness of PLLA is by kinetically trapping a continuous low Tg amorphous phase. This morphology has been accomplished by exploiting the significant difference in the crystallization temperatures of the neat PLLA versus its stereocomplex with the PDLA isomer. This morphology is formed by blending and co-crystallizing triblock copolymer with a configuration of the form PDLAn- Soft Blockm- PDLAn with PLLA. The type of morphology formed and the improvement in the sample toughness strongly depends on the miscibility of the midblock in the triblock copolymer with the matrix PLLA. This work explores the effect of the chemical nature of the midblock on the stereocomplex crystallization between the PDLA end-blocks and the PLLA matrix polymer and the blend morphology formed. It is found that miscible midblocks give rise to a soft continuous amorphous phase morphology while in case of immiscible midblocks a glassy phase separated amorphous phase morphology is formed. Dramatically different physical properties can be obtained for various PLLA/tri-block copolymer blends giving access to tough, semicrystalline PLLA blends.   

Molecular Dynamics Simulations of Polypropylene: Crystallization and Melting

The crystallization of polypropylene is studied using molecular dynamics (MD), using an all atom force field. Starting from basic ordered arrangements of oligomers, the $\alpha $ and $\beta $ phases for isotactic polypropylene are recovered, with cell parameters in excellent agreement with crystallographic data. A high pressure phase similar to the smectic phase is also observed. The melting temperatures of these crystals, obtained by isobaric heating, match with the experiments. Oligomers of syndiotactic polypropylene mirror all structural features observed in experiments. The all-trans state is found to be the most stable. The characteristic 2/1 helical structure of syndiotactic polypropylene is also formed along with the all-trans ``zigzag'' conformation.   

Molecular simulation of plastic deformation of semicrystalline polyethylene

The detailed structure and the high anisotropy of semicrystalline polymer at the lamellar length scale play an important role in determining its mechanical response. In this study, we performed molecular dynamics simulation of semicrystalline polyethylene under various industrially important deformations, such as extension, compression, and shear, to characterize the plastic deformation response. The semicrystalline polyethylene model empolyed in this study consists of a 1-D alternating stack in the longitudinal z direction of crystalline lamellae and interlamellar noncrystalline domains, that are infinite in the lateral x and y directions. The molecular dynamics simulations are carried out at the temperature of 350K using united atom model and two deformation strain rates (fast and slow) are considered in each deformation. Stress-strain curves, elastic moduli, yield stresses and so on, are examined under each deformation and compared to each other. In addition, the etanglement statistics of semicrystalline polyethylene under various deformation modes are investigated using the Z-code.   

Digestive Ripening: A Quantitative Thermodynamic Analysis of Stable Nanocrystals

Previous studies have shown that stable, monodisperse nanocrystals (NCs) have been produced using strongly binding surfactants, e.g. Au NCs with alkylthiols or Co NCs with oleic acid, to name a few. Through a first-principles theoretical investigation, we develop the full quantitative thermodynamic expression for the state of these surfactant-coated NCs. The general free energy expression allows for the crystal free energy, the surfactant binding energy, surfactant conformational entropy, and the surfactant interactions with other surfactants through excluded volume, solvent depletion, and energetic interactions between surfactant molecules. The energetics of the surfactant chains are treated quantitatively through Single Chain Mean Field theory, which determines the optimal number of grafted surfactants on the surface of an R-sized NC. Then, the size distribution function f(R) is calculated to determine the most favorable NC size and the equilibrium polydispersity. The theoretical conclusions will be compared quantitatively with experimental results. The full thermodynamic expression allows a parametric study of experimentally relevant conditions that govern whether Ostwald ripening vs. digestive ripening vs. dissolution will occur in a given nanocrystal-surfactant system.   

Morphology and Shear Viscosity for a Phase-separating Polymer Blend of Polybutadiene and Polyisoprene under Simple Shear Flow

The domain structure and shear viscosity of a phase-separated polymer blend of polybutadiene /polyisopreneare investigated with optical microscopy, light scattering, and rheometry. At the steady shear state, the shear-induced structures can be the nearly spherical droplets, the partially interconnected domains, the typical string-like domains, or the string-like domains with blurred interface, depending on the shear rate. The steady shear viscosity displays a rather non-Newtonian fluid behavior. In the transient flow experiments, the time dependence of viscosity and morphology after a stepwise increase of shear rate is studied and found to mainly depend on the final shear rate. In particular, as long as the final structures are the partially interconnected domains, the morphology evolution proceeds in the same way and the behaviors of the corresponding shear viscosity are similar.   

Dynamics of Polymer Blend Film Formation During Spin Coating

Spin casting is a process broadly used to obtain a uniform film on a flat substrate. A homogeneous film results from the balance between centrifugal and viscous forces. Here we revisit the Meyerhofer model of the spin casting process by taking in account the centrifugal forces, a uniform time dependent evaporation rate, and account for the changes in viscosity using the Huggins intrinsic viscosity. Time resolved light reflectometry is used to monitor the thickness changes of a polystyrene-poly(methyl methacrylate)(which we denote as PS and PMMA) film initially dissolved in toluene and spin cast for ten seconds at 1000 rpm. The experimental data are in good agreement with the model. We also investigate how the volume fraction of PS and PMMA influences the thinning of the film during spin casting. A distinct change in the temporal evolution of thickness as a function of time delimits the first phase of the spin casting process where centrifugal forces are dominant from a second phase dominated by the solvent evaporation. This hypothesis is supported by in-situ off specular scattering data. The time at which this change from centrifugal to evaporation-dominated behaviour is delayed as the volume fraction of PMMA increases.   

Session Q49: Focus Session: Organic Electronics and Photonics - Photophysics and Excited State Dynamics

Hybrid Phonoriton in Organic-Semiconductor Materials

In this work electronic structures and optical properties of organic-inorganic phonoriton, a new elementary excitation existing in heterostructures combining both organic and semiconductor materials, are studied. In those systems, Wannier-Frenkel hybrid exciton has unique and interesting properties that can improve the efficiency of optical materials. When an organic-semiconductor combined heterostructure is illuminated by high-intensity electromagnetic radiation with the frequency of the photons at or near the resonance frequency of the Wannier-Frenkel exciton, we obtain a macroscopically occupied system of hybrid polaritons that further interacts with phonons which will in turn generate the hybrid phonoriton. Electronic structure, energy and dispersion relation of phonoritons are theoretically determined. By analyzing the interactions between the hybrid exciton, photons and phonons, the conditions for phonoriton formation are discussed.   

Effect of structural distortion and polarization in localization of electronic excitations in organic semiconductor materials

Organic polymers find varied applications in optoelectronic devices such as solar cells, light emitting diodes and lasers. Detailed understanding of charge carrier transport by polarons and excitonic energy transfer producing singlet and triplet excitations is critical to improve their efficiency. We benchmarked the ability of current functional models to describe the spatial extent of self-trapped neutral and charged excitations for MEH-PPV owing to its superior luminescence and experimental evidence. Now we are interested in distinguishing between two distinct origins leading to localization; spatial localization of the wavefunction by itself on the undistorted geometry and localization of the wavefunction assured by distortion of the structure during its relaxation. We suggest localization is produced by electronic rearrangements and character of the functional. We also observe that different functionals place the highest occupied and lowest virtual orbitals at different positions in the energy band diagram based on their ability to predict the extent of localization of these states.   

The Effect of LUMO Level Offset on the Electron Dissociation Rates in Low Bandgap Polymer Heterostructures

In order to maximize the efficiency of polymer/fullerene bulk heterojunction solar cells, the voltage lost when the electron transfers from the polymer to the fullerene must be minimized. While the magnitude of this loss will significantly impact the maximum attainable efficiency of this technology, there have been relatively few attempts to quantify the dependence of the electron transfer rate and yield on the driving force for electron transfer. In order to isolate the effect of electrochemical potential difference on the exciton dissociation rate, we present results of photophysical measurements of a low bandgap copolymer mixed with a series of fullerene based acceptor materials in a bulk heterojunction geometry. The LUMO level of the acceptor material is varied relative to the polymer's so that the effect of the energy offset on the electron dissociation rate can be determined. Using photoluminescence and transient absorption measurements, we find that the exciton quenching rate varies systematically with increasing energy offset. We examine the mechanism of charge carrier generation by correlating the exciton quenching with charge carrier generation.   

First principles study of optical and electronic properties of anthradithiophene based organic conductors

Functionalized anthradithiophene (ADT) derivatives are high performance organic conductors where the addition of side groups such as triethylsilylethynyl (TES) to the ADT backbone induces a change in the morphology from a herringbone to a planar crystal structure in which improved intermolecular $\pi$-orbital overlap increases carrier mobility. Bulk type-II heterojunctions can be formed using matched pairs such as ADT-TES-F (donor) and ADT-TIPS-CN (acceptor). We report electronic and optical properties calculated from ab initio density functional theory (DFT) calculations for ADT derivatives. Exciton and exciplex formation and charge separation in ADT bulk heterojunctions is studied using 2 molecule model calculations for ADT-TES-F (donor) and ADT-TIPS-CN or C$_{60}$ (acceptor). We compare our results to available experimental results such as photo luminescence and photocurrent measurements.   

Ultrafast exciton energy transfer from giant nanocrystals to layered J-aggregate films

The integration of organic and inorganic materials at the nanoscale offers the possibility of developing new photonic devices that could combine the advantages of both classes of materials. Particularly interesting for such applications is a new class of core/shell CdSe/CdS nanocrystals (NQDs) with large number of shell monolayers (MLs) that are photostable, non-blinking and have an advantage of suppressed non-radiative Auger recombination leading to the existence of bright multiexcitonic (MX) states. However, due to large MLs thicknesses, the extraction of charge through such shells may pose considerable problems. In this work we studied hybrid structures composed of ``giant'', ({\#}ML$>$10) CdSe/CdS NQDs anchored on top of thin layers of strongly absorbing J-aggregates (JA) of cyanine dye (TDBC). We performed time-resolved and steady-state photoluminescence (PL) measurements to quantify the \textit{excitonic energy transfer }(ET) rates from the gNQDs to JA layer. By varying temperature (from RT to 80K) we observed change in ET rates in accordance with the overlap integral between NQD PL emission and JA absorption. In all cases, ET transfer rates exceeded 99{\%}. Hence, we foresee the utilization of gNQDs in applications in hybrid systems based on energy transfer.   

Ultrafast multidimensional spectroscopy of P3HT thin films

We report on measurements of morphology dependence of exciton/polaron dynamics in P3HT thin films. Intrachain and interchain electronic coupling has a significant impact on optical and electronic properties of polymers. Due to flexibility of polymers, slight differences in processing results in a variation of morphologies and electronic coupling between the chains. We employ ultrafast multidimensional spectroscopy techniques to resolve the resulting polaron formation dynamics in different polymer thinfilms spin casted from different solvents. Our results suggest, depending on the average conjugation length and crystallinity of the thin film, polaron formation dynamics exhibit spectrally homogeneous or inhomogeneous behavior.   

Charge transfer complex in diketopyrrolopyrrole polymers and fullerene blends: Implication for organic solar cell efficiency

Copolymers based on diketopyrrolopyrrole (DPP) have recently gained potential in organic photovoltaics. When blended with another acceptor such as PCBM, intermolecular charge transfer occurs which may result in the formation of charge transfer (CT) states. We present here the spectral photocurrent characteristics of two donor-acceptor DPP based copolymers, PDPP-BBT and TDPP-BBT, blended with PCBM to identify the CT states. The spectral photocurrent measured using Fourier-transform photocurrent spectroscopy (FTPS) and monochromatic photocurrent (PC) methods are compared with P3HT:PCBM, where the CT state is well known. PDPP-BBT:PCBM shows a stable CT state while TDPP-BBT does not. Our analysis shows that the larger singlet state energy difference between TDPP-BBT and PCBM along with the lower optical gap of TDPP-BBT obliterates the formation of a midgap CT state resulting in an enhanced photovoltaic efficiency over PDPP-BBT:PCBM.   

Dynamic Monte Carlo Modeling of Exciton Dissociation in Organic Donor-Acceptor Solar Cells

A general dynamic Monte Carlo model for exciton dissociation at a donor-acceptor interface including exciton delocalization and hot geminate pair dissociation has been developed to model the experimental behavior observed for the P3HT:PCBM system and predict the theoretical performance of future materials systems. The presence of delocalized excitons and the direct formation of separated charge pairs has been recently measured by transient photo-induced absorption experiments, and has been proposed to facilitate charge separation efficiency. The excess energy of the exciton dissociation process has also been observed to have a strong correlation with the charge separation yield for a range of thiophene polymer:PCBM systems, suggesting that a hot charge separation process is also occurring. Hot geminate pair dissociation has been previously theorized as a cause for highly efficient charge separation, however a detailed model for this process has not been implemented and tested. Here, both conceptual models have been implemented into a dynamic Monte Carlo simulation and tested using a model bilayer donor-acceptor system.   

Ultrafast Photo Physics of P3HT/PCBM blends for Organic Photovoltaic applications

We studied the ultrafast dynamics of photoexcitations in pristine polymer films of regio-regular polythiophene, regio-random polythiophene, and their blends with the fullerene derivative C$_{61}$-PCBM using the pump-probe photomodulation (PM) spectroscopy with $\sim $150 fs time resolution. Our transient PM spectrum covers the broad spectral range of 0.25 -- 2.4 eV using two different laser systems; which allows us to simultaneously monitor the dynamics of various photoinduced absorption bands such as intrachain excitons, charge transfer excitons, and polaron-pairs. Surprisingly, we have been able to monitor the decay of intrachain exciton on the polymer chains in films of polymer/fullerene blends, but unable to detect the subsequent generation of polarons in the donor (D) and acceptor (A) materials up to $\sim $ 1 ns. We explain this finding considering that the excitons in the polymer chains form charge transfer excitons upon reaching the D-A interface, rather than undergo a more direct dissociation on the D-A materials. The understanding of charge separation at the D-A interface is crucial for improving the power conversion efficiency of organic solar cell devices. Supported in part by the DOE grant No. DE-FG02-04ER46109.   

Can Singlet Fission Enhance the Performance of Organic Solar Cells?

The high efficiency of pentacene-fullerene (Pc-C$_{60}$) donor-acceptor solar cells has been ascribed to singlet fission, which generates two spin triplet excitons that each undergo ionization to give two pairs of electrons and holes [1,2]. For triplet ionization to give charge generation, the charge-transfer exciplex in the Pc-C$_{60}$ heterostructure should be energetically below the the molecular triplet state in Pc.Our initial calculations show that this is not a plausible scenario. We propose an alternate mechanism for the relatively high efficiencies of solar cells constructed from donors such as Pc, based on correlated-electron configuration interaction calculations [3] of ground state and photoinduced charge-transfer. \\[4pt] [1] Wilson M. W. B.; et al., J. Am. Chem. Soc, v133, 31, 11830-11833 (2011)\\[0pt] [2] Rao A.; et al., J. Am. Chem. Soc, v132, 36, 12698-12703 (2010)\\[0pt] [3] Yi Y.; Coropceanu V.; Br??das J. L.; J. Am. Chem. Soc, v131, 43, 15777-15783 (2009)   

Exciton self-trapping and Stark effect in the optical response of pentacene crystals from first principles

Pentacene is a prototypical organic semiconductor with optoelectronic and photovoltaic applications. It is known that the lowest-energy singlet excitation has a Stokes shift between absorption and emission of about 0.14 eV, but the deformation associated with this self-trapped exciton remains unknown. We begin with a calculation of the optical properties via the first-principles GW/Bethe-Salpeter (BSE) theory [ML Tiago, JE Northrup, and SG Louie, Phys. Rev. B 67, 115212 (2003); S Sharifzadeh, A Biller, L Kronik, and JB Neaton, arXiv:1110.4928 (2011)]. We then study the self-trapping phenomenon via our reformulation of the Bethe-Salpeter excited-state forces approximation of Ismail-Beigi and Louie [Phys. Rev. Lett. 90, 076401 (2003)], which can describe the structural relaxation after optical excitation. Whether excitons in pentacene have charge-transfer character has been controversial in electro-absorption experiments. We use the same BSE analytic derivatives approach to calculate the changes in excitation energies due to an applied electric field to understand this experimental controversy.   

Singlet Fission and Multi-Exciton Generation in Organic Systems

Multi-exciton generation (MEG) has been observed in a variety of materials and might be exploited in solar-cells to dramatically increase efficiency. In tetracene and pentacene MEG has been attributed to singlet fission (SF), however a fundamental mechanism for SF has not been previously described. Here, we use sophisticated ab initio calculations to show that MEG in pentacene proceeds by transition of the lowest optically allowed excited state S1 to a dark state (D) of multi-exciton character, which subsequently undergoes SF to generate two triplets (2$\times$T0). D satisfies the energy requirement for SF ($E_{D}>2E_{T0}$) and lies just below S1 in pentacene, but above S1 in tetracene, consistent with the observed thermally activated SF process in tetracene, but no thermal activation in pentacene. While S1 exhibits single exciton character, D shows multi-exciton character comprising two separated electron-hole pairs. Dimer simulations predict S1 excimer formation and that fission of D into triplets proceeds through the excimer. The predicted energetics, wavefunctions and excimer interaction support the proposed mechanism, which accounts for the observed rapid, unactivated SF in pentacene. Results for SF in polyacenes, grapheme nanoribbons, rubrene and carbon nanotubes will be presented.   

Session Q50: Focus Session: Dynamics of Polymers: Phenomena due to Confinement II

New insight into adsorption of polymer melts onto impenetrable surfaces

We report the novel structures of irreversibly adsorbed polystyrene (PS) layers composed of six different molecular weights ranging from 30k to 2,000k. Spin cast PS films (originally $\sim $ 100 nm in thickness) prepared onto hydrogen-passivated silicon substrates were annealed at 170 \r{ }C for about 50h under vacuum and subsequently rinsed with toluene (a good solvent for PS) thoroughly. X-ray reflectivity results show that the adsorbed layers are well described by a two-layer model: the one is a higher density layer relative to the bulk adjacent to the substrate and the other is a nearly bulk density layer on top of the bottom layer. On the other hand, a single-layer model with the higher density layer is valid for the adsorbed layers composed of low molecular weights PS. We will reveal the origin of the difference, shedding light on a new pathway for the formation of the equilibrium adsorbed polymer layers at the impenetrable interfaces.   

Effect of the interfacial interaction on the relaxation of polymer melts in nanofilms

The relaxation of polymer melts in nanofilms could be orders of magnitude slower than in bulk. To date, the governing mechanism remains unclear on the role of spatial confinement and interfacial interaction. Here we report the experimental results indicating that the polymer-substrate interfacial interaction plays a key role in the relaxation. Two perfluoropolyethers (PFPEs) with the same backbone and different endgroups, one polar and the other non-polar, have been studied. The relaxation of the nanofilms on silicon wafers was characterized by the contact angle measurement. For the PFPE with polar endgroups, the contact angle ``relaxes'' with time and the relaxation time constant, obtained from KWW model, is ten orders of magnitude higher than that of bulk polymer. However, for the PFPE with non-polar endgroups, the contact angle relaxation was not observed. The experimental results indicate that the relaxation is thermodynamically driven by the attractive interaction between the polar endgroups of the polymers and the polar sites on the solid substrate. The very slow kinetics of the relaxation has been attributed to the heterogeneity of the polymer-solid interfacial interaction and the cooperative nature of the molecular motions during the relaxation.   

Differential AC chip calorimeter for in situ investigation of vapor deposited thin films

Physical vapor deposition (PVD) can be used to produce thin films with particular material properties like extraordinarily stable glasses of organic molecules. We describe an AC chip calorimeter for in-situ heat capacity measurements of as-deposited nanometer thin films of organic glass formers. The calorimetric system is based on a differential AC chip calorimeter which is placed in the vacuum chamber for physical vapor deposition. The sample is directly deposited onto one calorimetric chip sensor while the other sensor is protected against deposition. The device and the temperature calibration procedure are described. The latter makes use of the phase transitions of cyclopentane and the frequency dependence of the dynamic glass transition of toluene and ethylbenzene. Sample thickness determination is based on a finite element modeling (FEM) of the sensor sample arrangement. A layer of toluene was added to the sample sensor and its thickness was varied in an iterative way until the model fits the experimental data.   

Methyl Methacrylate Polymerization in Nanoporous Matrix: Reactivity and Resulting Properties

Nanoconfinement is well known to affect the properties of polymers, including changes in the glass transition temperature (Tg). In this work, the focus is on the influence of nanoconfinement on free radical polymerization reaction kinetics and the properties of the polymer produced. Controlled pore glass (CPG) is used as a nanoconfining matrix for methyl methacrylate (MMA) polymerization with pore diameters of 13 nm, 50 nm, and 110 nm. The reaction is followed by measuring heat flow as a function of reaction time during isothermal polymerization at temperatures ranging from 60 \r{ }C to 95 \r{ }C using differential scanning calorimetry (DSC). After reaction, the properties of the polymer are measured, including Tg, molecular weight, and tacticity. Nanoconfiment is found to result in earlier onset of autoacceleration, presumablely due to a decrease in the rate of termination arising from decreases in chain diffusivity in the confined state. In addition, Tg and molecular weight of the resulting PMMA are found to increase. A model of the nanoconfined reaction is able to quantitatively capture these effects by accounting for changes in chain diffusivity, and in native pores, also accounting for changes in intrinsic reaction rates.   

Polystryene films confined between gold surfaces

The properties of thin short-chain polystyrene films between two parallel Au(111) surfaces are studied using a combination of density functional theory (DFT) and classical molecular dynamics (MD) simulations. The chemical interaction with the surface is calculated with DFT and the results are used to develop accurate atomistic classical surface potentials. These potentials are used in the MD simulations to investigate several systems with various film thickness and the effect of increasing confinement on the structural and dynamical properties of the films will be presented. A coarse-grained model is developed and used to study longer-chain polystyrene films and larger systems.   

Surface Mobility of Polymeric Systems of Varying Chain Lengths

Thin films of polymeric material can exhibit drastically altered glass transition temperatures, mechanical responses, and overall dynamics as compared to the bulk. Differences in surface and bulk mobility are often cited as a primary explanation for such differences, but it has remained difficult to quantify local mobility as within the film. We have recently shown that decay constants from Mullins' surface diffusion model correspond directly to surface mobility for small-molecule glasses. In the current work, we examine long-chain polymers via two types of systems: polymeric pillars where the cross sections evolve from square to circular, and large particles which sink into polymeric thin films. For the pillars, we use Mullins' model to interpret changes in curvature. It is found that Mullins' decay constants correspond to relaxation times that can be identified with distinct segmental relaxation processes. Such decay constants exhibit a strong dependence on chain length and temperature. For the particle-thin film systems, we relate the rate of particle sinking to various measures of local mobility in the film. This setup is a direct analog to recent experimental work. The results presented here provide a connection between surface shape transformations, mobility, and diffusion.   

Shear thinning near the rough boundary in a viscoelastic flow

It was first noticed by de Gennes, that because of huge difference between viscosities of entangled polymeric liquid and monomeric liquid, the boundary conditions for a polymer flow near microscopically smooth boundary should be assumed as ``slip''. Nevertheless, in the presence of surface roughness, or undulations, the flow is characterized by mixed boundary conditions. We had shown that at certain slip velocities the deformation of the melt near the rough (undulated) boundary might became more elastic than viscous. This results in ``shear thinning'' of the roughness of boundary. At higher velocities, near the slip boundary, the chains can be considered simply trapped in an entangled mesh of other chains. They are subjected to oscillating strain rate, comparable to frequencies of internal Rouse modes of these chains. We calculate the total dissipation of energy due to oscillating strain and calculate the slippage of the polymer melt near the boundary as function of velocity, undulation wavelength and amplitude.   

Relaxation of Capillary Wrinkles

We have investigated the relaxation of a wrinkle pattern on a thin viscoelastic film. The films are made from spin-coated PS (polystyrene) of thickness ranging from 40 to 240 nm that were floated on the surface of water. Viscoelastic behavior is introduced to the film by depressing the glass transition of PS with a soluble plasticizer, dioctyl phthalate. Wrinkle patterns are formed by placing a small droplet ($\sim $1$\mu $L) at the center of the floating disc. Due to the differential tension generated across the film, radial wrinkles form around the drop where the compressive axial force buckles the membrane. Thereafter, length of the wrinkles decays, and so does their wavelength. We have studied the relaxation of wrinkles as a function of PS molecular weight and plasticizer content, in order to understand the relationship with the bulk glass transition temperature.   

New insight into the melting behavior of nanoconfined semicrystalline polymers -The effect of an immobile interfacial layer at the substrate-

It is known that when semicrystalline polymer chains are confined on a nanometer length scale, the crystalline structures and dynamics differ from bulks, the so-called ``nanoconfinement effects.'' In this talk, we will report the anomalous melting behavior of nano-confined polyethylene spin cast films prepared on Si substrates by integrating various in-situ grazing incidence scattering techniques. We found that a very thin adsorbed layer at the weakly interactive substrate interface plays a crucial role in the melting behavior.   

Solvent Swelling as a Means to Modify the Properties of Polymer Thin Films

It has been observed that sample preparation can influence certain properties of polymer films. In particular, spin-coating from solutions of different solvent qualities result in films with different chain conformations. We surmise that upon formation by spin-coating, the chain conformation of a film is still adjustable by means of solvent swelling, resulting in modifications to the amount of entanglement and free volume. Initial measurements of thermal expansion upon heating after swelling suggest that there is a difference between polystyrene films swelled with a good solvent and a $\Theta$ solvent. We have begun a more detailed investigation by studying the effect of swelling on the dewetting behaviors. Preliminary data indicates that the quality of the solvent affects both the dewetting hole size and aging rate of the film.   

Equilibration of Polymer Films Cast from Solutions with Different Solvent Qualities

The preparation history can affect the physical properties of polymer thin films. In spin coating, films are made from a polymer solution. Due to rapid evaporation of solvent in this process, the polymer chains in the films cannot fully interpenetrate, resulting in a non-equilibrium conformation with reduced entanglement density. These in turn can affect the film's equilibration process and viscoelastic properties. On the basis that the chain conformation and entanglement density in a film depend on the conformation of the chains while in solution before spin-coating. We modify the structural properties of the films by adjusting the quality of the solvent used in spin-coating. We examine in detail how these adjustments affect the way polystyrene films approach equilibrium on annealing above the glass transition temperature. It is found that the equilibration time of the film is significantly increased as the solvent quality is decreased towards the $\Theta $ condition. We attribute this observation to reduced entanglement in the films with decreasing solvent quality.   

Tuning confinement effects at constant film thickness

We show experimental evidence confuting the commonly accepted idea that the deviation from bulk behavior can be explained in terms of finite size effects and interfacial interactions. By reproducing Guiselin's experiment and upon variation of the molecular weight, we could prepare films of polystyrene spincoated on aluminum and annealed for the same time, having constant thickness but different glass transition temperature and tracer diffusivity. The results can be rationalized in terms of t*, a dimensionless parameter obtained by the ratio of the annealing time and the adsorption time [1], quantifying the equilibrium character of the films. Further evidence on the relevance of t* on understanding the behavior of polymers at the nanoscale is provided [2].\\[4pt] [1] Napolitano, S. and W\"{u}bbenhorst, M., Nature Communications, 2, 260 (2011).\\[0pt] [2] Rotella, C.; W\"{u}bbenhorst, M. and Napolitano, S., Soft Matter, 7, 5260 (2011).   

Capillary levelling in thin polymer films as a nano-rheological tool to probe interface dynamics

Entanglement of polymer chains in confinement is modified as a result of altered chain conformations. According to Silberberg's principle, chain segments are reflected at an interface causing a reduction of the inter-chain entanglement density. If the interface is transient, local polymer conformation changes can be inferred from a temporal change in flow properties: over time polymer chains become more entangled, thus there is more resistance to flow. Here, we measure the gradual disappearance of an entropic interface between two melts of identical polymer chains during the flow of stepped bilayer polymer films. Samples are prepared in the glassy state and, when in the melt, flow to relieve the Laplace pressure gradient induced by a step in the topography (McGraw \emph{et al}., Soft Matter, 2011). Our results reveal the dynamics of re-entanglement across the transient entropic interface.   

Slow physical aging of thin polymer films of varying chain architecture

The physical aging rate of supported polystyrene (PS) films is influenced by film thickness, H, and by macromolecular architecture. For linear PS films, in the thickness range 300 nm to 50 nm, supported by silicon oxide substrates, the aging rate decreased by 15 percent. On the other hand, star-shaped PS, with functionality f=8 and with an average molecular weight per arm of Marm=25 kg/mol. exhibited a 25 percent decrease throughout the same thickness range. When Marm was decreased to 10 kg/mol the depression in aging rate was 45 percent. We reconcile these changes in physical aging in terms of model that accounts for gradients in the local Tg of the film in the vicinity of interfaces. These findings have important implications for the processing and function of thin polymer films for different applications.   

Diffusion of adsorbed theta-solvent polymers at a solid-liquid interface

We study how surface diffusion depends on temperature when this is varied below the theta temperature. In the polystyrene-cyclohexane system, we use FRAP (fluorescence recovery after photobleaching) to measure over times over 4 orders of magnitude, from 10 sec to 10$^{5}$ seconds. A fast component of motion is attributed to chains loosely bound to the surface. A slower component of motion is retained after rinsing; it is subdiffusive. At temperatures below the bulk coexistence temperature, the surface layer is thicker than a monolayer. We show that bulk phase separation of polymers in dilute solution produces a dense surface layer of emulsion and foamy near-surface structure.   

Session Q51: Gels, Complex Fluids and Vesicles

Linear Viscoelasticity and Swelling of Polyelectrolyte Complex Coacervates

The addition of near equimolar amounts of poly(diallyldimethylammonium chloride) to poly(isobutylene-alt-maleate sodium), results in formation of a polyelectrolyte complex coacervate. Zeta-potential titrations conclude that these PE-complexes are nearly charge-neutral. Swelling and rheological properties are studied at different salt concentrations in the surrounding solution. The enhanced swelling observed at high salt concentration suggests the system behaves like a polyampholyte gel, and weaker swelling at very low salt concentrations implies polyelectrolyte gel behavior. Linear viscoelastic oscillatory shear measurements indicate that the coacervates are viscoelastic liquids and that increasing ionic strength of the medium weakens the electrostatic interactions between charged units, lowering the relaxation time and viscosity. We use the time-salt superposition idea recently proposed by Spruijt, et al., allowing us to construct master curves for these soft materials. Similar swelling properties observed when varying molecular weights. Rheological measurements reveal that PE-complexes with increasing molecular weight polyelectrolytes form a network with higher crosslink density, suggesting time-molecular weight superposition idea.   

Multicomponent effects in diffusion within microemulsions

Holographic interferometry was used to monitor transport of hydrophobic solutes in systems containing nanometer-scale microemulsion droplets. In this technique, variations in the refractive index between a reference time and a later time are monitored via interference fringes that are formed with the help of a holographic plate. The refractive index change is driven by imposed concentration differences of either the solute (at constant surfactant concentration), or of the surfactant (at constant solute concentration). We find that, especially for hydrophobic solutes, the transport kinetics cannot be interpreted by using a pseudobinary approximation. Multicomponent interaction effects must be taken into account even at micelle concentrations as low as 6{\%}. By performing multiple experiments with different initial concentration gradients, and extending earlier analyses of the experimental interference fringes, the multicomponent effects can be resolved, yielding results for all the relevant diffusion coefficients.   

Determining the structure and properties of complex coacervate crosslinked triblock copolymer hydrogels

The mechanical properties and structures of functionalized P(AGE-b-EO-b-AGE) hydrogels utilizing complex coacervation as a physical crosslink have been studied. The effects of variables such as polymer concentration, salt concentration, pH, stoichiometric ratios and temperature have been investigated by rheology and SAXS. It was found that the organization of the cores has a very strong effect on the mechanical properties. This can be observed as the storage modulus increases significantly between 15 and 16 wt{\%} corresponding to a transition from a disordered gel to a BCC structure. Another dramatic change is observed when the storage modulus drops between 25 and 30 wt{\%} as the hexagonal structure becomes predominant. Just as polymer concentration causes changes in structure and thus the properties, salt concentration has a similar effect due to the electrostatic nature of the hydrogels. As salt is added, the electrostatic interactions in the cores are screened until they are weak enough that the polymers are dissolved into the matrix. The mechanical properties and the physical nature of the crosslinks lead to the possibility of these gels being used as an injectable drug delivery system.   

Density mode microrheology in polyacrylamide gels

In passive microrheology the viscoelastic properties of soft materials are deduced by observing thermal fluctuations of tracer particles embedded within the material, and the response function obtained from the spectrum of thermally excited modes is then related to the viscoelastic shear modulus. This approach is valid for single-component, isotropic, incompressible materials. However, for heterogeneous materials, such as hydrogels, a more comprehensive approach is needed. We measure the equilibrium density fluctuations of a cross-linked polymer gel swollen in a solvent and compare them to the predictions of the `two--fluid' model of the dynamics of polymer gels. We will describe a direct method of extracting the longitudinal response function of a soft material based on the temporal and spatial correlations of density fluctuations of fluorescent markers, called density mode microrheology (DMM). We will also present results of applying DMM to fluorescent polyacrylamide gels in an aqueous solvent of varying viscosity and comparing them with parameters obtained from conventional macrorheology.   

Effect of Polymer Molecular Weight and Synthesis Temperature on Structure and Dynamics of Microgels

Environmentally-sensitive microgels have been synthesized under varying conditions to study the dependences on polymer molecular weight (M$_{W})$ and synthesis temperature (T$_{syn})$. The dynamics and structure of the synthesized microgels below and above the LCST of the polymer (T$_{c}\sim $41$^{o}$C) were studied using dynamic and static light scattering spectroscopy. All microgels exhibit a volume phase transition above the LCST of the polymer and undergo a reversible 15-50-fold volume shrinkage. The size distribution, structure, deswelling ability, and temperature response of microgels strongly depend on synthesis conditions. T$_{syn}$ dependence was studied with 1000kDa polymer. Increasing $\Delta $T = T$_{syn}$ -- T$_{C}$ yields smaller microgels with a smaller swelling ratio up to $\Delta $T = 8.5$^{o}$C, after which the trend is reversed. The amphiphilic nature of the polymer may explain this trend. T$_{syn}$ also affects the structure of microgels; low T$_{syn}$ yields elongated particles, while high T$_{syn}$ microgels are more spherical. Polymer M$_{W}$ directly effects microgel polydispersity and temperature response. While microgels synthesized with 1000kDa polymer are relatively monodisperse, synthesis with low M$_{W}$ polymers (80-370kDa) yields systems with a large population (R$_{h} \quad \sim $1000nm) precipitating out of solution and a smaller population (R$_{h}$ $\sim $300nm) staying in suspension. M$_{W}$ also influences the temperature response of microgels; high M$_{W}$ microgels show a gradual shrinkage with increasing temperature while low M$_{W}$ microgels display a delayed and sudden shrinkage at high temperatures.   

Gelation and state diagram for a model nanoparticle system with adhesive hard sphere interactions

We provide the first comprehensive state diagram of thermoreversible gelation in a model nanoparticle system from dilute concentrations to the attractive driven glass. We show the temperature dependence of the interparticle potential is related to a surface molecular phase transition of the brush layer using neutron reflectivity (NR) and small-angle neutron scattering (SANS) [1]. We establish the temperature dependence of the interparticle potential using SANS, dynamic light scattering (DLS), and rheology. The potential parameters extracted from SANS suggest that, for this system, gelation is an extension of the Mode Coupling Theory (MCT) attractive driven glass line (ADG) to lower volume fractions and follows the percolation transition. Below the critical concentration, gelation proceeds without competition for phase separation [2]. These results are used to develop a complete state diagram for the sticky hard sphere reference system. \\[4pt] [1] A.P.R. Eberle, N.J. Wagner, B. Akgun, S.K. Satija, Langmuir \textbf{26} 3003 (2010).\\[0pt] [2] A.P.R. Eberle, N.J. Wagner, R. Castaneda-Priego, Phys. Rev. Let. \textbf{105704} (2011).   

Hydrodynamics and Rheology of Active Liquid Crystals

Active liquid crystals such as swimming bacteria, active gels and assemblies of motors and filaments are active complex fluids. Such systems differ from their passive counterparts in that particles absorb energy and generate motion. They are interesting from a more fundamental perspective as their dynamic phenomenons are both physically fascinating and potentially of great biological significance. In this talk, I will present a continuum model for active liquid crystals and analyze the behavior of a suspension subjected to a weak Poiseuille flow. Hydrodynamics, stability and rheology will also be discussed.   

Electrostatics-driven assembly of uni-lamellar catanionic facetted vesicles

Nature utilizes shape to generate function. Organelle and halophilic bacteria wall envelopes, for example, adopt various polyhedral shapes to compartmentalize matter. The origin of these shapes is unknown. A large variety of shell geometries, either fully faceted polyhedra or mixed Janus-like vesicles with faceted and curved domains that resemble cellular shells can be generated by coassembling water-insoluble anionic (--1) amphiphiles with high valence cationic (+2 and +3) amphiphiles. Electron microscopy, X-ray scattering, theory and simulations demonstrate that the resulting faceted ionic shells are crystalline, and stable at high salt concentrations. The crystallization of the co-assembled single tail amphiphiles is induced by ionic correlations, and modified by the solution pH. This work promotes the design of faceted shapes for various applications and improves our understanding of the origin of polyhedral shells in nature.   

Modeling controlled release from responsive microgel capsules

We introduce a coarse-grained computational method that explicitly captures the release of nanoparticles and macromolecules from responsive microgel capsules. The model is based on the dissipative particle dynamics. Our simulations reveal that not only swelling, but also deswelling of hollow microcapsules can be harnessed for controlled release. We show that the release from swollen capsules is diffusion driven, whereas the release from deswelling gel capsules occurs due to the flow of encapsulated solvent that is expelled from the shrinking capsule interior. The latter hydrodynamic release is burst-like and continues only during capsule deswelling. We find that deformable polymer chains that can easily penetrate thorough membrane pores are released in larger amounts from deswelling capsules, than nanoparticles that are filtered out by shrinking membrane pores. Our simulations further demonstrate that the inclusion of rigid microrods inside deswelling capsules mitigates the membrane pore closing, and, in this fashion, provides an effective method for regulating the rate of hydrodynamic release of nanoparticles.   

Thermoresponsive microcapsules for controlled release of hydrophilic cargo

Thermoresponsive microcapsules that collapse upon increasing the temperature above their lower critical solution temperature (LCST) such as poly(N-isopropyl acrylamide) (PNIPAM) capsules are well known. However, capsules consisting of thermoresponsive polymers that possess an upper critical solution temperature (UCST) and therefore swell upon increasing the temperature above their UCST are scarce. We will present a microfluidic method to assemble thermoresponsive poly([2-(methacryloyloxy)-ethyl]-dimethyl-[3-sulfopropyl-ammoniumhzdroxide) (PMEDSH) microcapsules that have UCST. These capsules are in a collapsed state at room temperature and become highly water permeable upon increasing the temperature above the UCST. To simultaneously allow for encapsulation of hydrophilic cargo and enable the water based polymerization reaction of the PMEDSH shell, these microcapsules are assembled as water/water/oil emulsions using capillary microfluidic devices. The resulting PMEDSH microcapsules are envisaged as delivery vehicles and microreactors that allow for temperature induced controlled release of hydrophilic cargo. .   

A Nano Engineered Membrane for Oil-Water Separation

Oil and water separation is an extremely costly problem in the petroleum industry. Pumping the complete emulsion to the surface requires substantially more power than pumping the oil alone. A membrane that can efficiently separate oil from water at the source would revolutionize this process. To this end a novel, layered, hierarchical thermoplastic membrane was fabricated with both nanoscale and microscale features. Modifying the length scales involved in fabrication of the membrane yields interesting and non-obvious implications. Under certain regimes, the microscale features independently control the membrane's permeability, while the microscale features control only the membrane's breakthrough pressure. By operating in this regime, separation efficiencies can be realized that are otherwise unattainable by conventional membranes. Taking it a step further, chemical treatments have been used to achieve higher hydrophobicity for the membrane by lowering the surface energy of the membrane surface. Although this research focused on oil-water separation, the results have implications for other multiphase systems and hold for many other filtration and separation technologies including in lab-on-chip devices and micro/nanofluidic devices.   

Tether formation on a settling vesicle

When submitted to a point-like force, a phospholipid vesicle (a lipid membrane enclosing a drop) is known to develop a narrow tether. This tether formation is reminiscent of drop pinch-off, but the peculiar properties of the vesicle interface prevents the apparition of a finite-time singularity. It is shown that a settling vesicle may develop such tethered shapes, with hydrodynamic stresses acting as the pulling force. These shapes are studied numerically and theoretically, and continuous families of stationary tethered shapes are found, depending on two control parameters. Dynamics of formation is studied and it is shown that changing the initial condition can lead to complex transients, with formation of pearls onto the tether.   

Electrohydrodynamic instabilities of biomimetic bilayer membranes

Living cells actively maintain electrochemical potentials across their membranes, which regulates cell migration, motility, and development. In this presentation, we focus on the effect of an external electric field on membrane dynamics. We present a physical model for the dynamic coupling between transmembrane potential and deformation of biomimetic membranes. We perform linear stability analysis to clarify and quantify the effects of the lipid bilayer properties (conductivity and capacitance), and asymmetry in the embedding electrolyte solutions, on membrane deformation.   

Polyoxometalate (POM) Nanocluster-Induced Phase Transition and Structural Disruption in Lipid Bilayers.

Polyoxometalate (POM) nanoclusters that are transition metal oxygen clusters with well defined atomic coordination structures have recently emerged as new and functional nanocolloidal materials used as catalysts, anti-cancer medicines, and building blocks for novel functional materials. However, their implications to human health and environment remain poorly investigated. In this work, we examine the interaction of highly charged anionic POM nanocluters with lipid bilayers as a model cell membrane system. It is observed that upon the adsorption of anionic POMs, lipid dynamics is significantly suppressed and lipid bilayers are disrupted with resultant pore and budding-like structural formation. Direct calorimetric experiment of POM interaction with lipid bilayers of varied lipid compositions confirms the POM-induced fluid-to-gel phase transition in lipid bilayers, due to strong electrostatic interaction between POM nanocluster and lipid head groups.   

Liquid-to-solid transition in suspensions of swollen microgels

We investigate the phase and non-equilibrium behavior of suspensions comprised of swollen, ionic microgels as a function of particle stiffness. We find that stiff particles exhibit all three phases observed in hard sphere suspensions, liquid, crystal and glass. For particles with intermediate stiffness, the crystal phase disappears and the microgel suspension transitions from a liquid to a glassy state at certain particle concentration. For even softer particles, no glassy state is observed. Instead the system remains liquid within the experimentally accessed concentration range. Interestingly, for microgels with intermediate stiffness, we find that the bulk modulus of individual particles seems to control the mechanical properties of the microgel suspension in the overpacked regime, emphasizing the relevance of being compressible.   

Session Q52: Focus Session: Extreme Mechanics - Shells & Snapping

Mechanics and Dynamics of a Snapping Arch

Snap-buckling of geometric arches and thin spherical shells occur in a variety of different geometric situations, exhibiting a highly nonlinear response dictated by the geometry and material properties of the system. As this elastic instability often precedes the catastrophic failure of a mechanical system, significant work has focused on the stability criteria for such structures. In order to properly understand the biomechanics of plants that rely on this instability, and in addition use snap-buckling in the design of advanced materials, it is necessary to also develop a fundamental understanding of the timescale and post-buckling response of a snapping structure. Currently, a fundamental understanding of the osmotically-induced snap-buckling phenomena is lacking. In this presentation, we examine the osmotic swelling of a bistable arch to identify the stability criteria, relevant snap-through timescale, and the impact of geometric confinement on snap-through symmetry and damping.   

Elastocapillary-driven snap-through instability

The snap-through instability, which is present in a wide range of systems ranging from carnivorous plants to MEMS, is a well-known phenomenon in solid mechanics : when a buckled elastic beam is subjected to a transverse force, above a critical load value the buckling mode is switched. Here, we revisit this phenomenon by studying snap-through under capillary forces. In our experiment, a droplet (which replaces the usual dry load) is deposited on a buckled thin strip, clamped horizontally at both ends. In this setup both the weight of the drop and capillary forces jointly act toward the instability. The possibility of reverse elastocapillary snap-through, where the droplet is put under the beam, is then tested and successfully observed, showing the predominance of capillary forces at small enough scales.   

Fast Motion of Plants through mechanical instability: Mechanics without Muscles

Plants are not well known for fast motions, yet some plants such as the Venus flytrap can move in a fraction of a second to capture insects, even though they do not have nerves or muscles. This type of rapid motion has intrigued scientists for centuries. Darwin did a first systematic study on the trap closure mechanism, and considered the plant as ``one of the most wonderful in the world". Thereafter, several physical mechanisms have been proposed, such as the rapid loss of turgor pressure, an irreversible acid-induced wall loosening mechanism, and the snap-through model by mechanical instability, but with no unanimous agreement among researchers. Here we propose a coupled mechanical bistable mechanism that explains the rapid closure of the Venus flytrap in a comprehensive manner, consistent with a series of experimental observations. Such bistabile behaviors are theoretically modeled and validated with table-top experiments. Based on the principles learnt from the Venus flytrap, we are also able to manufacture a preliminary ``flytrap robot''. Hence, it is promising to design smart bio-mimetic materials and devices with snapping mechanisms as sensors, actuators, artificial muscles and biomedical devices.   

Strange instabilities of simple elastic structures

A class of simple elastic structures is shown exhibiting bifurcation and instability under tensile dead loading, multiple bifurcations, and softening/hardening behaviour in the postcritical regime. These structures evidences new and unexpected behaviours which are theoretically predicted and experimentally verified. These nonlinear behaviours can be exploited in the design of flexible mechanics devices and open new perspective in the control of vibrations.   

Materials with Tunable Behavior due to Constrained Instabilities: Performance and Stability Analysis

Combining several materials into a composite permits the creation of new materials with overall properties tunable via a careful choice of the constituent materials with favorable specifics. The probably simplest example is a particle-matrix system, in which particles of one material enhance the mechanical behavior of the matrix material. Recent advances have confirmed that the overall performance of such a composite (e.g., its viscoelastic properties) can be dramatically altered, and stiffness and damping can be tuned to an extreme if one allows for temporarily negative elastic moduli in the inclusion. Such incremental negative moduli imply instability; e.g. a free-standing body of negative stiffness is thermodynamically unstable. However, through its geometric constraint a matrix phase can stabilize the otherwise unstable state of the inclusion phase, thus rendering the overall composite stable. In this contribution, we show, based on dynamic stability analyses, that the matrix constraint does indeed allow for the existence and use of negative moduli, and that this effect can be utilized to design novel composites of superior performance. Approaches to stabilize the negative-stiffness effect will be discussed as well as the performance of such composites.   

Snap-Through of Graphene: An Elasto-Capillary Perspective

Understanding the interaction between graphene flakes and various substrates is of crucial importance for nanoelectromechanical systems (NEMS) applications, among others. The `snap-through' instability of graphene flakes placed onto corrugated substrates has recently received much attention as a potential assay for the study of this interaction. A sharp transition has been found in the morphology of the graphene between a) closely adhering to the corrugations of the substrate and b) lying almost completely flat on top. Which of these morphologies is observed depends on the geometry of the substrate and the mechanical properties of the flake. In this talk we shall focus on understanding the nature of this transition and, in particular, the 'sharpness' of the transition. We investigate how the location of snap through and its sharpness might be used to yield estimates of adhesion strength and friction with the substrate.   

Electromechanical phase transition in dielectric elastomers under uniaxial tension and electrical voltage

Subject to forces and voltage, a dielectric elastomer may undergo electromechanical phase transition. A phase diagram is constructed for an ideal dielectric elastomer membrane under uniaxial force and voltage, reminiscent of the phase diagram for liquid-vapor transition of a pure substance. We identify a critical point for the electromechanical phase transition. Two states of deformation (thick and thin) may coexist during the phase transition, with the mismatch in lateral stretch accommodated by wrinkling of the membrane in the thin state. The processes of electromechanical phase transition under various conditions are discussed. A reversible cycle is suggested for electromechanical energy conversion using the dielectric elastomer membrane, analogous to the classical Carnot cycle for a heat engine. The amount of energy conversion, however, is limited by failure of the dielectric elastomer due to electrical breakdown. With a particular combination of material properties, the electromechanical energy conversion can be significantly extended by taking advantage of the phase transition without electrical breakdown.   

Soft Dielectrics: Heterogeneity and Instabilities

Dielectric Elastomers are capable of large deformations in response to electrical stimuli. Heterogeneous soft dielectrics with proper microstructures demonstrate much stronger electromechanical coupling than their homogeneous constituents. In turn, the heterogeneity is an origin for instability developments leading to drastic change in the composite microstructure. In this talk, the electromechanical instabilities are considered. Stability of anisotropic soft dielectrics is analyzed. Ways to achieve giant deformations and manipulating extreme material properties are discussed. 1. S. Rudykh and G. deBotton, ``Instabilities of Hyperelastic Fiber Composites: Micromechanical Versus Numerical Analyses.'' Journal of Elasticity, 2011. http://dx.doi.org/2010.1007/s10659-011-9313-x 2. S. Rudykh, K. Bhattacharya and G. deBotton, ``Snap-through actuation of thick-wall electroactive balloons.'' International Journal of Non-Linear Mechanics, 2011. http://dx.doi.org/10.1016/j.ijnonlinmec.2011.05.006 3. S. Rudykh and G. deBotton, ``Stability of Anisotropic Electroactive Polymers with Application to Layered Media.'' Zeitschrift f\"ur angewandte Mathematik und Physik, 2011. http://dx.doi.org/10.1007/s00033-011-0136-1 4. S. Rudykh, A. Lewinstein, G. Uner and G. deBotton, ``Giant Enhancement of the Electromechanical Coupling in Soft Heterogeneous Dielectrics.'' 2011 http://arxiv.org/abs/1105.4217v1   

Modeling of dielectric elastomeric materials: theory, finite element simulation, and applications

Elastomeric materials that undergo large deformations in response to an electric field have garnered attention in recent years. Applications of these dielectric elastomeric materials include actuators capable of converting electrical energy to mechanical work and energy harvesting devices that convert mechanical energy into electrical energy. Furthermore, dielectric elastomers exhibit interesting instabilities, especially under constrained geometries, opening the door for possible applications in active surfaces. Interest has increased in the mechanics community concerning the formulation of a finite-deformation constitutive theory for an electro-mechanically-coupled material. While the details of the formulation of such a theory are beginning to come into focus in the literature, numerical techniques for solving these equations are in their infancy. In this work, we have developed a finite-element-based numerical simulation capability for dielectric elastomers. This talk will highlight the application of our numerical simulation capability to dielectric elastomeric actuators, energy harvesting devices, as well instabilities of small dielectric elastomeric structures on a constraining substrate.   

Giant linear voltage-induced deformation of a dielectric elastomer actuator

For dielectric elastomers, one of the most conspicuous attributes is large deformation of actuation induced by voltage. However, electromechanical instability may limit their deformation. In this seminar, I will illustrate how dielectric elastomers survive or eliminate electromechanical instability, through mechanical designs. For example, I will analyze a dielectric elastomer with a ``pure shear'' boundary condition. The membrane is first prestretched along the transverse direction, and then fixed by a rigid bar. As a result, the stretch in transverse direction is fixed, and the membrane can only be actuated along the vertical direction. The theory shows that the actuator can avert electromechanical instability, and achieve a giant linear deformation of actuation. The experiments confirm the theoretical predictions. For SEBS material, the linear strain of actuation can be 80{\%}. For VHB material, the linear strain of actuation can be 300{\%}. The actuator shows advantages compared to the classic designs (say, tube and circular actuators), and can be used as artificial muscles in soft robots.   

Geometry-induced rigidity in pressurized elastic shells

We study the indentation of pressurized thin elastic shells, with positive Gauss curvature. In our precision desktop-scale experiments, the geometry of the shells and their material properties are custom-controlled using rapid prototyping and digital fabrication techniques. The mechanical response is quantified through load-displacement compression tests and the differential pressure is set by a syringe-pump system under feedback control. Focus is given to the linear regime of the response towards quantifying the geometry-induced rigidity of pressurized shells with different shapes. We find that this effective stiffness is proportional to the local mean curvature in the neighborhood of the locus of indentation. Combining classic theory of shells with recent developments by D. Vella et al. (2011), we rationalize the dependence of the geometry-induced rigidity on: i) the mean curvature at the point of indentation, ii) the material properties of the shell and iii) the in-out differential pressure. The proposed predictive framework is in excellent agreement with our experiments, over a wide range of control parameters. The prominence of geometry in this class of problems points to the relevance and applicability of our results over a wide range of lengthscales.   

S-cones in thin shells under indentation

We perform a hybrid experimental and numerical investigation of the localization of deformation in indented thin spherical elastic shells. Past the initial linear response, an inverted cap develops as a Pogorelov circular ridge. For further indentation, this ridge looses axis-symmetry and sharp points of localized curvature form. We refer to these localized objects as \emph{s-cones} (for shell-cones), in contrast with their developable cousins in plates (d-cones). We quantify the effect of systematically varying the indenter's radius of curvature (from point to plate load) on the formation and evolution of s-cones. In our precision desktop-scale experiments we use rapid prototyped elastomeric shells and rigid indenters of various shape. The mechanical response is measured through load-displacement compression tests and the deformation process is further characterized through digital imaging. In parallel, the experimental results are contrasted against nonlinear Finite Element simulations. Merging these two complementary approaches allows us to gain further physical insight towards rationalizing this geometrically nonlinear process.   

Folding and buckling pathways in spherical shells with soft spots

Thin elastic spherical shells subject to an external pressure undergo a buckling transition when the pressure reaches a critical value. Past the buckling instability, the shell typically takes on a shape with one or more inversions that focus the elastic deformation energy within narrow circular regions on the sphere. These inversions are associated with large volume changes and hysteresis, and their location is highly sensitive to very slight imperfections in the sphere. Recently, it has been demonstrated [1] that natural pollen grains have evolved soft sectors in their hard outer walls which guide them toward particular folding pathways when their internal volume is reduced due to dessication, thus avoiding sudden and uncontrolled changes in shape. Motivated by these results, we study the effect of circular soft spots on the buckling of otherwise uniform spherical shells. Through a combination of scaling arguments and numerical simulations, we demonstrate that the shell can be tuned to follow distinct buckling pathways by varying the size and stiffness of the soft spot. [1] E. Katifori \textit{et al}, \textit{Proc. Natl. Acad. Sci. USA} \textbf{107}, 7635 (2010)   

Buckliballs: Buckling-Induced Pattern Transformation of Structured Elastic Shells

We present a class of continuum shell structures, the buckliball, which, undergo a structural transformation induced by buckling under pressure loading. The geometry of the buckliball comprises a spherical shell patterned with a regular array of circular voids. Moreover, we show that the buckling-induced pattern transformation is possible only with five specific hole arrangements. These voids are covered with a thin membrane, thereby making the ball air tight. Beyond a critical internal pressure, the thin ligaments between the voids buckle leading to a cooperative buckling cascade of the skeleton of the ball. Both precision desktop-scale experiments and finite element simulations are used to explore the underlying mechanics in detail and proof of concept of the proposed structures. We find excellent qualitative and quantitative agreement between experiments and simulations. This pattern transformation induced by a mechanical instability opens the possibility for reversible encapsulation, over a wide range of length scales.   

Wrinkling of a collapsing viscous bubble

Thin-sheets of sufficiently viscous liquid can behave similar to elastic sheets and buckle under certain external forces. A classic example is the ``parachute instability'' for which a ruptured viscous bubble wrinkles as it relaxes, with the explanation for the wrinkles being based on the liquid film falling under its own weight. In this talk we revisit the viscous bubble-bursting experiments and demonstrate that gravity is responsible for neither the collapse nor the resulting wrinkling instability. Using a combination of experiments and theory, we highlight the importance of capillary forces and elucidate their role in the wrinkling instability.   

Session Q53: Packing, Self-Assembly, and Granular Memory

Cooperative effects in DNA nanotile attachment

In the context of realising a DNA nanotile system capable of exponentially replicating an information string encoded in a tile pattern with the aid of thermal and UV cycling [1], we encountered the problem of predicting the hybridisation transition temperatures of DNA tile pairs with multiple single strand connectors (sticky ends). For the common single-helix hybridisation transition, sufficiently accurate predictions can be derived from SantaLucia's nearest-neighbour parameter analysis [2]. However, the case of several DNA strands hybridising cooperatively while attached to a rigid object is entropically different and we had to develop a method to factor in the resulting phase space restrictions (cf. a similar approach for DNA-covered colloids [3]). We were able to test our thermodynamic model by fluorescently labelling DNA tile pairs with variable numbers of sticky ends and recording the hybridisation transition using FRET. The data fit our prediction within an acceptable parameter range.\\[4pt] [1] T. Wang et al., {\em Nature}, 478(7368):225--228, 2011;\\[0pt] [2] J. SantaLucia, {\em PNAS}, 95(4):1460--1465, 1998\\[0pt] [3] R.~{Dreyfus} et al.; {\em Phys. Rev. Lett.}, 102(4):048301, 2009.   

Minimal energy packings of weakly semiflexible polymers: Application to targeted self-assembly of nanostructures

Using exact enumeration, we characterize how structure, mechanical and thermodynamic stability of minimal energy packings of short ``sticky tangent sphere'' (SHS) polymer chains vary with angular interaction strength $k_b$ and equilibrium bond angle $\theta_0$. While flexible SHS polymers possess highly degenerate ground states (i.\ e.\ many differently ordered ``macrostates'' [1]), angular interactions dramatically break this degeneracy. The macrostate associated with the ground state semiflexible packing changes as $k_b$ and $\theta_0$ are varied. Further degeneracy breaking arises from angular interactions' influence on packing size, asymmetry, and vibrational entropy. The strength of these effects increases with chain length $N$. Our exact analysis provides design principles for self-assembly of polymers into a variety of structures that can be tuned by varying $N$, $k_b$ and $\theta_0$. \\[4pt] [1] R. S. Hoy and C. S. O'Hern, Phys. Rev. Lett. \textbf{105}, 068001 (2010).   

Self-assembly of Low-coordinated Ground States via Monotonic Pair Potentials

Monotonically decreasing radially symmetric pair potentials can lead to the self assembly of unusual low-coordinated ground states. The states include, but are not limited to, the square, honeycomb, and simple cubic crystals in two and three-dimensional Euclidean spaces $R^2$ and $R^3$. We can determine optimal potentials for targeted ground states using inverse statistical mechanical techniques. Using a linear programming method, we are able to search over a wide parameter space while still enforcing constraints such as motonicity and convexity on optimized potentials. The features present in the classes of short-ranged potentials that conform to these constraints suggest sufficient requirements for colloids to self assemble into a desired ground state.   

Dense packings of spheres in cylinders

We develop a simple analytical theory that relates dense hard sphere packings in a cylinder to corresponding disk packings on its surface. It applies for ratios R=D/d (where d and D are the diameters of the hard spheres and the bounding cylinder, respectively) up to R=2.738. Within this range the densest packings are such that all spheres are in contact with the cylindrical boundary. The detailed results elucidate extensive numerical simulations by others and ourselves by identifying the nature of various competing phases. We also present results for the regime R greater than 2.738. These preliminary results explore packings that include internal spheres (i.e. spheres that do not contact the cylinder). This is done through a combination of experiments and numerical simulation (simulated annealing). Our experiments involve the packing of monodisperse bubbles in narrow micron-sized capillaries. Such ``wet foams'' are an excellent model of the hard sphere packing problem and are analyzed by X-ray tomography to provide structural information.   

Novel structures from the densest binary sphere packings

The densest binary sphere packings have historically been very difficult to determine. The only rigorously known packings in the $\alpha$-$x$ plane of small to large sphere radius ratio $\alpha$ and small sphere relative concentration $x$ are at the Kepler limit $\alpha \rightarrow 1$, where packings are monodisperse. Utilizing an implementation of the Torquato-Jiao linear programming algorithm, we find many distinct families of novel densest binary packings and construct a phase diagram for all known densest packings over the $\alpha$-$x$ plane. In particular, these families of densest binary packings are examples of complicated, mechanically stable structures that can appear in colloidal systems without any anisotropic or attractive interactions.   

Random and ordered phases of off-lattice rhombus tiles

We study the covering of the plane by non-overlapping rhombus tiles, a problem well-studied only in the limiting case of dimer coverings of regular lattices. We go beyond this limit by allowing tiles to take any position and orientation on the plane, to be of irregular shape, and to possess different types of attractive interactions. Using extensive numerical simulations we show that at large tile densities there is a phase transition from a fluid of rhombus tiles to a solid packing with broken rotational symmetry. We observe self-assembly of broken-symmetry phases, even at low densities, in the presence of attractive tile-tile interactions. Depending on tile shape and interactions the solid phase can be random, possessing critical orientational fluctuations, or crystalline. Our results suggest strategies for controlling tiling order in experiments involving ``molecular rhombi.''   

Structure and stability of finite sphere packings via exact enumeration

We analyze the geometric structure and mechanical stability of complete sets of isostatic and hyperstatic sphere packings obtained via exact enumeration techniques. The number of nonisomorphic isostatic packings grows exponentially with the number of spheres $N$, and the fraction of packings possessing soft modes (for ``sticky'' spheres with contact attractions) grows faster. The diversity of structure and symmetry increases with $N$ and decreases with the degree of hyperstaticity. We further show that maximally contacting packings are in general neither the densest nor the most symmetric. Our studies of the geometry of complete sets of sphere packings provide a basis for future work on ground and metastable states in systems with hard-core plus short-range attractive interactions including attractive colloids, collapsed proteins, and jammed particulate media.   

Fabrication of sophisticated two-dimensional organic nanoarchitectures thought hydrogen bond mediated molecular self assembly

Complex supramolecular two-dimensional (2D) networks are attracting considerable interest as highly ordered functional materials for applications in nanotechnology. The challenge consists in tailoring the ordering of one or more molecular species into specific architectures over an extended length scale with molecular precision. Highly organized supramolecular arrays can be obtained through self-assembly of complementary molecules which can interlock via intermolecular interactions. Molecules forming hydrogen bonds (H-bonds) are especially interesting building blocks for creating sophisticated organic architectures due to high selectivity and directionality of these bindings. We used scanning tunnelling microscopy to investigate at the atomic scale the formation of H-bonded 2D organic nanoarchitectures on surfaces. We mixed perylene derivatives having rectangular shape with melamine and DNA base having triangular and non symmetric shape respectively. We observe that molecule substituents play a key role in formation of the multicomponent H-bonded architectures. We show that the 2D self-assembly of these molecules can be tailored by adjusting the temperature and molecular ratio. We used these stimuli to successfully create numerous close-packed and porous 2D multicomponent structures.   

Exploiting Mixed Self-Assembled Monolayers for Design and Fabrication of Patchy Particles

Previous computational studies [1,2] explained the formation of patterns (stripes and patches) in binary mixtures of immiscible surfactants adsorbed on gold nanoparticles [3]. These patterns can confer to the particles unexpected properties, including novel wetting behavior [4]. As an extension of those studies, we performed atomistic and mesoscale simulations of ternary and quaternary mixed self-assembled monolayers (SAMs) on nanosphere surfaces. Here we present predictions for new and unexpected patterns for patchy particles that could be synthesized through judicious choice of surfactant architecture, nanoparticle geometry, and SAM stoichiometry. \\[4pt] [1] C. Singh et al. Physical Review Letters 99, 226106 (2007)\\[0pt] [2] C. Singh et al. Nanoscale 3, 3244-3250 (2011)\\[0pt] [3] A.M. Jackson et al. Nature Materials, 3, 330-336 (2004)\\[0pt] [4] J.J. Kuna et al. Nature Materials, 8, 837-842 (2009)   

Entropy density and Mutual Information measures to quantify the complexity of a nanoscale system

Information-theoretic approach is the most general way to quantify complexity of nanoscale systems. In this study the entropy density and mutual information measures were used to identify the optimal interaction parameters between nanoparticles, which lead to the maximum geometric complexity of self-assembled nanostructures. A generalization of complexity measures at a finite temperature and for nonequilibrium systems is also presented. The developed theory can be used for efficient in silico design of new self-assembled nanostructures with a complex geometry not achievable before.   

Road Usage Heterogeneity and Mitigation of Traffic Congestion

Road networks form the backbone of the social and economic life of a city. Until recently, however, data have not been available to study the impact of trip selection on traffic congestion at an urban scale. To that end, we combined the most complete record of daily trips with the detailed road GIS data to analyze the road usage patterns in two US metropolitan areas. We classify the importance of road segments based on their ability to attract drivers from diverse sources and find that most of them are mainly used by drivers from very few sources. Thanks to this heterogeneity, we find that it is possible to design an efficient strategy to largely reduce the travel time in the road system.   

Rippling ``instability'' in granular jet impact is a memory effect

Experiments and simulations of a dense granular jet impacting a target give rise to a collimated outflow despite the lack of cohesion in the system. This outflow eventually breaks up far away from the target. The breakup, however, is not a uniform dilution but rather takes the form of a series of wave-like undulations with a wavelength much larger than the grain scale. We investigate the possibility that this is another continuum hydrodynamic analog reproduced by bulk granular motion using 2D simulations. We find that these waves, unlike a Helmholz instability, cannot readily be nucleated by perturbations of the granular flow surface. Instead, we find that they point to relics of the velocity fluctuations caused by the impact itself. We show that the ripples are an effect of the effectively ballistic flow far from the target remembering these original velocity fluctuations.   

Transient Memories in Non-Equilibrium Disordered Systems

Some non-equilibrium systems can store information of their external driving in an unexpected manner. They ``learn'' multiple driving amplitudes that can subsequently be read out. Notably, only one memory is retained after many driving cycles, even if all of the amplitudes are continually fed in. This behavior has been observed in diverse scenarios such as traveling charge-density waves [1] and simulations of sheared suspensions [2]. Here we explore this latter system experimentally using a suspension of neutrally buoyant non-Brownian particles in a very viscous fluid that is sheared cyclically in a Couette cell geometry. Starting from a random configuration, the particle trajectories are irreversible at first but, as had been shown [3], eventually settle into a configuration where they retrace their paths exactly during each cycle. We show that the resulting configuration comprises a memory of the driving amplitude, which can be read out by measuring the degree of particle reversibility versus shear amplitude. We also discuss this system's capacity for storing multiple memories.\\[4pt] [1] S. N. Coppersmith et al., PRL 78, 3983 (1997).\\[0pt] [2] N. C. Keim, S. R. Nagel, PRL 107, 010603 (2011).\\[0pt] [3] L. Cort{\'e}, P. M. Chaikin, J. P. Gollub, D. J. Pine, Nature Phys. 4, 420 (2008).   

Role of interaction in the formation of memories in paste

A densely packed colloidal suspension with plasticity, called paste, remembers the directions of vibration and flow. These memories in paste can be visualized by the morphology of desiccation crack patterns. We investigate the role of interaction in the formation of memories in paste. First, interparticle attractive forces, such as van der Waals interaction, are needed to construct a macroscopic network structure with plasticity. With the help of attractive interaction, a water-poor paste remembers the direction of vibration and a water-rich paste remembers the flow direction [1]. When particles are charged in water, however, Coulombic repulsive interaction prevents formation of dilute network structure under flow, which leads to the experimental result that a water-rich charged paste cannot remember flow direction. Addition of sodium chloride to such a paste gives the ability to remember flow direction due to the screening effect of Coulombic repulsive interaction between particles [2].\\[4pt] [1] A. Nakahara, Y. Shinohara and Y. Matsuo, J. Phys.: Conf. Ser. 319 (2011) 012014.\\[0pt] [2] Y. Matsuo and A. Nakahara, arXiv:1101.0953v1 [cond- mat.soft].   

Resonances arising from hydrodynamic memory - The Color of Brownian motion

Observation of the Brownian motion of a small probe interacting with its environment is one of the main strategies to characterize soft matter. Initially, the particle is driven by rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Later, the friction between the particle and the viscous solvent damps its motion. Conventionally, thermal force is taken to be characterized by a Gaussian white noise spectrum. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times, when inertia becomes negligible. Here, we measured the noise spectrum of the thermal forces by tracking with high resolution a single micron-sized sphere suspended in a fluid, and confined by a stiff optical trap [1]. Coupling between sphere and fluid gives rise to hydrodynamic memory [2] and a resonance, equivalent to a colored peak in the power spectral density of the sphere's thermal fluctuations. Our results reveal that motion is not overdamped, even at long times. In view to exploit the particle-fluid-trap system as a nanomechanical resonator, we disentangle the two regimes in which the detected resonance is either sensitive to the fluid properties or to the particle's mass.\\[4pt] [1] Jeney et al. Nature 2011.\\[0pt] [2] Jeney et al. PRL 2008.   

Session Q54: Superconductivity: Mesoscopic and Nanometer Scale

Designing high-impedance/low-noise superinductances for quantum electronics

Superinductances are essential circuit elements which enable the suppression of charge fluctuations in superconducting fluxonium qubits [1] and in other Josephson junction devices [2]. Commonly implemented as an array of Josephson junctions, superinductances have two main limitations. Firstly, the spurious capacitive coupling of the chain islands to ground lowers the plasma frequency of the chain, and consequently limits the operational bandwidth. Secondly, coherent quantum phase-slips (CQPS) [3] in the Josephson junction chain induce time dependent inductance fluctuations via the Aharonov-Casher effect [4]. We present the application of a novel lithographic technique [5] which enables the fabrication of arrays with optimal junction-capacitance to ground-capacitance ratio. We also present new superinductance designs which topologically suppress the CQPS, allowing the implementation of practically phase-slip free high inductance Josephson junction.\\[4pt] [1] Manucharyan et al., Science, 326 (2009)\\[0pt] [2] Guichard and Hekking, PRB, 81 (2010)\\[0pt] [3] Matveev et al. PRL, 89 (2002)\\[0pt] [4] Pop et al., arXiv:1105.6204 and Manucharyan et al., arXiv:1012.1928\\[0pt] [5] Lecocq et al., Nanotechnology, 22 (2011)   

Powerful coherent terahertz emission from $\rm{Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}}$ mesa array

Stacks of intrinsic Josephson junctions (IJJs) in high-temperature superconductors enable the fabrication of compact sources of coherent THz-radiation. Here we demonstrate 150 microwatts of radiation power at 0.51 THz, using three synchronized stacks patterned on a single $\rm{Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta}}$ crystal. The emitted power scales roughly as the square of the number of energized stacks, while the total power spectrum is monochromatic to within observational limits. These results imply that the stacks radiate coherently.   

DC SQUID RF magnetometer with 200 MHz bandwidth

Because of periodic flux-to-voltage transfer function, Superconducting QUantum Interference Device (SQUID) magnetometers operate in a closed-loop regime [1], which linearizes the response, and increases the dynamic range and sensitivity. However, a transmission line delay between the SQUID and electronics fundamentally limits the closed-loop bandwidth at 20 MHz [1], although the intrinsic bandwidth of SQUIDs is in gigahertz range. We designed a DC SQUID based RF magnetometer capable of wideband sensing coherent magnetic fields up to 200 MHz. To overcome the closed-loop bandwidth limitation, we utilized a low-frequency flux-modulated closed-loop to simultaneously lock the quasi-static magnetic flux and provide AC bias for the RF flux. The SQUID RF voltage is processed by RF electronics based on a double lock-in technique. This yields a signal proportional to the amplitude and phase of the RF magnetic flux, with more than four decades of a linear response. For YBaCuO SQUID on bi-crystal SrTiO substrate at 77 K we achieved a flux noise density of 4 \textit{$\mu $}$\Phi _{0}$/$\surd $Hz at 190 MHz, which is similar to that measured at kHz frequencies with conventional flux-locked loop. [1] D. Drung, \textit{et al.}, Supercond. Sci. Technol. \textbf{19, }S235 (2006).   

Wideband S-parameter characterization of DC-SQUID amplifiers at GHz frequencies

Superconducting quantum interference devices (SQUIDs) are widely used as gain elements to achieve ultra-low noise amplification from DC to microwave frequencies. SQUID amplifiers typically have high input and output stray reactance and therefore proper impedance matching is needed to couple enough power into the device. Broadband impedance matching could be obtained by measuring the microwave S-parameters of a SQUID amplifier and then treating it as an equivalent ``black box'' to which standard microwave design techniques can be applied. In this talk measurement results of the full 2-port S-parameter matrix of DC-SQUID amplifiers operating at 20mK will be presented. Accurate microwave calibration was performed with an automated Through-Reflect-Line (TRL) calibration system, operating at 20mK. Input and output reflection coefficients as well as forward and backward transmission were characterized in the 1 to 8GHz range. Implications for the design of wideband SQUID amplifiers and device stability will be discussed.   

Characterization of Low Noise Superconducting Microwave Amplifiers

We have developed an experimental setup to characterize low noise amplifier chains with a six port low temperature microwave switch controlled via room temperature electronics. This switch allows us to do a traditional Y-factor measurement, a reflection measurement with an open input, or a measurement using a Shot Noise Tunnel Junction(SNTJ) device developed by J. Aumentado and L. Spietz at NIST. The SNTJ allows one to measure system gain, system noise, and junction temperature as fit parameters. The SNTJ is sensitive enough characterize amplifiers with noise due primarily to photon ground state fluctuations or quantum limited amplifiers. We first tested our setup using a HEMT and room temperature amplifier chain with calibrated noise and gain characteristics. We then characterized several iterations of the theoretically quantum limited SLUG amplifier developed by R. McDermott at U Wisconsin Madison.   

Shot noise measurements in diffusive wire NSN structures

Subgap transport across a normal metal/superconductor interface requires a conversion from normal to supercurrent. We study the conversion process in superconducting wire samples by attaching two short diffusive normal metal wires at a distance comparable to the coherence length in the superconductor. In addition to ordinary Andreev reflection, nonlocal processes involving electronic states in both contacts (Crossed Andreev reflection, and Elastic Co-tunneling) are expected to contribute and to give rise to a cross-conductance signal in transport measurements. As one of the wire contacts is biased into the shot noise regime, a significant increase of current fluctuations is observed in the other (unbiased) contact. Only a small fraction of the noise measured in the two contacts is correlated. The magnitude of the correlated signal scales with the observed cross-conductance. We will compare our results with theoretical predictions for nonlocal transport and previous experimental work.   

Toward a Passive Lossless on-Chip Circulator in the 4-8 GHz Range

We present further progress toward constructing a passive microwave circulator from Josephson junction circuits. We have designed, built and tested a circuit which demonstrates the basic properties required to construct a gyrator in the 4-8 GHz range. We describe the theory and present the data on this circuit and point to the path from these results to practical passive lossless on-chip circulators.   

Calibration of a Microfabricated Phonon Spectrometer

Non-thermal distributions of phonons may be locally excited and detected in silicon micro- and nanostructures by decay of quasiparticles injected into an adjacent superconducting tunnel junction [1]. Using this technique, narrow frequency bands of phonons may be isolated and applied to investigate phonon transport through nanostructures at sub-kelvin temperatures [2]. In our prototype phonon spectrometer we have demonstrated spatial resolution below 1 micron and frequency resolution of ~10 GHz. We describe ways to control the spatial resolution, frequency resolution, frequency range, dynamic range and signal-to-noise ratio in this technique, by using different superconducting materials in the tunnel junctions and by inserting absorber materials into the phonon transmission path. This work is supported by DOE (DE-SC0001086). \\[4pt] [1] H. Kinder. Phys. Rev. Lett. 28, 1564 (1972)\\[0pt] [2] J. B. Hertzberg et al, Rev. Sci. Inst. 82, 104905 (2011).   

Microwave Spectroscopy of a Cooper-Pair Transistor Coupled to a Lumped-Element Resonator

We have studied the microwave response of a single Cooper-pair transistor (CPT) coupled to a lumped-element microwave resonator. The resonance frequency of this circuit, $f_{r}$ , was measured as a function of the charge $n_{g}$ induced on the CPT island by the gate electrode, and the phase difference across the CPT, $\phi_{B}$ , which was controlled by the magnetic flux in the superconducting loop containing the CPT. The observed $f_{r}(n_{g},\phi_{B})$ dependences reflect the variations of the CPT Josephson inductance with $n_{g}$ and $\phi_{B}$ as well as the CPT excitation when the microwaves induce transitions between different quantum states of the CPT. The results are in excellent agreement with our simulations based on the numerical diagonalization of the circuit Hamiltonian. This agreement over the whole range of $n_{g}$ and $\phi_{B}$ is unexpected, because the relevant energies vary widely, from 0.1K to 3K. The observed strong dependence $f_{r}(n_{g},\phi_{B})$ near the resonance excitation of the CPT provides a tool for sensitive charge measurements.   

Superconducting Low-Inductance Undulatory Galvanometer Microwave Amplifier: Theory

We present numerical studies of a phase-insensitive microwave linear amplifier based on the Superconducting Low-Inductance Undulatory Galvanometer (SLUG). Direct integration of the junction equations of motion provides access to the full scattering matrix of the SLUG element. We discuss the optimization of SLUG amplifiers and calculate amplifier gain and noise temperature in both the thermal and quantum regimes. The microwave SLUG amplifier is expected to achieve noise performance approaching the standard quantum limit in the frequency range from 5-10 GHz, with gain around 15 dB for a single-stage device and instantaneous bandwidth of order hundreds of MHz. We compare our numerical model with measured performance of state-of-the-art devices.   

Superconducting Low-inductance Undulatory Galvanometer Microwave Amplifier

We describe a novel microwave linear amplifier based on the Superconducting Low-inductance Undulatory Galvanometer (SLUG). The compact SLUG element is straightforward to model at microwave frequencies, allowing separate optimization of the SLUG element and the resonant input matching network; we expect optimized devices based on high-Jc junctions to achieve gains around 15 dB in the range from 5-10 GHz, with instantaneous bandwidth of order hundreds of MHz and noise performance approaching the standard quantum limit. Using amplifiers based on low-Jc Al/AlO$_{x}$/Al junctions, we have achieved gain in excess of 20 dB at 3 GHz and greater than 15 dB at 9 GHz with bandwidth of several MHz. We discuss progress toward the incorporation of high-Jc Nb/AlOx/Nb junctions in the SLUG amplifier, and describe strategies to promote the thermalization of the SLUG shunt resistors at dilution refrigerator temperatures by integrating large-volume normal metal cooling fins with the shunts.   

Development and Implementation of a 1 GHz SQUID amplifier for the Axion Dark Matter Experiment

The Axion Dark Matter eXperiment (ADMX) was designed to detect ultra-weakly interacting relic axion particles by searching for their conversion to microwave photons in a resonant cavity positioned in a strong magnetic field. Given the extremely low expected axion-photon conversion power we have designed, built and operated a microwave receiver based on a Superconducting QUantum Interference Device (SQUID). We describe the implementation of a SQUID amplifier in the ADMX microwave receiver chain and discuss progress made at the Washington Micro-Fabrication Facility toward the production of SQUID amplifiers from a ${\rm Nb}-{\rm Al}_x{\rm O}_y-{\rm Nb}$ trilayer.   

Quantum pumping of electrons at the Josephson frequency

A macroscopic fluid pump works according to the law of Newtonian mechanics and transfers a large number of molecules per cycle. By contrast, a nano-scale charge pump can be thought as the ultimate miniaturization of a pump, with its operation being subject to quantum mechanics and with only few electrons or even fractions of electrons transfered per cycle. It generates a direct current in the absence of an applied voltage exploiting the time-dependence of some properties of a nano-scale conductor. So far, nano-scale pumps have been realised only in system exhibiting strong Coulombic effects, whereas evidence for pumping in the absence of Coulomb-blockade has been elusive. Here we report the experimental detection of charge flow in an unbiased InAs nanowire embedded in a superconducting quantum interference device (SQUID). In this system, pumping occurs via the cyclic modulation of the phase of the order parameter of different superconductors. The symmetry of the current with respect to the enclosed flux and SQUID current is a discriminating signature of pumping. Currents exceeding 20 pA are measured at 250 mK, and exhibit symmetries compatible with a pumping mechanism.   

NIS cooler platform: from 300 mK to 100 mK

Normal-insulator-superconducting (NIS) tunnel junctions allow cooling of the normal metal by electrons tunneling across the insulating barrier. With proper biasing, hot electrons leave the normal metal and cold electrons enter from the superconductor, lowering the electronic temperature. The heat dissipation is determined primarily by the quasiparticle relaxation in the superconducting leads. We explore the effects of magnetic field, electrode geometry, direct quasiparticle traps and other fabrication modifications on cooler effectiveness. The overall aim is to produce a general electronic cooler for efficient, solid state, cooling of small devices from 300 to 100 mK.   

Implementation and test of an Levitov's n-electron coherent source

Injecting a controlled number of electrons in a quantum ballistic conductor opens the way to new kind of quantum experiments, yet never done. It is well known that a voltage biased contact applied on a single mode quantum conductor, such as a Quantum Point Contact, inject continuously single electrons at a rate \textit{eV/h} , a remarkable property of the Fermi sea. Here we consider the injection of electrons during a very short time where is is expected that a voltage pulse with \textit{$\smallint $eV(t)dt = nh }injects exactly n-electrons, n being integer. If in addition, if the voltage pulse has the form of a Lorentzian shape in time, Levitov has shown that the n-electron are not accompanied by neutral spurious electron-hole pair excitations and thus form a minimal excitation n-electron source. The electron being indistinguishable if the time-scale is shorter than the coherence time, the Levitov's source is coherent and new quantum experiments involving interference with serveral electrons become at reach. We present here experimental realization of the n-electron source using short sub-nanosecond pulses and tests of the minimal excitation number using the shot noise created by repeatedly sending n-electrons toward a quantum point realized in clean ballistic 2D electrons. The square-wave, sine-wave and Lorentzian shape pulses are compared. This is also accompanied by photon-assisted current measurements. J. Dubois, T. Jullien, P. Roulleau, F. Portier, P. Roche, and D.C. Glattli, in preparation.