Session T1: Hybrid Systems, Optomechanics and Macroscopic Systems at the Quantum Limit II

Coupling propagating acoustic waves to quantum circuits

We present a method for coupling propagating Surface Acoustic Waves (SAW) to charge sensitive quantum circuits, by direct piezoelectric charge induction. Using an RF-Single Electron Transistor\footnote{R.J. Schoelkopf, P. Wahlgren, A.A. Kozhevnikov, P. Delsing, and D.E. Prober, Science.~{\bf 280}, 1238 (1998).} as a high-performance electrometer, and employing an on-chip mixing technique\footnote{R. Knobel, C.S. Yung, and A.N. Cleland, Appl. Phys. Lett.~{\bf 81}, 532 (2002).}, we demonstrate ultra-high displacement sensitivity in the gigahertz frequency range, and an averaged detection sensitivity below the single-phonon level. Based on these experimental results, we discuss how the method can be enhanced and extended to superconducting qubits, and what roles Surface Acoustic Waves could potentially play in novel hybrid quantum devices.   

Single Crystal Diamond Mechanical Resonators

We report on the fabrication and measurement of single crystal diamond mechanical resonators. This is an important step towards realizing diamond photonics, optomechanics, and diamond-based scanning magnetometers. We present measurements of mechanical quality factors in excess of 10,000 as well as estimates of the coupling to embedded nitrogen-vacancy (NV) centers through strain. Strain tuning the NV's zero-phonon line could facilitate coupling its spin state to a photonic network. We also discuss strain as a coupling mechanism between the spin and mechanical degree of freedom in a diamond based resonator.   

Resonant Optical Forces in Silicon Carbide Nanostructures

Silicon carbide (SiC) materials are widely used for their exceptional electronic, mechanical, and thermal properties. For example, given its high stiffness to density ratio, SiC is an ideal material for mechanical resonators, and it has been explored for applications in nanoelectromechanical systems (NEMS). SiC also supports strong surface phonon-polariton resonances in the infrared region, which could enable its use for optomechanics. Similar to surface plasmon-polaritons supported by metal-dielectric interfaces, these surface waves at a SiC-vacuum interface can be used to guide and confine intense electromagnetic energy. Here, we investigate the resonant optical forces induced by phonon-polariton modes in different SiC nanostructures. Specifically, we calculate optical forces using the Maxwell Stress Tensor for three geometries: spherical particles, slab waveguides, and rectangular waveguides. We find that the high quality factor phonon-polariton modes in SiC can produce very large forces, more than two orders of magnitude larger than the plasmonic forces in similar metal nanostructures. These strong resonant forces, combined with its mechanical and thermal properties, make SiC a promising material for optomechanical applications.   

Quantum Mechanical Scattering in Nanoscale Systems

We investigate quantum scattering using the finite element method. Unlike textbook treatments employing asymptotic boundary conditions (BCs), we use modified BCs, which permits computation close to the near-field region and reduces the Cauchy BCs to Dirichlet BCs, greatly simplifying the analysis. Scattering from any finite quantum mechanical potential can be modeled, including scattering in a finite waveguide geometry and in the open domain. Being numerical, our analysis goes beyond the Born Approximation, and the finite element approach allows us to transcend geometric constraints. Results of the formulation will be presented with several case studies, including spin dependent scattering, demonstrating the high accuracy and flexibility attained in this approach.   

Modeling time domain spectroscopy of electron-phonon coupled systems out of equilibrium

Recent advances in Terahertz large-electric field generation and pump-probe spectroscopies resolving pico- and even femtosecond time scales allow to study the behavior of photoexcited solids out of equilibrium. The relaxation after the pump pulse typically involves very fast processes related to purely electronic degrees of freedom, but for the slower return back to equilibrium it is essential to understand the interplay of electronic and lattice degrees of freedom. We present a theoretical investigation of electron-phonon coupled systems out of equilibrium, with results for various quantities (electronic distribution function, time-resolved angle-resolved photoemission, charge current). Our results show that the experimentally observed behavior can be related to the underlying microscopic properties of the system.   

Modeling lattice interaction in non-equilibrium pump-probe experiments

In past years, advances is experimental laser technology have allowed for the study of materials at ever shorter timescales. In these pump-probe experiments, after excitation by the pulse, the systems evolve back to equilibrium through its inherent relaxation processes, which are typically temporally separated by their characteristic timescales. Among the slower processes are the electron-phonon interactions, which carry the majority of the energy transferred to the electrons away into the lattice. We present a direct calculation of the characteristic timescales for systems driven out of equilibrium via a short pulse and allowed to relax via electron-phonon interactions. We make a direct connection between the observable timescales and the microscopic specifics, both via decay rates and oscillations in various photon-spectroscopies.   

Fluctuation Induced Forces for Surface Relief Gratings

In 1948 H.~G.~B.~Casimir predicted that two flat parallel neutral perfectly conducting plates would attract each other due to the quantum fluctuations of the electromagnetic field. Since then progress has been made to allow one to calculate the interaction energy due to both quantum and thermal fluctuations between two objects of almost arbitrary shape and material properties. This work focuses on interaction with at least one object described by a surface relief grating. The Casimir energy is calculated using the scattering matrix approach, and the scattering matrix of the periodic surface is calculated using the C method from electromagnetic grating theory. The strengths and limitations of the method with regards to calculating the Casimir energy are discussed, and the results for simple 1-D and 2-D periodic structures are shown.   

Superfluid to Mott-Insulator Transition in Thermodynamic Limit of 1D Coupled Cavity Array

In recent years, there has been great interest in simulating condensed matter models with quantum optical systems, which are usually characterized by a high degree of experimental control. One such model is the Jaynes-Cummings-Hubbard (JCH) model, an analog for the Bose-Hubbard (BH) model, in which mobile photons interact with atoms localized within a regular lattice of weakly coupled cavities. Finite system Density Matrix Renormalization Group (DMRG) studies have predicted a superfluid (SF) to Mott insulator (MI) transition in the phase diagram of the JCH model, and finite-size scaling has been used to determine the phase boundary in the thermodynamic limit. In this work, we directly numerically investigate the JCH model in the thermodynamic limit using infinite-system DMRG. The preliminary results indicate that the properties of the expected SF state are not wholly consistent with those of a conventional superfluid.   

Dirac Exciton-Polariton Condensates in a Triangular Lattice

Microcavity exciton-polaritons are quantum bose particles arising from the strong light-matter coupling between cavity photons and quantum well excitons. Recently, we have investigated the behavior of condensates in artificial lattice geometries in two-dimension (2D). Coherent $p$- and $d$-orbital state in a 2D square lattice is recently observed. Here we investigate exciton-polariton condensates at Dirac points formed in a 2D triangular lattice and experimental mapping of Dirac dispersion and discuss the interaction effect. We anticipate that the preparation of high-orbital condensates can be further extended to probe dynamical quantum phase transition in a controlled manner as quantum simulation applications.   

Numerical Study of the Bose-Einstein Condensation of Exciton-Polaritons

Using the complex Gross-Pitaevskii equation (cGPE) with pumping and decay terms that models the Bose-Einstein condensate of exciton-polaritons, we numerically investigate the dynamics of instability of its radially symmetric steady solutions. We develop accurate algorithms for computing the steady state solution, the linear stability spectra, as well as the full nonlinear solutions of the cGPE. We accurately compute the thresholds of instability that depend, e.g. on the strength and size of the polariton pumping spot and observe the formation of vortices and such complex dynamics as the formation of vortex lattices and nucleation.   

Formation and decay of a Bose-Einstein condensate of trapped dipole excitons

We study the nonlinear dynamics of formation and decay of a Bose-Einstein condensate of dipole excitons trapped in an external confining potential in coupled quantum wells. The problem is considered within an analytical approach and in numerical simulations. The trap restricts the spatial distribution of excitons and results in non-uniform density distribution in the exciton cloud. We demonstrate that under typical experimental conditions, regardless of a long-range nonlocal interaction of the dipole excitons, the system can be described by a generalized Gross-Pitaevskii equation with the local interaction between the excitons, and we find the effective interaction constant. In the numerical simulations, we account for the finite lifetime of dipole excitons and generation of the excitons due to continuous laser pumping. We also discuss formation and decay of vortex states in the condensate.   

Measurement of Casimir force with magnetic materials Alexandr Banishev, Chia-Cheng Chang, Umar Mohideen Department of Physics and Astronomy, University of California, Riverside, USA

The Casimir effect is important in various fields from atomic physics to nanotechnology. According to the Lifshitz theory of the Casimir force, the interaction between two objects depends both on their dielectric permittivity and magenetic permeability. Thus the role of magnetic properties on the Casimir force is interesting particularly due to the possibility of a reduction the Casimir force. In this report we will present the results of a Casimir force measurement between a magnetic material such as nickel coated on SiO2 plate and a Au-coated sphere.   

Geometry and fluctuation induced (Casimir) forces

Since the original prediction of attraction between parallel, perfectly conducting plates by Casimir there has been significant amount of work done in extending the calculations to real materials, finite temperatures and micro or nanostructured geometries. Majority of the experimental work has been carried out in the sphere-plane geometry. In this talk we will present ongoing experimental work on sphere--cylinder and sphere--cone geometries using frequency modulated atomic force microscopy. We will discuss numerical results in the sphere cylinder geometry and the range of validity of the point force approximation(PFA).   

Temperature dependence of Casimir force

Most of the experimental work till date on Casimir forces have been performed at or near room temperature. We report on our measurements of Casimir forces performed at liquid helium and liquid nitrogen temperatures using gold coated sphere and plate. These measurements were performed on a home built Atomic Force Microscope with a phase locked loop to track the frequency shift. We will discuss the results in the context of current theoretical understanding of temperature dependence in the sphere -- plate geometry.   

Enhanced light-matter interactions of a single emitter coupled to a slot waveguide

Traditionally, enhanced light-matter interactions are achieved using either plasmonic structures or photonic crystals. However, these structures suffer from inherent metal losses or narrow operating bandwidth. Instead, here we use an all-dielectric waveguide structure with ultra-small mode volume and low-loss and broadband capabilities. A slot-waveguide architecture is used for deep sub-wavelength light confinement in a low-index material surrounded by high-index barriers. Individual colloidal quantum dots are controllably coupled to this waveguide mode. A large Purcell enhancement is observed from lifetime measurements of the spontaneous emission rate of the quantum dot before and after coupling to the waveguide. Second order intensity correlation measurements verify that the observed fluorescence is indeed due to a single quantum dot. The demonstrated system is a promising broadband and low-loss platform for quantum information applications.   

Session T2: Invited Session: PIRE in Condensed Matter

Terahertz Dynamics in Carbon Nanomaterials

This NSF Partnerships for International Research and Education (PIRE) project supports a unique interdisciplinary and international partnership investigating terahertz (THz) dynamics in nanostructures. The 0.1 to 10 THz frequency range of the electromagnetic spectrum is where electrical transport and optical transitions merge, offering exciting opportunities to study a variety of novel physical phenomena in condensed matter. By combining THz technology and nanotechnology, we can advance our understanding of THz physics while improving and developing THz devices. Specifically, this PIRE research explores THz dynamics of electrons in carbon nanomaterials, namely, nanotubes and graphene --- low-dimensional, $sp^2$-bonded carbon systems with unique finite-frequency properties. Japan and the U.S. are global leaders in both THz research and carbon research, and stimulating cooperation is critical to further advance THz science and to commercialize products developed in the lab. However, obstacles exist for international collaboration --- primarily linguistic and cultural barriers --- and this PIRE project aims to address these barriers through the integration of our research and education programs. Our strong educational portfolio endeavours to cultivate interest in nanotechnology amongst young U.S. undergraduate students and encourage them to pursue graduate study and academic research in the physical sciences, especially those from underrepresented groups. Our award-winning International Research Experience for Undergraduates Program, NanoJapan, provides structured research internships in Japanese university laboratories with Japanese mentors --- recognized as a model international education program for science and engineering students. The project builds the skill sets of nanoscience researchers and students by cultivating international and inter-cultural awareness, research expertise, and specific academic interests in nanotechnology. U.S. project partners include Rice University, the University of Florida, the University of Tulsa, the State University of New York at Buffalo, Southern Illinois University at Carbondale, and Texas A\&M University. Japanese partners include: Osaka University, Chiba University, Shinshu University, Tohoku University, the University of Tokyo, the National Institute of Information and Communications Technology, the National Institute of Materials Science, Hokkaido University, RIKEN, and the University of Aizu.   

Petascale Many Body Methods for Complex Correlated Systems

Correlated systems constitute an important class of materials in modern condensed matter physics. Correlation among electrons are at the heart of all ordering phenomena and many intriguing novel aspects, such as quantum phase transitions or topological insulators, observed in a variety of compounds. Yet, theoretically describing these phenomena is still a formidable task, even if one restricts the models used to the smallest possible set of degrees of freedom. Here, modern computer architectures play an essential role, and the joint effort to devise efficient algorithms and implement them on state-of-the art hardware has become an extremely active field in condensed-matter research. To tackle this task single-handed is quite obviously not possible. The NSF-OISE funded PIRE collaboration ``Graduate Education and Research in Petascale Many Body Methods for Complex Correlated Systems'' is a successful initiative to bring together leading experts around the world to form a virtual international organization for addressing these emerging challenges and educate the next generation of computational condensed matter physicists. The collaboration includes research groups developing novel theoretical tools to reliably and systematically study correlated solids, experts in efficient computational algorithms needed to solve the emerging equations, and those able to use modern heterogeneous computer architectures to make then working tools for the growing community.   

Polymers at Interfaces: US-Korea International Research and Education Partnership

Our NSF program of Partnership for International Research and Education (PIRE) is focused on the development and training of graduate, undergraduate students and faculty members in the field of polymer physics by promoting both domestic and international research collaborations with specific exchange opportunities for both US and Korean participants. This collaborative effort by a group of 5 US faculty members is motivated by the global partnership with Korean polymer physicists to promote novel opportunities in polymer science research and education. Our PIRE program involves a focused research plan at the forefront of polymer physics based on the synthesis, separation, characterization, and theory of synthetic polymers in bulk and at interfaces. The multifaceted research activities spanning the areas of polymer synthesis, characterization, property modifications and their modeling will be presented to advance our knowledge on polymer behaviors at interfaces.   

SPIRE, the ``Spin Triangle'': Athens, Hamburg, Buenos Aires: Advancing Nanospintronics and Nanomagnetism

Future technological advances at the frontier of `elec'tronics will increasingly rely on the use of the spin property of the electron at ever smaller length scales. As a result, it is critical to make substantial efforts towards understanding and ultimately controlling spin and magnetism at the nanoscale. In SPIRE, the goal is to achieve these important scientific advancements through a unique combination of experimental and theoretical techniques, as well as complementary expertise and coherent efforts across three continents. The key experimental tool of choice is spin-polarized scanning tunneling microscopy -- the premier method for accessing the spin structure of surfaces and nanostructures with resolution down to the atomic scale. At the same time, atom and molecule deposition and manipulation schemes are added in order to both atomically engineer, and precisely investigate, novel nanoscale spin structures. These efforts are being applied to an array of physical systems, including single magnetic atomic layers, self-assembled 2-D molecular arrays, single adatoms and molecules, and alloyed spintronic materials. Efforts are aimed at exploring complex spin structures and phenomena occurring in these systems. At the same time, the problems are approached, and in some cases guided, by the use of leading theoretical tools, including analytical approaches such as renormalization group theory, and computational approaches such as first principles density functional theory. The scientific goals of the project are achieved by a collaborative effort with the international partners, engaging students at all levels who, through their research experiences both at home and abroad, gain international research outlooks as well as understandings of cultural differences, by working on intriguing problems of mutual interest. A novel scientific journalism internship program based at Ohio University furthers the project's broader impacts.   

Super-PIRE: International Consortium for Proving Novel Superconducors

The Super-PIRE project aims to study high-Tc cuprates, FeAs, heavy-ferimon and other unconventional superconductors by using neutron scattering, muon spin relaxation, X-ray scattering, optical conductivity, ARPES and STM measurements in international collaboration. The project includes US PI's Billinge, Pasupathy, Uemura (Columbia), amd Dai (UTK/ORNL), Project Patner (PP) Balatsky (LANL), and foreign PI's Uchida, Tajima, Maekawa, Eisaki (Japan), Hayden (UK), Wang (China), Luke (Canada), and about 40 additional ``Local Experts'' from institutions of the PI/PP's. In this talk, we introduce the organization of the project, initial scientific products including 4 papers published in Nature group journals, and the out-reach effort centered in organizing special graduate and undergraduate courses at Columbia recorded as voice-synchronized ppt presentations, and then broadcasted in a class-room of Tokyo University. Homepage address: http://www.phys.utk.edu/superpire/members.html   

Session T4: Vortices, Rotation, and Synthetic Gauge Fields

Rotating Ultracold Fermi Gases: Reduction in the Moment of Inertia Above the Superfluid Transition Temperature

There has been considerable interest in the viscosity of ultracold Fermi gases which is found to be anomalously suppressed even in the normal phase. This suppression, believed to derive from pseudogap effects, is also associated with a reduction in the moment of inertia, as measured by the Duke group. In this talk we address the relationship between viscosity and the reduced moment of inertia. We emphasize the very strong relation of the latter to the anomalous normal state diamagnetism of the high temperature superconductors. We present a simple physical picture for the origin of these related phenomena. Our picture gains strong support from establishing sum rule compatibility and leads to testable predictions.   

Vortices in spin-orbit-coupled Bose-Einstein condensates

We discuss realistic methods to create vortices in spin-orbit-coupled Bose-Einstein condensates. We show that, contrary to common intuition, rotation of the trap containing a spin-orbit-coupled condensate does not lead to an equilibrium state with static vortex structures but gives rise instead to intrinsically time-dependent Hamiltonian. We propose alternative methods to create stable static vortex configurations: (1) to rotate both the lasers and the anisotropic trap; and (2) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. We derive the effective Hamiltonians for spin-orbit condensates under such perturbations for most currently known realistic laser schemes that induce synthetic spin-orbit couplings and we solve the Gross-Pitaevskii equation for several experimentally relevant regimes. The new interesting effects include spatial separation of left- and right-moving spin-orbit condensates and the appearance of unusual vortex arrangements.   

2D Vortex Dynamics and Quantum Tunneling in the Lowest Landau Level Limit

We examine the collective excitation spectrum of a rapidly rotating cold Bose gas in the lowest Landau level regime. The Gross-Pitaevskii action can be equivalently expressed in terms of the angular momentum state expansion of the boson field or in terms of 2D vortex positions. We emphasize the very different role of visible and invisible vortices in the latter formulation and discuss the significance of non-standard non-local Berry phase coupling between separated vortices in the boson action. We also consider dissipative quantum tunneling of a single vortex, allowing for linear coupling to a bath of quadratic fluctuations of the lattice following the Caldeira-Leggett model, and comment on differences between the lowest Landau level limit and the case of vortices in a slowly rotating superfluid.   

Screening properties and phase transitions in unconventional plasmas for Ising-type quantum Hall states

Utilizing large-scale Monte-Carlo simulations, we investigate an unconventional two-component classical plasma in two dimensions that interacts with two different Coulomb interactions. This plasma controls the behavior of the norms and overlaps of the quantum-mechanical wavefunctions of Ising-type quantum Hall states. It also relates to a model for a rotating two-component Bose-Einstein condensate with an Andreev-Bashkin drag interaction. The plasma differs fundamentally from that which is associated with the two-dimensional XY model and Abelian fractional quantum Hall states. We find that this unconventional plasma undergoes a Berezinskii-Kosterlitz-Thouless phase transition from an insulator to a metal and that the parameter values corresponding to Ising-type quantum Hall states lie on the metallic side of this transition. This result verifies the required properties of the unconventional plasma used to demonstrate that Ising-type quantum Hall states possess quasiparticles with non-Abelian braiding statistics.   

Edge excitations of bosonic fractional quantum Hall phases in optical lattices

With the rapid development in ultracold gases, the realization of a fractional quantum Hall state on a lattice draws nearer. We investigate the impact of finite size effects in these kind of systems including different trapping potentials. A good understanding of finite size effects is essential for designing experiments and the edge excitations will likely be the best way to experimentally determine the topological order of the bulk. We find different fractional quantum Hall phases for bosons in a circular harmonic trap as the flux of the synthetic gauge field is varied, including phases like $\nu=1/2$ and $\nu=2/3$ with different edge spectra.   

Finite temperature phase structures of hard-core bosons in an optical lattice with a synthetic magnetic field

We study finite temperature phase structures of hard-core bosons in a two-dimensional optical lattice subject to a synthetic magnetic field by employing the gauged CP$^1$ model. Based on the extensive Monte Carlo simulations, we study their phase structures at finite temperatures for several values of the magnetic flux per plaquette of the lattice and mean particle density. Despite the presence of the particle number fluctuation, the thermodynamic properties are qualitatively similar to those of the frustrated XY model with only the phase as a dynamical variable.   

Modulated superfluid phases of lattice bosons in a non-abelian gauge field

We consider the two-component Bose-Hubbard model subject to non-abelian gauge fields that give rise to spin-orbit coupling. We obtain the phase diagram based on an extended mean field theory and find many exotic superfluid phases (polarized, striped, checkerboard). We characterize the superfluid phases by finding their collective excitations within random phase approximation (RPA) and discuss the possibility of novel topological defects.   

Bosons under an artificial staggered magnetic field in an optical ladder

We calculate the ground state properties of cold bosons in an frustrated optical ladder due to an artificial staggered magnetic field. By investigating the momentum distribution of bosons via a Lanczos diagonalization method, we find the signature of the transition from the Meissner to vortex states as a function of the staggering strength of the field. Various states with different frustrations are discussed.   

Chiral Mott insulator of kinetically frustrated bosons

We study the phase diagram of the fully frustrated Bose Hubbard (FFBH) model - the presence of a $\pi$-flux through each plaquette leads to kinetic frustration for the bosons making this a nontrivial model of quantum frustration. The FFBH model is equivalent to a model of frustrated quantum XY spins, or a fully frustrated Josephson junction array where one tunes the ratio of the charging energy to the Josephson coupling. Using Monte Carlo simulations and DMRG calculations on a ladder, we show that the ground state of this model is, at intermediate correlations, a Chiral Mott insulator which supports staggered loop currents. We characterize this Mott phase as a vortex supersolid or an exciton condensate and discuss experimental observables and generalizations.   

Mean Field Dynamics of Spin-Orbit Coupled Bose-Einstein Condensates

We derive the mean-field Gross-Pitaevskii equation for spin-orbit coupled Bose-Einstein conden-sates by taking account that the pseudospin states of atoms are superpositions of the hyperfine states with different scattering lengths. The ground state phases of the condensate in a harmonic trap are obtained numerically in various parameter regions. We find a new oscillation period in the center of mass motion of the condensate subject to a sudden shift of the harmonic trap. The oscillation period is dependent on the direction of the shift of the harmonic trap, linearly proportional to the spin-orbit coupling strength, and independent on the interaction strength.   

Rotation of supersolids in cold atomic condensates

In the framework of Gross Pitaevskii equation, with non-local interaction, we study the formation of Supersolid phase and the effect of rotation on such a system. The effect of rotation is to induce vortex patterns in such Supersolid phase, whose structures are in principle, different from the ordinary vortex in Superfluids. At sufficiently high rotation, these vortices arrange in the form of a lattice and thus, one has to take into account the interplay of two lattice structures, the Supersolid crystal lattice and the vortex lattice induced by rotation. We aim to study the elastic properties of such a system and compare it with the corresponding superfluid phase.   

Rashbons: Emergent bosonic fermion-pairs in synthetic non-Abelian gauge fields

In presence of a synthetic non-Abelian gauge field that produces a Rashba like spin-orbit interaction, a collection of weakly interacting fermions undergoes a crossover from a BCS ground state to a BEC ground state when the strength of the gauge field is increased [PRB {\bf 84}, 014512 (2011)]. The BEC that is obtained at large gauge coupling strengths is a condensate of tightly bound bosonic fermion-pairs called rashbons. This study reveals a new qualitative aspect that the rashbon state ceases to exist when the center of mass momentum of the fermions exceeds a critical value of the order of the gauge coupling strength. The study allows us to estimate the transition temperature of the rashbon BEC, and suggests a route to enhance the exponentially small transition temperature of the system with a fixed weak attraction to the order of the Fermi temperature by tuning the strength of the non-Abelian gauge field. The absence of the rashbon states at large momenta, suggests a regime in parameter space where the normal state of the system will be a dynamical mixture of uncondensed rashbons and unpaired helical fermions. Such a state should show many novel features including pseudogap physics.   

Evolution of the structure of vortex core across the BCS-BEC crossover induced by a synthetic non-Abelian gauge field

We study the evolution of the structure of vortex core of fermionic superfluids with increasing strength of a non-Abelian gauge field which induces a spin-orbit interaction. Using the Bogoliubov de-Gennes formulation, we study the spectrum of core states both in the BCS limit (small gauge coupling) and in the rashbon BEC limit where the superfluid is a condensate of rashbons. We show that the novel features of rashbon dispersion, the vanishing of the bound state at finite centre of mass momentum, result in a larger core region for vortices in the rashbon BEC.   

Session T5: Assembly of Atoms and Molecules in Adsorption Systems

Chirality Recognition and Transition Mechanism of prochiral Molecules on metals

The self-assemble behavior of prochiral species and the induced high-order chirality by 2D confinement on solid surfaces, including (1) QA16C molecules on a Au(111) surface and (2) molecule-metallic (TPA-Fe) complex on Cu(110) as well as their transferring process will be presented. Initial stages of a chiral phase transition in the molecule monolayer on metal surfaces were investigated by scanning tunneling microscopy (STM) at submolecular resolution. The prochiral QA16C molecules form a homochiral lamella phase at low coverages upon adsorption. A transition to a racemate lattice is observed with increasing coverage. Enantiomers of a homochiral lamella line become specifically substituted by opposite enantiomers such that a heterochiral structure evolves. A ``chiral replacement'' model is proposed for the transition: enantiomers replace QA molecules in enantiopure phase, leading to racemic one. Our findings are significant for the understanding and control of chiral phase transitions in related molecular systems like liquid crystals.   

A Library of the Nanoscale Self-Assembly of Amino Acids on Metal Surfaces

The investigation of the hierarchical self-assembly of amino acids on surfaces represents a unique test-bed for the origin of enantio-favoritism in biology and the transmission of chirality from single molecules to complete surface layers. These chiral systems, in particular the assembly of isoleucine and alanine on Cu(111), represent a direct link to the understanding of certain biological processes, specifically the preference for some amino acids to form alpha helices vs. beta-pleated sheets in the secondary structure of proteins. Low temperature, ultra-high vacuum, scanning tunneling microscopy (LT UHV-STM) is used to study the hierarchical self-assembly of different amino acids on a Cu(111) single crystal in an effort to build a library of their two-dimensional structure with molecular-scale resolution for enhanced protein and peptide studies. Both enantiopure and racemic structures are studied in order to elucidate how chirality can affect the self-assembly of the amino acids. In some cases, density functional theory (DFT) models can be used to confirm the experimental structure. The advent of such a library with fully resolved, two-dimensional structures at different molecular coverages would address some of the complex questions surrounding the preferential formation of alpha helices vs. beta-pleated sheets in proteins and lead to a better understanding of the key role played by these amino acids in protein sequencing.   

Surface Patterning of Benzene Carboxylic Acids on Graphite: Influence of structure, solvent, and concentration on molecular self-assembly

Scanning tunneling microscopy (STM) was used to investigate the molecular self-assembly of four different benzene carboxylic acid derivatives at the liquid/graphite interface: pyromellitic acid (1,2,4,5-benzenetetracarboxylic acid), trimellitic acid (1,2,4-benzenetricarboxylic acid), trimesic acid (1,3,5-benzenetricarboxylic acid), and 1,3,5-benzenetriacetic acid. A range of two dimensional networks are observed that depend sensitively on the number of carboxylic acids present, the nature of the solvent, and the solution concentration. We will describe our recent efforts to determine (a) the preferential two-dimensional structure(s) for each benzene carboxylic acid at the liquid/graphite interface, (b) the thermodynamic and kinetic factors influencing self-assembly (or lack thereof), (c) the role solvent plays in the assembly, (e) the effect of \textit{in situ} versus \textit{ex situ} dilution on surface packing density, and (f) the temporal evolution of the self-assembled monolayer. Results of computational analysis of analog molecules and model monolayer films will also be presented to aid assignment of network structures and to provide a qualitative picture of surface adsorption and network formation.   

Distinct Monolayer Structure of DH6T Films Grown on Untreated SiO$_{2}$

Due to the relatively weak interactions between neighboring molecules, thin films of vacuum evaporated organic semiconductors can have different properties in monolayer films as compared to several monolayer and bulk-like films. We have structurally characterized monolayer and several monolayer films of dihexyl-sexithiophene (DH6T) using grazing incidence diffraction and near-edge x-ray absorption fine structure spectroscopy (NEXAFS), and electrically characterized low-coverage FET structures during deposition. The structural data indicate a distinct phase of DH6T in the monolayer which has a distorted unit cell and a distinct NEXAFS signature compared to thicker films. The hole mobility of $\sim$0.8 cm$^{2}$/V-s is approximately an order of magnitude higher than previously reported for vacuum deposited thick films of DH6T on unmodified SiO$_{2}$ surfaces.   

Nucleation of C$_{60}$ on ultrathin SiO$_2$

We utilize scanning tunneling microscopy to characterize the nucleation, growth, and morphology of C$_{60}$ on ultrathin SiO$_2$ grown at room temperature. C$_{60}$ thin films are deposited in situ by physical vapor deposition with thicknesses varying from $<$0.05 to $\sim $1 ML. Island size and capture zone distributions are examined for a varied flux rate and substrate deposition temperature. The C$_{60}$ critical nucleus size is observed to change between monomers and dimers non-monotonically from 300 K to 500 K. Results will be discussed in terms of recent capture zone studies and analysis methods. Relation to device fabrication will be discussed. doi:10.1016/j.susc.2011.08.020   

Scanning Tunneling Spectroscopy of Self-assembled Nanoribbons of C$_{60}$-Diamantane Hybrid Molecules

As transistors approach the nanoscale, single molecules become viable alternatives for macroscopic devices. In terms of utilizing carbon, diamondoids -- single cages of the bulk diamond lattice -- have recently become available as the smallest units to explore these structures. We use low temperature scanning tunneling microscopy to perform electron mapping studies on self-assembled monolayers of novel hybrid molecules consisting of a single C$_{60}$ fused with the double diamond cage called diamantane. Unlike standard C$_{60}$ self-assembled monolayers, these hybrid molecules tend to form strips or nanoribbon assemblies as opposed to large-scale single sheets. We find spectroscopic differences between these hybrid molecules and the ``parent'' molecule C$_{60}$, and utilize spatial mapping to find electronic differences in the edge states of these ribbons. We discuss these results in terms of rectification and the potential of these hybrid molecules for molecular electronics.   

Pentacene pinwheels: chiral heterostructures between C$_{60}$ and pentacene

Pentacene and C$_{60}$ are archetypal molecules for optically active acceptor-donor molecular heterojunctions and for the study of self-assembly on surfaces. Using UHV STM, we demonstrate that these molecules - despite their high degree of symmetry - can self-assemble into {\it chiral} heterostructures when C$_{60}$ is deposited on a 'random-tiling' [1] of pentacene (Pn) on Cu(111). Two different chiral heterostructures with a central C$_{60}$ surrounded by 6 Pns in a 'pinwheel' formation are identified: one with interlocking Pns of mixed chirality and one with shared Pns of the same chirality. The latter is observed in single chirality domains that include hundreds of pinwheels. These complex structures are solved unambiguously through the analysis of the STM images and an understanding of Pn adsorption on Cu(111) [2]. Chiral light-absorbing acceptor-donor heterojunctions may provide a powerful platform for detecting and manipulating charge, spin, and optical polarization; we will discuss the electronic properties of these structures, and the prospect for studying the interaction of these types of systems with light using our laser-STM approach.\\[4pt] [1] J. A. Smerdon et al., Phys. Rev. B {\bf 84}, 165436 (2011).\\[0pt] [2] J. Lagoute et al, Phys. Rev. B {\bf 70}, 245415 (2004).   

Interaction of CO$_{2}$ with Oxygen Adatoms on Rutile TiO$_{2}$(110) Surface

On TiO$_{2}$(110), oxygen vacancies (V$_{O}$'s) act as the primary catalytic sites and as such they have been extensively investigated. However, only a few studies have been reported about the interactions of adsorbates with oxygen adatoms (O$_{a}$'s) that are created by O$_{2}$ dissociation in V$_{O}$'s. Here, we report a combined scanning tunneling microscopy (STM) / density functional theory (DFT) study of CO$_{2}$ on bare and O$_{a}$ covered TiO$_{2}$(110). STM images of TiO$_{2}$(110) surfaces obtained before and after in-situ dose at $\sim $50 K show that CO$_{2}$ molecules preferentially adsorb next to O$_{a}$'s forming CO$_{2}$/O$_{a}$ complexes. Temperature dependent studies further reveal that the CO$_{2}$ binding energy next to O$_{a}$'s is similar to that on V$_{O}$'s. Additional CO$_{2}$ molecules are found to diffuse rapidly along the Ti row between two CO$_{2}$/O$_{a}$ complexes. Due to the slow STM sampling rate the images display a time average of all CO$_{2}$ binding configurations on the Ti rows and reveal differences in the populations found on ideal Ti sites and Ti sites next to V$_{O}$'s.   

Adsorption of CO$_{2}$ in porous MCM-41 and MCM-48 using small angle scattering

Adsorption of CO$_{2}$ onto the surface of nanopores in organic rich materials, such as shale and coals, is of great interest for understanding the processes associated with geological sequestration. These natural materials have complex pore structures which make the interpretation of experimental sorption measurements complicated. MCMs are synthetic materials with a well-defined regular porous structure that provides an ideal substrate to evaluate the models for the adsorption of gases (CO$_{2})$ into nanopores. Samples of MCM-41 and MCM-48 were synthesized at Indiana University and were characterized by nitrogen adsorption isotherms and Small Angle X-ray Scattering (SAXS). SANS studies were carried out on MCMs with different pore sizes as a function of pore filling and the results are interpreted in terms of layer growth models.   

Self-Assembly of Metal Phthalocyanine on Silicon Studied by Scanning Probe Microscopy

Integration of molecular electronics into modern electronics requires an improved understanding and control of hetero-interfaces between organic molecules and semiconductor surfaces. Supramolecular assembly provides flexibility in building up complex and functional materials with nanometer scale precision over large surface areas. To study behavior at the hetero-interface, we perform supramolecular assembly of Zinc Phthalocyanine (ZnPc) on deactivated Si(111)B $\surd $3x$\surd $3 and on Si(111) 7x7. Using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) methods both the morphology and electronic structures of the self-assembled monolayer are investigated. Molecule-molecule and molecule-substrate interactions will be discussed.   

Decomposition of NH$_{3}$ and H$_{2}$ on ZrB$_{2}$ (0001) surface

Group III nitride semiconductors (AlN, GaN, InN, and their alloys) are important materials for applications in solid-state lighting, optoelectronics, and photovoltaics. However, the lack of lattice--matched substrates for their growth results in less than optimal material quality. In the last decade, zirconium diboride (ZrB$_{2})$ has been demonstrated as a promising substrate for GaN growth because of its similar lattice constant and thermal expansion properties when compared to the nitride. Moreover, the high electrical conductivity of ZrB$_{2}$ makes it desirable for many GaN-based device applications. In this talk, we present results of density functional theory calculations for the reactivity of the ZrB$_{2}$(0001) surface towards the N precursor, NH$_{3}$, and the carrier gas, H$_{2}$, commonly used in metal organic chemical vapor deposition and molecular beam epitaxy of nitrides. Two different terminations of ZrB$_{2}$(0001) surface, the Zr and B terminations, are considered and assessed in terms of their catalytic properties toward NH$_{3}$ and H$_{2}$ decomposition. The theoretical results are analyzed in connection with our recent XPS and RAIRS measurements.   

Morphology of monolayer films on quasicrystalline surfaces from the phase field crystal model

We present a computational study of the morphology of adsorbed monolayers on quasicrystalline surfaces with five- and seven-fold symmetry. The Phase Field Crystal model is employed to first simulate the growth of the quasicrystal surfaces and a two-dimensional film is then coupled elastically to the substrate. We find several different pseudomorphic phases for different types of surfaces and monolayer/substrate interactions, and quantify them by computing local order parameters. In agreement with recent experiments using colloids in quasiperiodic light fields, we find that the formation of quasicrystalline order is greatly inhibited on the seven-fold surfaces.   

Depolarization and bonding in quasi-one-dimensional Na structures on Cu(001)

The formation of quasi-one-dimensional (Q1D) $p(n\times2)$-Na/Cu(001) structures is addressed by density-functional theory investigations for adsorbate coverage from low to the saturation one. A general dependence of the dipole moment on the given configuration is deduced by extending that for uniform distributions, and is greatly affecting the energetics of the Na overlayer. Larger stability for Q1D arrangements aligned along $[110]$ and $[1\overline{1}0]$ holds at coverage larger than $0.2$~ML, in agreement with low-temperature He scattering experiments, and can be explained by a reduced dipole-dipole repulsion for the $p(4\times2)$ with respect to hex-like distributions. Interatomic bonding charge displacements along zig-zag rows of Na atoms further support the Q1D structure and contribute significantly to the surface corrugation as seen by the He probe.   

Adsorption of In atoms on In/Si(111)-8$\times $2 studied by variable-temperature STM

We have investigated adsorption of In atoms on In/Si(111) surface by using variable-temperature scanning tunneling microscope. At room temperature, the adsorbed In atoms on 4$\times $1 are invisible due to its high mobility on a 4$\times $1 phase. As the temperature decreases below the phase transition temperature, additional In atoms begin to appear being fixed on a 8$\times $2 phase. The In atoms are mostly adsorbed as an isolated atoms (monomers) and paired ones (dimers) on In chains. The adsorbed In atom induces a local phase-flipping in the vicinity, resulting in a phase shift along the chain direction. Occasional hopping of isolated In atoms along the chain direction are observable at 80K. The hopping occurs preferentially in the direction of the local phase-flipping side. Formation of dimers in relation to the preferential hopping direction will be discussed   

Session T6: Focus Session: Graphene Devices - Spin, Charge, and Superconductivity

Spin Relaxation and Spin Transport in Graphene

In this talk we are going to present our theoretical investigations on spin dynamics of graphene under various conditions based on a fully microscopic kinetic-spin-Bloch-equation approach [1]. We manage to nail down the solo spin relaxation mechanism of graphene in measurements from two leading groups, one in US and one in the Netherland. Many novel effects of the electron-electron Coulomb interaction on spin relaxation in graphene are addressed. Our theory can have nice agreement with experimental data.\\[4pt] [1] M. W. Wu, J. H. Jiang, and M. Q. Weng, ``Spin dynamics in semiconductors,'' Phys. Rep. \textbf{493}, 61 (2010).   

Spin and charge transport in high-mobility suspended graphene

Recent developments in graphene device fabrication techniques have made it possible to study the intrinsic properties of graphene by removing the substrate and making it suspended. Here we report electronic spin and charge transport measurements in high-mobility (over 70 000 cm$^{2}$/Vs) suspended graphene devices. To achieve this high quality we apply a large DC current density to heat the graphene flake, removing contaminations. We show that using the current annealing technique it is possible to produce ballistic nanoconstrictions, where quantized conductance at zero magnetic field is observed [N. Tombros et al., Nat. Phys. 7, 697 (2011)]. Studying the evolution of the position of the conductance plateaus in magnetic field we determine the width of the constriction. Spin transport measurements using ferromagnetic electrodes were also performed in our suspended graphene devices [M.H.D. Guimar\~{a}es et al., in preparation]. Analyzing non-local Hanle precession measurements we extract the spin relaxation time and the spin diffusion constant as a function of the charge carrier density. Combining our measurements with computer simulations we show that the measured spin relaxation times are limited by the non-cleaned regions of the device.   

Conductance Quantization in Graphene Nanoconstrictions

We present measurements of conductance quantization in a narrow Graphene constriction, of approximate width 200nm. Graphene is exfoliated on top of a Silicon Dioxide, and is not suspended. In high mobility samples ($>$10000cm$^{2}$V$^{-1}$s$^{-1})$ , we observe pinch-off at the Diract point, with a resistance at 4.2K of $\sim $ 40k$\Omega $. As a function of gate voltage at zero magnetic field, the conductance displays a few plateaus with the quantized value close to G$_{0}$=2e$^{2}$/h, indicating valley degeneracy splitting. At high carrier density ($>$5x10$^{12}$/cm$^{2})$ in a weak magnetic field, conductance exhibits ~strong beating in the Shubnikov-de Haas oscillations, which is also attributed to the valley splitting, analogous the Rashba interaction beats observed in the Shubnikov-de Haas oscillations in semiconducting quantum wells. In the Quantum Hall regime, the conductance of the constriction has quantized values nG$_{0}$, ..,. In comparison, measurements in the leads of the constriction display normal graphene behavior without the valley splitting.   

Chiral orbital current and anomalous magnetic moment in gapped graphene

We present a low-energy effective theory to describe chiral orbital current and anomalous magnetic moment in graphene monolayer and multilayers with band gap. We show that an electronic state of general Bloch system may intrinsically contain a quantum mechanical current circulation due to interband matrix elements. In gapped graphene, the current circulation is opposite between different valleys (K,K'), and the corresponding magnetic moment accounts for valley splitting of Landau levels. In gapped bilayer and ABC-stacked multilayer graphenes, in particular, the valley-dependent magnetic moment causes a huge paramagnetism at low energy, and a full valley polarization is possible up to relatively high electron density. The formulation also applies to gapped surface states of three-dimensional topological insulator, where the chiral orbital current is related to the magneto-electric response of the system.   

Quantum coherence versus dephasing effects in the giant spin Hall current and nonlocal voltage in magnetotransport through multiterminal graphene bridges

Motivated by the recent experiments [D. A. Abanin {\em et al.}, Science {\bf 323}, 328 (2011)] probing magnetotransport near the Dirac point in six-terminal graphene bridges from low to room temperature, we develop a nonequilibrium Green function (NEGF) theory of this phenomena. In the quantum-coherent regime, we find giant spin Hall (SH) conductance in four-terminal bridges, where the SH current is pure only at the Dirac point (DP), as well as the nonlocal voltage at a remote location in six-terminal bridges where the direct and inverse SH effect operate at the same time. The momentum-relaxing dephasing reduces their values at the DP by two orders of magnitude while washing out features away from the DP. Our theory is based on the linearized version of the Meir-Wingreen formula applied to multiterminal devices where dephasing is introduced through the self-energy within the active region of the bridge and currents and voltages are connected via generalized matrix of conductance coefficients.   

Magneto-transport studies of hydrogenated graphene

We study the magnetoresistance of hydrogenated graphene devices on a SiO$_{2}$ substrate. A large negative magnetoresistance of up to 30{\%} in a field of 2.5T is observed at low temperatures and at the film's charge neutrality point without any sign of saturation. A detailed analysis of the gate voltage dependence demonstrates a suppression of the large, negative magnetoresistance, which appears to be driven by a crossover from strong localization at low carrier concentrations to weak localization at higher carrier concentrations. Evidence of electron-hole symmetry breaking is found in the magnetic field traces at low temperature.   

In-plane magnetotransport in gapped bilayer graphene

The tunability of the band gap in bilayer graphene using a perpendicular electric field makes this material a promising candidate for future carbon electronics.\footnote{J. B. Oostinga et al., \emph{ Nat. Mat.}, \textbf{7}, 151 (2007) Y. Zhang et al., \emph{Nature}, \textbf{459}, 820 (2009)} Recent studies show that the residual conductivity at low temperature in the gapped state with zero total carrier density is a result of hopping transport.\footnote{T. Taychatanapat and P. Jarillo-Herrero, \emph{Phys. Rev. Lett.}, \textbf{105}, 166601, (2010)} We have studied the transport in this regime as a function of an in-plane magnetic field. We find a strikingly strong positive magnetoresistance that leads to a increase of the resistance by an order of magnitude at 10 Teslas in-plane magnetic field compared to the value at 0 T. The temperature dependence of the resistance is well described by variable range hopping transport for all magnetic field values, and suggests that the hopping range is strongly dependent on the in-plane magnetic field.   

Direct measurements of the current-phase relation in graphene Josephson junctions

The current-phase relation (CPR) of a Josephson junction can provide key information about the microscopic processes and symmetries that influence the supercurrent. In this talk, we present CPR results on Josephson junctions containing single-layer graphene as a weak link. The measurements are based on a phase-sensitive SQUID technique in which we determine the supercurrent amplitude and phase as a function of both temperature and electrostatic doping (gate voltage). We present CPR measurements of narrow junctions (5 - 12 $\mu$m) in the diffusive regime spanning the temperature range of 25 - 800 mK. We compare these data with previous CPR measurements on wide junctions in the temperature range of 800 - 900 mK.   

Anomalous supercurrent switching in graphene under proximity e

We report a study of hysteretic current-voltage characteristics in superconductor-graphene-superconductor (SGS) junctions. The stochastic nature of the phase slips is characterized by measuring the distribution of the switching currents. We find that in SGS junctions the dispersion of the switching current scales with temperature as $\sigma_I\propto T^{\alpha_G}$ with $\alpha_G\approx 1/3$. This observation is in sharp contrast with the known Josephson junction behavior where $\sigma_I\propto T^{\alpha_J}$ with $\alpha_J=2/3$. We propose an explanation using a modified version of Kurkijarvi's theory for the flux stability in rf-SQUID and attribute this anomalous effect to the temperature dependence of the critical current which persists down to low temperatures.   

Gate Tuning of Different Phase-Particle Escape Regimes in Graphene-Based Josephson Junctions

Graphene-based Josephson junctions (GJJs) provide a unique system to investigate superconducting proximity effect with in-situ tunable Josephson coupling strength. While the phase-coherent behaviors of a GJJ under a magnetic field and microwave irradiation have been observed previously\footnote{H. B. Heersche et al., Nature 446, 56 (2007); D. Jeong et al. Phys. Rev. B 83, 094503 (2011).}, we investigated the stochastic switching behavior of the supercurrent in this system. Here, we present the observation of the three different escaping regimes for a phase particle from a washboard potential of the GJJ; macroscopic quantum tunneling (MQT), thermal activation (TA), and phase diffusion (PD).\footnote{G.-H. Lee et al., Phys. Rev. Lett. 107, 146605 (2011).} The crossover temperature ($T^*_{MQT}$) between the classical to quantum regime can be controlled by the gate voltage, implying that discrete energy levels of a phase particle are also gate-tunable. Moreover, direct observation of energy level quantization (ELQ) by microwave spectroscopy shows the consistent gate dependence of $T^*_{MQT}$. A new class of hybrid quantum devices such as a gate-tunable phase qubit is potentially realized by utilizing the MQT and ELQ behavior of the GJJs.   

Tunable resistance anomaly in graphene-superconductor hybrid structure

Junctions between superconductors and normal metals often exhibit a resistance anomaly: near the superconducting transition temperature, the resistance increases above the normal-state value. The magnitude of the excess resistance varies over a wide range, decreases in a magnetic field and can depend on the driving current and the history of thermal cycling. Several physical mechanisms have been proposed to explain the origin of the excess resistance, including the fluctuation-induced resistive state, nonequilibrium quasiparticle charge imbalance around NS boundary or phase-slip centers. Here we present an electronic transport study of superconductor-graphene hybrid structures that show a large resistance anomaly which survives even in presence of a relatively large magnetic field. We will show that, by changing the graphene resistance, we can tune the magnitude and position of the resistance peak and will examine the applicability of existing models to explain our results.   

Session T7: Focus Session: Computational Design of Materials: Electronic Structure Methods for Materials - Faster and More Accurate

How accurate is Density Functional Theory in Predicting Reaction Energies Relevant to Phase Stability?

Density Functional Theory (DFT) computations can be used to build computational phase diagrams that are used to understand the stability of known phases but also to assess the stability of novel, predicted compounds. The quality and predictive power of those phase diagrams rely on the accuracy of DFT in modeling reaction energies and we will present in this talk the results of a large scale comparison between experimentally measured and DFT computed reaction energies. For starters, we will show that only certain reaction energies are directly relevant to phase stability of multicomponent systems and that very often those reaction energies are not the commonly studied reactions from the elements. Using data from different experimental thermochemical tables and DFT high-throughput computing, we will present the results of a statistical study based on more than 130 reaction energies relevant to phase stability and from binary oxides to ternary oxides. We will show that the typical error are around 30 meV/at and therefore an order of magnitude lower than the errors in reaction energies from the elements. Finally, we will discuss the broad implications of our results on the evaluation of ab initio phase diagrams and on the computational prediction of new solid phases.   

Correcting Density Functional Theory for Accurate Predictions of Compound Enthalpies of Formation:Fitted elemental-phase Reference Energies (FERE)

The first step in the Inverse Design of materials is the assessment of their thermodynamic stability and the needed growth conditions. The compound enthalpy of formation ($\Delta \mbox{H}_f$) is a quantity that provides these information. However, standard ab-initio approaches are known for their large errors in calculating $\Delta \mbox{H}_f$ of semiconducting and insulating compounds. In this talk I will present an approach, based on GGA+U total energies for compounds and fitted elemental-phase reference energies (FERE), that corrects GGA+U for the incomplete error cancellation between compound total energies and those of the pure elements, thereby resulting in $\Delta \mbox{H}_f$ values for insulating and semiconducting solids calculated with chemical accuracy. The FERE for 50 chemical elements we fit to a set of 252 measured $\Delta \mbox{H}_f$ of binary compounds (pnictides, chalcogenides and halides) and show accurate predictions also when applied to ternary compounds. I will discuss the application of the FERE approach in predicting new compounds, assess the accuracy of such predictions as well as comment on experimental efforts of our collaborators in growing some of the predicted materials.   

Correction to DFT Interaction Energies by an Empirical Dispersion Term Valid for a Range of Intermolecular Distances

The computation of intermolecular interaction energies via commonly used density functionals is hindered by their inaccurate inclusion of medium and long range dispersion interactions. Computation of inter- and intra-molecule interaction energies as well as computational design of (bio)materials, requires a fairly accurate yet not overly expensive methodology. It is also desirable to compute intermolecular energies not only at their equilibrium (lowest energy) configurations but also over a range of distances. We present a method to compute intermolecular interaction energies by including an empirical correction for dispersion which is valid over a range of intermolecular distances. This is achieved by optimizing parameters that moderate the empirical correction by explicit comparison of density functional (GGA) energies with distance-dependent (DD) reference values obtained at the CCSD(T)/CBS limit. The resulting GGA-DD method yields interaction energies with an accuracy generally better than 1 kcal/mol for different types of noncovalent complexes, over a range of intermolecular distances and interaction strengths, relative to the expensive CCSD(T)/CBS standard   

Accurate predictions of biomolecular interactions using density functional theory based semi-empirical alchemical derivatives in chemical compound space

A small but relevant sub-set of chemical compound space is explored in terms of biomolecular interaction energies, and using analytical derivatives. When transmutating any two iso-electronic ligands their intermolecular energies are not necessarily monotonic functions, consequently the corresponding Hellmann-Feynman derivatives can fail to predict the right trends. Semi-empirical corrections, effectively linearizing the intermolecular energy in the interpolation parameter, promise to drastically improve the predictive power of these first order derivatives. For various biomolecules, including ellipticine interacting with DNA, we show that these semi-empirical derivatives yield predictions superior to alternative prediction schemes that are additive and derivative-free. As such, new evidence is presented in support of the conclusion that quantitative estimates of relevant properties of new molecules can be made without additional self-consistency calculations.   

Preliminary results in data mining for materials

In recent years, materials scientists have started exploiting data mining techniques, i.e., methods for extracting meaningful information and patterns from data, for the discovery and design of materials. One of the grand challenges in this methodology is to establish correlations and intrinsic features in materials database in order to facilitate the extraction of useful information that can be exploited to discover new hypothetical materials. Using an atomic properties database of 110 elements, obtained from quantum mechanical calculations and several macroscopic properties database of binary compounds, we explored several sample data mining techniques to study the correlations among them with the goal of predicting macroscopic properties from knowledge of the atomic constituents. In this talk, preliminary results of such efforts will be presented to demonstrate how simple data mining can be applied in materials science and what they can achieve. These preliminary results indicate a good potential for data mining applications in materials science.   

Expediting Solutions for the Electronic Structure of Large Systems: A Spectrum Slicing Algorithm

Solving the Kohn-Sham equation requires computing a set of low lying eigenpairs. The standard methods for computing such eigenpairs require two procedures: (a) maintaining the orthogonality of an approximation space, and (b) forming approximate eigenpairs with the Rayliegh-Ritz method. These two procedures scale cubically with the number of desired eigenpairs. We present a method, applicable to {\it any} large Hermitian eigenproblem, by which the spectrum is partitioned among distinct groups of processors. This ``divide and conquer'' approach serves as a parallelization scheme at the level of the solver, making it compatible with existing schemes that parallelize at a physical level, {\it e.g.}, {\bf k}-points or symmetric representations, and at the level of primitive operations, matrix-vector multiplication. In addition, among all processor sets, the size of any approximation subspace is reduced, thereby reducing the cost of orthogonalization and the Rayleigh-Ritz method. We will explain the key aspects of the algorithm that give reliability, and demonstrate the accuracy of the algorithm by computing the electronic structure of a core-shell nanocrystal and a DNA segment. Overall scaling and the utility of the method for a wide variety of applications will be discussed.   

Density Functional Theory using Multiresolution Analysis with MADNESS

We describe the first implementation of the all-electron Kohn-Sham density functional periodic solver (DFT) using multi-wavelets and fast integral equations using MADNESS (multiresolution adaptive numerical environment for scientific simulation; http://code.google.com/p/m-a-d-n-e-s-s). The multiresolution nature of a multi-wavelet basis allows for fast computation with guaranteed precision. By reformulating the Kohn-Sham eigenvalue equation into the Lippmann-Schwinger equation, we can avoid using the derivative operator which allows better control of overall precision for the all-electron problem. Other highlights include the development of periodic integral operators with low-rank separation, an adaptable model potential for the nuclear potential, and an implementation for Hartree-Fock exchange.   

GPU speedup of the plane wave pseudopotential density functional theory calculations

Plane wave (PW) pseudopotential density functional theory (DFT) calculation is the most widely used method for computational design of new materials. In this talk, we will present our recent work in using the graphics processing unit (GPU) to accelerate the PW-DFT calculations. Compared with the pure CPU calculation, the GPU machine with CUDA coding can speed up the calculation by 20 times for systems with a few hundred atoms, while still being able to scale to hundreds of CPU/GPU units. However, to reach this speedup, some algorithm changes are necessary. We will discuss these algorithm changes, and various computational kernels in a PW-DFT code, and their speedups in the GPU code. These include the FFT, the nonlocal projector, the orthogonalization and the diagonalization. We will also discuss the computational times for MPI communication, CPU/GPU memory copy, and floating point operation. We will present the hardware and library requirement to further speed up the calculations. Finally, the implication of the GPU speed up for new material design will be discussed.   

Linear-scaling DFT+U applied to hole localization and Friedel oscillations in very dilute (Ga,Mn)As

System-size and strong electronic correlation are two factors inhibiting the routine first-principles simulation of transition-metal doped nanostructures. Tackling these issues simultaneously, we have developed a linear-scaling implementation of the DFT+$U$ method within the ONETEP code,\footnote{Hine, Haynes, Mostofi, Skylaris \& Payne, {\it Comp. Phys. Commun.,} {\bf 180}, 1041 (2009).} demonstrating scaling upto $7,000$ atoms. Our implementation allows for nonorthogonal projectors,\footnote{O'Regan, Payne \& Mostofi, {\it PRB} {\bf 83}, 245124 (2011).} which may be self-consistently optimized.\footnote{O'Regan, Hine, Payne \& Mostofi, {\it PRB} {\bf 82}, 081102(R) (2010).} We apply our approach to the prototypical dilute magnetic semiconductor (Ga,Mn)As. The ferromagnetic interaction between distant localized magnetic moments in (Ga,Mn)As is mediated by defect-induced holes, whose long-range character is critical. Our large-scale calculations on $1,728$ atom super-cells enable us to study the localization and symmetry of the magnetization and hole in the very dilute ($0.1\%$) limit, and to analyze the long-range Friedel oscillations.   

G0W0 implementation using Lanczos algorithm and Sternheimer equation

The G0W0 approach is an accurate method to give a physical meaning to the eigenvalues obtained in adensity-functional theory (DFT) calculation.However, the calculation of such corrections with plane wave codes is currently prohibitive for systems with more than a few hundreds of electrons. What limits calculations to this system size is the need in current implementations to invert the dielectric matrix and the need to carry out summations over conduction bands. This talk presents a strategy to avoid both of these bottlenecks. In traditional plane wave implementations of G0W0, the dielectric matrix is expressed in a plane wave basis, which needs to be relatively big to properly describe the matrix. Here, we will explain how a Lanczos basis can be generated to substantially reduce the size of the matrix. Also, the number of conduction bands needed to reach convergence in the summations is usually an order of magnitude larger than the number of valence bands. Here, the calculation of the conduction states is avoided by reformulating the summations into linear equation problems (Sternheimer equations), which also substantially reduces the computation time. Preliminary results will be presented.   

Dynamical Cluster Approximation: Cluster Extension of CPA for Disordered System

The dynamical mean-field approximation (DMFA) or the coherent potential approximation (CPA) provides a convenient and effective method for studying disordered systems; however, non-local short range correlations of the disorder potential are neglected leading to a self-consistent single-site approximation. We combine the recently developed first principles method of Wei Ku and co-workers for the simulation of disordered systems with the dynamical cluster approximation (DCA) to develop a highly efficient means to treat disordered systems. We solve this model system using the DCA, which systematically incorporates short-range nonlocal correlations to the CPA. We apply this method to a number of model systems to illustrate where the DCA or a finite size simulation is more appropriate.   

Analyzing electron-electron correlations at nanoscale: a DFT+DMFT code for nanosystems

We propose a DFT+DMFT approach to study electron-electron correlation effects in nanosized systems containing atoms with localized d- and f-electron states. For the purpose we have developed a nanoDFT+DMFT code which allows one to study the properties of systems containing up to several hundred atoms. The system geometry is first optimized using ab-initio electron structure calculations based on density-functional theory (DFT), and correlation effects are analyzed employing nonhomogeneous Dynamical Mean-Field Theory (DMFT) calculations with the iterated perturbation theory (IPT) approximation for the quantum impurity solver. To test the formalism we have evaluated the magnetic properties of several transition metal atom clusters and compared the results with those obtained from the exact diagonalization method (a few-atom clusters) and available experimental data (2-19 atom clusters). In particular, we find that the IPT-DMFT gives magnetic moments much closer to experimental values as compared to DFT calculations. We discuss possible extensions of the approach including application of more accurate quantum impurity solvers, such as Hirsch-Fye and Continuous-Time Quantum Monte Carlo. The application of the methodology to the nonequilibrium case is in progress.   

Using Machine Learning to Accelerate Complex Atomic Structure Elucidation

Workers in various scientific disciplines seek to develop chemical models for extended and molecular systems. The modeling process revolves around the gradual refinement of model assumptions, through comparison of experimental and computational results. Solid state Nuclear Magnetic Resonance (NMR) is one such experimental technique, providing great insight into chemical order over Angstrom length scales. However, interpretation of spectra for complex materials is difficult, often requiring intensive simulations. Similarly, working forward from the model in order to produce experimental quantities via ab initio is computationally demanding. The work involved in these two significant steps, compounded by the need to iterate back and forth, drastically slows the discovery process for new materials. There is thus great motivation for the derivation of structural models directly from complex experimental data, the subject of this work. Using solid state NMR experimental datasets, in conjunction with ab initio calculations of measurable NMR parameters, a network of machine learning kernels are trained to rapidly yield structural details, on the basis of input NMR spectra. Results for an environmentally relevant material will be presented, and directions for future work.   

Session T8: Focus Session: Helical Phases and Skyrmions

Spin waves in a skyrmion crystal

We derive the spectrum of low-frequency spin waves in skyrmion crystals observed recently in noncentrosymmetric ferromagnets [1-4]. We treat the skyrmion crystal as a superposition of three helices whose wavevectors form an equilateral triangle [1]. The low-frequency spin waves are Goldstone modes associated with displacements of skyrmions. Their dispersion is determined by the elastic properties of the skyrmion crystal and by the kinetic terms of the effective Lagrangian, which include both kinetic energy and a Berry phase term reflecting a non-trivial topology of magnetization. The Berry phase term acts like an effective magnetic field, mixing longitudinal and transverse vibrations into a gapped cyclotron mode and a twist wave with a quadratic dispersion [5]. \\[4pt][1] Muehlbauer, Binz, Jonietz, Pfleiderer, Rosch, Neubauer, Georgii, Boeni, Science \textbf{323}, 915 (2009). \\[0pt][2] Muenzer, Neubauer, Adams, Muehlbauer, Franz, Jonietz, Georgii, et al., Phys. Rev. B \textbf{81}, 041203 (2010). \\[0pt][3] Yu, Onose, Kanazawa, Park, Han, Matsui, Nagaosa, Tokura, Nature \textbf{465}, 901 (2010). \\[0pt][4] Yu, Kanazawa, Onose, Kimoto, Zhang, Ishiwata, Matsui, Tokura, Nat. Mater. \textbf{10}, 106 (2011). \\[0pt][5] Petrova, Tchernyshyov, arXiv:1109.4990v2 [cond-mat.mes-hall]   

Skyrmion contribution to thermopower of MnSi

Skyrmions have recently been theoretically predicted [1] and experimentally observed [2] in MnSi. To identify whether skyrmions contribute to thermoelectric transport, we present a detailed map of the temperature, pressure and magnetic field behavior of thermopower $S$ in MnSi. $S/T(p,T)$ confirms the established phase diagram with Fermi liquid, non-Fermi liquid and partial order phases. In the high pressure non-Fermi liquid phase, $S(T)$ increases in the vicinity of the boundary with the Fermi liquid phase, at critical pressure $p_c\sim14.5$ kbar. This may be linked to the scattering of conduction electrons on fluctuating amorphous skyrmions [1]. On the contrary, the thermopower decreases when an ordered lattice of skyrmions is established in the magnetic field. A small suppression of $S(T)$ is observed in a narrow region, for 27 K $ [Preview Abstract]

Quantum order-by-disorder near criticality and the secret of the partially ordered phase of MnSi

The vicinity of quantum phase transitions has proven fertile ground in the search for new quantum phases. We propose a physically motivated and unifying description of the phase reconstruction near metallic quantum-critical points using the idea of quantum order-by-disorder. Certain deformations of the Fermi surface associated with the onset of competing order enhance the phase space available for low-energy, particle-hole fluctuations and self-consistently lower the free energy. Applying the notion of quantum order-by-disorder to the itinerant helimagnet MnSi, we show that near to the quantum critical point, fluctuations lead to an increase of the spiral ordering wave vector and a reorientation away from the lattice favoured directions. The magnetic ordering pattern in this fluctuation-driven phase is found to be in excellent agreement with the neutron scattering data in the partially ordered phase of MnSi.   

Density-functional electronic structure and the origin of the Dzyaloshinskii-Moriya spin interaction in MnSi

The metallic helimagnet MnSi has been found to exhibit skyrmionic spin textures when subjected to magnetic fields at low temperatures. The Dzyaloshinskii-Moriya (DM) interaction plays a key role in stabilizing the skyrmions, which arises from the anisotropic part of the super-exchange coupling and is of the form $\vec{D}\cdot(\vec{S_i}\times\vec{S_j})$. The constant $\vec{D}$ depends on the strength of spin-orbit interaction of Mn $d$ states and the orbital mixing induced by the distortion of MnSi$_6$ octahedra from the centrosymmetric rock salt phase. Using density functional theory based electronic structure calculations and symmetry analysis, we study the nature of the electronic ground state and the origin of the DM interaction in the B20 phase of MnSi. The ground state in the undistorted phase corresponds to $d^6$ configuration at Mn and $p^2$ at Si sites. The distortion reduces bandwidths and intermixes the ground state with the excited states, leading to a significant DM spin-orbit interaction.   

Criticality Induced First-Order Phase Transition in Dzyaloshinskii-Moriya Helimagnets

Almost two centuries of research on phase transitions have repeatedly highlighted the importance of critical phenomena. One fascinating implication of critical phenomena is that critical fluctuations may drive the associated phase transition first order if symmetry allows them to assume enough phase space. As discussed by Brazovski, this is in particular the case if critical fluctuations become soft on a sphere in momentum space. By means of combined specific heat, magnetic susceptibility and neutron scattering measurements of the model helimagnet MnSi we show that this scenario is realized for the helimagnetic phase transition in Dzyaloshinskii-Moriya(DM) helimagnets with weak magnetic anisotropy. The remarkable agreement observed between experiment and theory clarifies the longstanding issue of the nature of the helimagnetic transition in MnSi, but more importantly, our calculations are entirely based on symmetry arguments, making this result relevant to DM helimagnets in general. This is in particular noteworthy in the light of a series of new discoveries that show that DM helimagnetism is at the heart of problems such as topological magnetism, multiferroics, and spintronics.   

Tricriticality and giant magneto-elasticity in CoMnSi

Tricritical magnets have previously facilitated the study of different critical phenomena and scaling laws by varying external parameters (pressure, field and temperature) instead of composition. We have studied tricritical magnets driven by interest in the enhanced magnetocaloric effects seen at the first order side of a tricritical point where hysteresis can be minimised. Here we describe the results of microcalorimetry, Hall probe imaging, dilatometry, magnetometry and neutron diffraction experiments and density functional calculations. We build a picture of the relation between structure and magnetism in CoMnSi and find a giant magneto-elasticity that underpins the evolution of first order behavior in this metamagnetic helical antiferromagnet [2]. We are then able to use density functional theory to predict new metamagnets based on this insight. These have been successfully synthesized [3]. \\[4pt] [1] K.G. Sandeman, Magnetics Technology International \textbf{1} 32 (2011).\\[0pt] [2] A. Barcza et al., Phys. Rev. Lett. \textbf{104} 247202 (2010).\\[0pt] [3] Z. Gercsi, K. Hono and K.G. Sandeman, Phys. Rev. B \textbf{83} 174403 (2011) and references therein.   

Hall effect of spin-chirality origin in a triangular-lattice helimagnet $\mbox{Fe}_{1.3} \mbox{Sb}$

We report on a topological Hall effect possibly induced by scalar spin chirality in a quasi-two-dimensional helimagnet$\mbox{Fe}_{1+x} \mbox{Sb}$. In the low-temperature region where the spins on interstitial-Fe (concentration $x\approx 0.3)$ intervening the $120^\circ $ spin-ordered triangular planes tend to freeze, a non-trivial component of Hall resistivity with opposite sign of the conventional anomalous Hall term is observed under magnetic field applied perpendicular to the triangular-lattice plane. The observed unconventional Hall effect is ascribed to the scalar spin chirality arising from the heptamer spin-clusters around the interstitial-Fe sites, which can be induced by the spin modulation by the Dzyaloshinsky-Moriya interaction.   

Vortex walls in helical magnets

The structure of domain walls determines to a large extent the properties of magnetic materials, in particular their hardness and switching behavior, it represents an essential ingredient of spintronics. In Bloch and Neel domain walls the magnetization rotates around a fixed axis in a one-dimensional magnetization profile. Surprisingly, domain walls in helical magnets, most relevant in multiferroics and metals, were never studied. We show that domain walls in helical magnets are fundamentally different from Bloch and Neel walls. They are generally two-dimensional patterns formed by a regular lattice of vortex singularities. Only at discrete exceptional orientations, domain walls are free of vortices, but still remain two-dimensional textures. In helical magnets with weak anisotropy the domain wall width and energy only weakly depend on the anisotropy, though domain wall does not exist without it. In conical phases vortices carry Berry phase flux resulting in the anomalous Hall effect. In multiferroics vortices are electrically charged allowing manipulating magnetic domain walls by the electric field. Our theory allows the interpretation of magnetic textures observed in helical magnetic structures.   

Spin scalar chiral ordering and hidden positive biquadratic interaction in frustrated Kondo lattice systems

Recently, noncoplanar spin configurations with spin scalar chirality have drawn considerable attention as an origin of the anomalous Hall effect. In this mechanism, itinerant electrons acquire an internal magnetic field according to the solid angle spanning three spins through the so-called Berry phase, which can result in the anomalous Hall effect. In order to explore such nontrivial magnetic states in spin-charge coupled systems, we investigate a ferromagnetic Kondo lattice model on a triangular lattice by variational and perturbative calculations. As a result, we find that a noncoplanar four-sublattice spin ordering emerges near 1/4 filling, in addition to the 3/4 filling reported in the previous study. This new phase is stabilized in a wider parameter region compared to the 3/4 filling phase [1]. We also find that a kinetic-driven positive biqaudratic interaction is critically enhanced and plays a crucial role on stabilizing a spin scalar chiral ordering near 1/4 filling. The origin of large positive biquadratic interaction is ascribed to the Fermi surface connection by the four sublattice ordering wave vectors, which we call the higher-order Kohn anomaly [2]. [1] Y. Akagi and Y. Motome, J. Phys. Soc. Jpn. 79 (2010) 083711. [2] Y. Akagi, M. Udagawa, and Y. Motome, submitted.   

First Principles Calculation of Helical Spin Order in Iron Perovskite SrFeO3 and BaFeO3

Motivated by recent discovery of ferromagnetism in cubic perovskite BaFeO3 under small magnetic field, we investigate spin order in BaFeO3 and isostructual SrFeO3 by a first principles calculation using local spin density approximation (LSDA). We find that on-site Coulomb interaction U is necessary for obtaining helical spin order consistent with experiments. SrFeO3 exhibits G-type helical order, while BaFeO3 exhibits the A-type with very small wave vector. The A-type order is stabilized by lattice expansion. Small energy difference between the A-type and ferromagnetic orders explains ferromagnetism under small field. The LSDA+U results are consistent with model calculation where negative charge-transfer energy in these compounds is explicitly taken into account.   

Investigation of the role of spin-texture on the Na0.46CoO2

We will present magnetotransport properties and their relationship to a possible chiral spin texture in ultra-thin Na$_{0.46}$CoO$_{2}$ devices in high magnetic fields. This composition exhibits a weakly insulating state, with a frustrated local spin texture, unique, among the hexagonal Na$_{x}$CoO$_{2}$ family. Previous a large large Hall effect was found for composition $x$=0.5 (M. Foo \textit{et al.}, Phys. Rev. Lett. 92, 247001 (2004)) and prior high-field studies (L. Balicas \textit{et al.}, Phys. Rev. Lett. 94, 236402 (2005).) have found the existence of a small Fermi surface in the system and a two-fold angular magnetoresistance. To date however, the Hall-conductivity has not been investigated in magnetic fields strong enough to suppress the charge-order, above 41~T. Herein, we investigate the role of local spin-texture (in the charge-ordered state) on the Hall conductance by measuring both bulk and devices with only several monolayers thick in strong magnetic fields. Our investigations under magnetic fields ($B<$60 T) show that the high resistivity charge-order region is suppressed with out-of-plane field at $B\sim $41 T with highly non-monotonic -\textit{$\rho $}$_{xy}$ with a maximum at $B\sim $27 T and rapidly decreases to zero. However, magnetization measurements show no significant features within measurement accuracy indicating that magnetization changes are small at the field-induced phase transition. Recent theoretical advances suggest that this compound exhibits a quantum Hall state coupled with spin chirality (I. Martin, C. D. Batista, Phys. Rev. Lett. 101, 156402 (2008)).   

Spin spiral state in hexagonal NiS

Previous nesting function calculations on NiS have found instabilities for the magnetic ordering vectors q=(2/3,2/3,0) and q=(1/2,2/9,1) suggesting that the magnetic structure of NiS is non- collinear which does not agree with the experimentally determined antiferromagnetic state. We investigated the electronic and magnetic structure of NiS by means of a full-potential linearized augmented plane wave method within the local spin density approximation plus the Hubbard parameter U. Our method is specially suitable to study noncollinear magnetism where the magne- tization density is allowed to vary in magnitude and direction continuously everywhere in space. Our results show that the ground state is metallic and that the antiferromagnetic state is almost degenerate with spin spirals along certain directions of the Brillouin zone.   

Incommensurate antiferromagnetism in GdSi

Rare earth magnets are interesting model systems to study correlated spin, orbital and lattice degrees of freedom. Here we present a study of the antiferromagnetism in single crystal GdSi, using high-resolution, x-ray magnetic diffraction techniques. Our results clearly show an incommensurate magnetic structure at 6.5 K, with a lattice distortion from orthorhombic to monoclinic accompanying the magnetic phase transition in a second order fashion. We discuss implication to the anisotropic susceptibility in lights of the detailed magnetic structure.   

Spin-Orbital Locking, Emergent Pseudo-Spin, and Magnetic order in Na$_2$IrO$_3$

The nature of magnetic order in the honeycomb lattice Iridate Na$_2$IrO$_3$ is explored by considering trigonal crystal field effect and spin-orbit coupling. An effective Hamiltonian is derived in terms of an emergent pseudo-spin-1/2, resulting from a spin-orbital locking, which is different from $j_{\rm eff}=1/2$ that is obtained when the spin-orbit coupling dominates. The resulting Hamiltonian is anisotropic and frustrated. Mean field theory suggests a ground state with 4-sublattice {\em zig-zag} magnetic order in the relevant parameter regime, in conformity with experiments. Various properties of the phase, the spin-wave spectrum and experimental consequences are discussed. Our approach contrasts with the recent proposal of a Heisenberg-Kitaev system for this material, and we point out the intrinsic difficulties with the latter approach for describing the magnetic properties of Na$_2$IrO$_3$.   

Magnetic order on a frustrated lattice due to orbital degrees of freedom in $R$O$_2$ hyperoxides

The alkali $R$O$_2$ hyperoxides ($R$=Rb,Cs,K) crystallize in a frustrated bct lattice. Nevertheless, all of the members of the family of alkali $R$O$_2$ hyperoxides have long range layered $C$-type antiferromagnetic ($C$-AF) order at low temperature. We show that including the almost degenerate $p$-orbital degrees of freedom in a realistic spin-orbital model can resolve this contradiction [1]. Although {\it a priori} the orbital degrees of freedom do not remove frustration in spin system, we show that the anomalously large interorbital hopping together with the orbital order induced by the lattice stabilize the $C$-AF order in this class of compounds, in agreement with generalized Goodenough-Kanamori rules formulated here. \\[4pt] [1] K. Wohlfeld, M. Daghofer, and A.M. Ole\'{s}, EPL \textbf{96}, 27001 (2011).   

Session T9: Focus Session: Magnetic Oxide Thin Films And Heterostructures - Interactions at Interfaces and in Superlattices

Upper limit to magnetism in LaAlO$_{3}$/SrTiO$_{3}$ heterostructures

In 2004 Ohtomo and Hwang reported unusually high conductivity in LaAlO$_{3}$ and SrTiO$_{3}$ bilayer samples. Since then, metallic conduction, superconductivity, magnetism, and coexistence of superconductivity and ferromagnetism have been attributed to LaAlO$_{3}$/SrTiO$_{3}$ interfaces. Very recently, two studies have reported large magnetic moments attributed to interfaces from measurement techniques that are unable to distinguish between interfacial and bulk magnetism. Consequently, it is imperative to perform magnetic measurements that by being intrinsically sensitive to interface magnetism are impervious to experimental artifacts suffered by bulk measurements. Using polarized neutron reflectometry, we measured the neutron spin dependent reflectivity from four LaAlO$_{3}$/SrTiO$_{3}$ superlattices. Our results indicate the upper limit for the magnetization averaged over the lateral dimensions of the sample induced by an 11 T magnetic field at 1.7 K is less than 2 G. SQUID magnetometry of the neutron superlattice samples sporadically finds an enhanced moment (consistent with past reports), possibly due to experimental artifacts. These observations set important restrictions on theories which imply a strongly enhanced magnetism at the interface between LaAlO$_{3}$ and SrTiO$_{3}$. Work performed in collaboration with N.W. Hengartner, S. Singh, M. Zhernenkov (LANL), F.Y. Bruno, J. Santamaria (Universidad Complutense de Madrid), A. Brinkman, M.J.A. Huijben, H. Molegraaf (MESA+ Institute for Nanotechnology), J. de la Venta and Ivan K. Schuller (UCSD). \\[4pt] Work supported by the Office of Basic Energy Science, U.S. Department of Energy, BES-DMS and DMR under grant DE FG03-87ER-45332. Work at UCM is supported by Consolider Ingenio CSD2009-00013 (IMAGINE), CAM S2009-MAT 1756 (PHAMA) and work at Twente is supported by the Foundation for Fundamental Research on Matter (FOM).   

Magnetotransport behavior in (LaNiO$_3$)$_n$/(LaMnO$_3$)$_2$ superlattices

Recent advances in the deposition of epitaxial complex oxides have enabled the fabrication of a wide range of materials structures with atomically abrupt interfaces, that are characterized by novel electronic and magnetic ground states. In particular, superlattices that combine the paramagnetic metal, LaNiO$_3$, with various band insulators, such as SrTiO$_3$ and LaAlO$_3$, have attracted considerable theoretical and experimental interest. In this work, (LaNiO$_3$)$_n$/(LaMnO$_3$)$_2$ ($2 \leq n \leq 5$) superlattices that combine LaNiO$_3$ with an antiferromagnetic insulator are prepared on (001) SrTiO$_3$ substrates using ozone-assisted oxide molecular beam epitaxy. The total superlattice thickness is fixed at $\sim$30 nm. X-ray reflectivity and x-ray diffraction reveal single-crystalline growth with interfacial and surface roughnesses of $\sim$0.2 nm and $\sim$0.5 nm, respectively. Electrical transport measurements carried out on superlattices with $n \leq 3$ show insulating behavior between 5 K and 300 K, while samples with $n$ = 4,5 are metallic with resistivity minima at 90 K and 30 K, respectively, below which we observe negative magnetoresistance. We discuss the role of charge transfer between LaNiO$_3$ and LaMnO$_3$ in understanding these results.   

Confinement induced metal-to-insulator transition in strained LaNiO$_3$/LaAlO$_3$ superlattices

Using density functional theory calculations including a Hubbard $U$ term we explore the effect of strain and confinement on the electronic ground state of superlattices containing the band insulator LaAlO$_3$ and the correlated metal LaNiO$_3$. Besides a suppression of holes at the apical oxygen, a central feature is the asymmetric response to strain in single unit cell superlattices: For tensile strain a band gap opens due to charge disproportionation at the Ni sites with two distinct magnetic moments of 1.45$\mu_{\rm B}$ and 0.71$\mu_{\rm B}$. Under compressive stain, charge disproportionation is nearly quenched and the band gap collapses due to overlap of $d_{3z^2-r^2}$ bands through a semimetallic state. This asymmetry in the electronic behavior is associated with the difference in octahedral distortions and rotations under tensile and compressive strain. The ligand hole density and the metallic state are quickly restored with increasing thickness of the (LaAlO$_3$)$_n $/(LaNiO$_3$)$_n$ superlattice from $n=1$ to $n=3$.   

Electronic structure, charge modulation, and orbital polarization of LaNiO3/SrTiO3 superlattice

First-principles density functional theory calculations have been performed to understand the detailed electronic structure for the various (m, n) combinations of (LaNiO3)m/(SrTiO3)n superlattices. Due to the strong covalency of Ni-O bonds, the valence bands are dominated by Ni-d character and the electronic structure is mainly affected by the local environment rather than the ionic potential. Heterostructuring-induced quantum states and the interaction between them leads to the charge redistribution around the Fermi level, which may be responsible for the charge modulation and metal-insulator transition observed in the related systems.   

Electronic, magnetic, and structural coupling across oxide interfaces

Many complex oxide materials exhibit a strong interplay between spin, charge, and lattice effects. This coupling leads to a variety of novel electronic and magnetic properties, including charge ordered and magnetic states, ``colossal'' magnetoresistance (CMR), and a range of electron transport behavior. The possibility of integrating these different kinds behavior with other types of functionalities has motivated the development of new, artificially structured complex oxide-based materials systems, such as composite multiferroic heterostructures. In certain cases, the atomic-scale interface of these structures can dominate the observed behavior, with new physical properties emerging. For example, in epitaxial ferromagnetic/ferroelectric heterostructures, it is possible to achieve large magnetoelectric coupling that is controlled directly by the charge degrees of freedom. We have studied this coupling using a variety of techniques, including magnetization, magneto-optic Kerr effect magnetometry, and x-ray absorption spectroscopy. In addition, structural distortions that arise exclusively at the interface can influence simultaneously the interfacial electronic transport and magnetic properties. Using high resolution synchrotron scattering, we have determined the interplay between new interfacial structural motifs and the resulting electronic and magnetic function at the interface.   

Ferroelectric control of magnetocrystalline anisotropy and orbital magnetism in thin-film Fe/BaTiO$_{3}$ heterostructures

Correlations between magnetocrystalline anisotropy energy (MAE), ferroelectric (FE) polarization, and orbital magnetic moment are studied for ferroelectric/ferromagnetic heterostructures consisting of barium titanate (BaTiO$_{3})$ and thin-film iron (Fe). Using first-principles calculations we investigated different geometries of the BaTiO$_{3}$/Fe system, in particular with 1, 3, and 5 monolayers of Fe with either a free vacuum surface or Cu as a capping layer. We show that there is a large MAE change ($\sim $20{\%}) upon switching of the polarization sign in the case of a vacuum layer, while the presence of Cu effectively removes the difference in MAE for opposite FE polarization directions in BaTiO$_{3}$. This is explained by analyzing the correlation between MAE and orbital magnetic moments for different geometries and opposite polarization directions, as well as the film thickness. We show that the magnetoelectric coupling between MAE and FE polarization is directly linked to the degree of the magnetoelectric coupling between orbital moment and FE polarization.   

Electron-mediated ferromagnetic behavior in CoO/Al:ZnO multilayers

(111)-oriented epitaxial CoO/Al-doped ZnO (AZO) multilayers show a ferromagnetic behavior up to room tempareture. Their magnetization exhibits an oscillatory behavior as a function of $(i)$ the number of Co layers in the insulating antiferromagnetic CoO, and \textit{(ii)} the thickness of the AZO layers. The ferromagnetism vanishes if AZO is replaced by intrinsic ZnO. This behavior can be explained by the existence of an RKKY-coupling, mediated by the free electrons of the non-magnetic AZO layers, between the uncompensated (111) ferromagnetic planes of insulating CoO when there is an odd number of planes in the layer. The oscillation period of the spontaneous magnetization as a function of the AZO layer thickness matches the Fermi wavevector calculated from the carrier concentration that was deduced from Hall effect measurements. The spin-polarization of the carriers in the AZO layer is confirmed via anomalous Hall effect.   

Towards Room Temperature Spin Filtering in Oxide Tunnel Junctions

Spin filtering, in which the magnetic tunnel barrier preferentially filters spin-up and spin-down electrons from a nonmagnetic electrode, has been demonstrated in junction heterostructures. By incorporating two spin filtering barriers, double spin filter magnetic tunnel junctions (DSF-MTJs) were predicted to yield magnetoresistance (MR) values orders of magnitude larger than that of conventional magnetic tunnel junctions. Recently, DSF-MTJs have exhibited spin filtering with magnetic electrodes at room temperature and at low temperature with nonmagnetic electrodes in EuS-based devices [1,2]. We have fabricated DSF-MTJs with nonmagnetic SrRuO$_{3}$ electrodes and room temperature ferrimagnets, NiFe$_{2}$O$_{4}$ and CoFe$_{2}$O$_{4,}$ for spin filters in pursuit of room temperature functionality. Atomic force microscopy shows smooth films quantified by roughness values between 0.1--0.5nm. X-ray magnetic circular dichroism reveals ferromagnetic Ni$^{2+}$ and Co$^{2+}$, and element-specific hysteresis loops indicate the independent switching of the two spin filters. Transport data reveals junction MR and non-linear I-V characteristics consistent with tunneling. \\[4pt] [1] M.G. Chapline et al., PRB, 74, 014418 (2006).\\[0pt] [2] G.- X. Miao et al., PRL, 102, 076601 (2009).   

Magnetic Behavior of Complex Oxide Magnetic Tunnel Junctions

Half metallic manganese oxides have the potential of producing a large tunneling magnetoresistance (TMR) due to their high spin-polarization. To explore their applicability we investigated magnetic tunnel junctions (MTJs) with ferromagnetic La$_{0.7}$Ca$_{0.3}$MnO$_3$(LCMO) electrodes and an insulating PrBa$_2$Cu$_3$O$_7$(PBCO) barrier. In these MTJs, with temperature, the TMR peaks rather than increasing with decreasing T [1]. Our Polarized Neutron Reflectivity studies reveal differences in the magnetization, reversal behavior, and anisotropy, between the bottom and top LCMO layers. As was observed in the YBa$_2$Cu$_3$O$_7$(YBCO)/LCMO system[2,3], with X-Ray Magnetic Circular Dichoism we have found a non-zero net moment on the Cu of PBCO at low temperature, originating at the interface. Unlike for YBCO, the Cu moment does not persist up to T$_C$ of LCMO. These combined results provide a possible origin of the anomalous TMR behavior.\\[0pt] [1] Z. Sefrioui et al., Appl. Phys. Lett. 88, 022512 (2006) [2] J. Chakhalian et al., Nature Phys. 2, 244 (2006); Science 318, 1114 (2007) [3] C. Visani et al., Phys. Rev. B 84, 060405(R) (2011)   

Ferroelectric control of orbital occupancy in manganites

Recent successful fabrication of epitaxial and coherent ferroelectric/manganite interfaces makes it possible to dynamically control charge and spin in manganites [1]. We demonstrate with \textit{ab initio} calculations that in this system, $d$-orbital occupancies of the interfacial Mn atom can also be modulated by flipping the ferroelectric polarization (i.e. flippable orbital polarization). The underlying mechanism is the structural distortions of the oxygen octahedron and the Mn atom inside induced by the ferroelectric polarization. The in-plane orbital $d_{x^2-y^2}$ is stablized by rumpling in MnO$_2$ layers, while the Jahn-Teller distortion ($c/a>1$) favors the out-of-plane orbital $d_{3z^2-r^2}$. This ferroelectric control of orbital occupancy serves as a new approach separate from strain for engineering orbital orderings in transition metal oxides. \\[4pt] [1] C.A.F.Vaz et al., Phys. Rev. Lett. 104, 127202 (2010)   

Giant tunneling electroresistance (up to $\sim $10,000{\%}) in La$_{0.7}$Sr$_{0.3}$MnO$_{3}$/BaTiO$_{3}$/La$_{0.5}$Ca$_{0.5}$MnO$_{3}$/La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ ferroelectric tunnel junctions

Tunnel junction with a Ferroelectric (FE) barrier (FTJ) presents an opportunity for nanoelectronics because of the bi-stable electric field control of the tunneling resistance. FTJs of La$_{0.7}$Sr$_{0.3}$MnO$_{3}$/BaTiO$_{3}$/La$_{0.5}$Ca$_{0.5}$MnO$_{3}$/La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ have been fabricated with pulsed-laser deposition. The special feature in the FTJ design is to insert an ultrathin (0.4 - 1.2 nm) La$_{0.5}$Ca$_{0.5}$MnO$_{3}$ film between La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ Ferromagnetic (FM) electrode and BaTiO$_{3}$ FE barrier. A giant and reproducible tunneling electroresistance effect ($\sim $10,000{\%}) was obtained with the reversal of FE polarization, about two orders of magnitude larger than the similar sized FTJ without the inserted La$_{0.5}$Ca$_{0.5}$MnO$_{3}$ layer. This result is consistent with the theoretical prediction [PRL 106, 157203 (2011)] that at a BaTiO$_{3}$/La$_{0.5}$Ca$_{0.5}$MnO$_{3}$ interface, an anti-FM insulating - FM metallic phase transition can occur in La$_{0.5}$Ca$_{0.5}$MnO$_{3}$ when the polarization of the BaTiO$_{3}$ is reversed due to the interfacial charge doping effect.   

Session T10: Invited Session: Earth-Abundant Materials for Critical Technologies

An Overview of Rare Earth Science and Technology

Currently rare earth science and technology is robust: this includes all the major branches of science -- biochemistry, chemistry, materials and physics. There are, however, currently some anomalies and distortions especially in the technology and applications sector of the rare earth field, which is caused by the dominance of China on the sales of rare earths and rare earth containing products. For the past 5 to 10 years $\sim $95{\%} of rare earths utilized in commerce came from China. Although Chinese actions have lead to sudden and large price spikes and export embargoes, the rare earths are still available but at a higher cost. The start up of production in 2011 at mines in the USA and Australia will alleviate this situation in about two years. Basic and applied research on the condensed matter physics/materials science has hardly been impacted by these events, but new research opportunities are opening up especially with regard to the USA's military and energy security. Magnets seems to be the hottest topic, but research on battery materials, phosphors and catalysts are also (or should be) strongly considered.   

Replacing critical rare earth materials in high energy density magnets

High energy density permanent magnets are crucial to the design of internal permanent magnet motors (IPM) for hybride and electric vehicles and direct drive wind generators. Current motor designs use rare earth permanent magnets which easily meet the performance goals, however, the rising concerns over cost and foreign control of the current supply of rare earth resources has motivated a search for non-rare earth based permanent magnets alloys with performance metrics which allow the design of permanent magnet motors and generators without rare earth magnets. This talk will discuss the state of non-rare-earth permanent magnets and efforts to both improve the current materials and find new materials. These efforts combine first principles calculations and meso-scale magnetic modeling with advance characterization and synthesis techniques in order to advance the state of the art in non rare earth permanent magnets. The use of genetic algorithms in first principle structural calculations, combinatorial synthesis in the experimental search for materials, atom probe microscopy to characterize grain boundaries on the atomic level, and other state of the art techniques will be discussed. In addition the possibility of replacing critical rare earth elements with the most abundant rare earth Ce will be discussed.   

Solar to Fuel Conversion with Earth Abundant Materials

Studies in the Nocera group have led to the creation of a new earth-abundant catalyst that captures many of the functional elements of photosynthesis and in doing so provides a highly manufacturable and inexpensive method to effect a carbon-neutral and sustainable method for solar storage - solar fuels from water-splitting. This discovery enables an inexpensive 24/7 solar energy system for the individual, a capability that is attractive in the underdeveloped as well as the developed world.   

Organic-inorganic hybrid materials for energy efficiency

Quantum dot (QD) semiconductor nanocrystals are unique hybrid materials that have been considered in a broad range of energy production and energy efficiency applications including LEDs, displays, lighting and solar cells. In their photoluminescent mode of operation, QDs are currently in lighting products, and have the promise to be in liquid crystal display products in the near future, in both cases offering energy efficiency gains in the range of 25-40{\%}. In electroluminescent mode, quantum dot light emitting devices (QLEDs) are an emerging class of thin-film hybrid organic-inorganic structures that can potentially achieve best-in-class performance amongst large-area emissive light sources. Indeed, efficiencies which double that of the most efficient OLEDs have been suggested. The hybrid nature of these materials offers the key design parameters that have enabled QD technology to reach market in lighting products, and promises to soon revolutionize the display industry.   

Photovoltaic devices using inexpensive, abundant inorganic materials: experiences with copper zinc tin sulfide (CZTS)

For photovoltaics to be able to contribute a significant percentage of global electricity, we ideally desire a cheap, efficient, safe, and abundant solar cell that can be treated more as a construction material than as a delicate semiconductor. We are not quite there yet, though thin film polycrystalline solar cells on cheap substrates represent a potential way to accomplish this objective. I will describe some of the requirements for a solar cell with this application objective, describe some of the challenges when we desire to transform a ``polycrystalline,'' ``mineral-like'' absorber into an efficient p-n junction solar cell, and in this context will describe our results with the kesterite compound copper zinc tin sulfide (CZTS).   

Session T11: Focus Session: Graphene Structure, Stacking, Interactions: Twisted Layers

Continuum Model of the twisted graphene bilayer

The electronic structure of the twisted bilayer was first considered [1] in the context of a continuum description of the two layers, coupled by a spatially modulated hopping. The model's predictions were subsequently confirmed by experiments [2,3], including a scanning tunneling spectroscopy finding of two low energy Van-Hove peaks in the density of states [4], and by band structure calculations [5,6]. We discuss the extension of the model in several directions: the two families of commensurate structures discovered by Mele [7], will be characterized by elementary geometrical arguments; it will be shown that it is possible to calculate analytically \emph{all} Fourier components of the hopping amplitudes for any kind of commensurate structure with large period; the calculations will be extended beyond the perturbative regime in the interlayer coupling to address the electronic structure and local density of states in the very small angle limit. \\[4pt] [1] J.~M.~B. Lopes dos Santos, \emph{et. al}, Phys. Rev. Lett. \textbf{99}, 256802, (2007).\\[0pt] [2] Z.~Ni, \emph{et. al.}, Phys. Rev. B \textbf{77}, 235403, 2008.\\[0pt] [3] A.~Luica, \emph{et. al}, Phys. Rev. Lett. \textbf{106}, 126802 (2011).\\[0pt] [4] G.~Li, \emph{et. al}, Nature Physics \textbf{6}, 109 (2010).\\[0pt] [5] S. Shallcross, \emph{et. al}, Phys. Rev. B \textbf{81}, 165105 (2010).\\[0pt] [6] G.~de Laissardiere, \emph{et. al}, Nano Letters \textbf{10},804 (2010).\\[0pt] [7] E.~J. Mele, {Phys. Rev. B} \textbf{81}, 161405 (2010).   

Moire Bloch Bands in Twisted Bilayer Graphene

A moir\'{e} superlattice pattern is formed when two copies of a periodic lattice are overlaid with a relative twist. I will address the electronic structure of a twisted two-layer graphene system by generalizing the Dirac equation continuum models that are used to describe single-layer graphene and untwisted bilayers. In the Dirac model electrons in graphene have a pseudospin degree-of-freedom corresponding to the honeycomb sublattice dependence of wavefunction amplitudes. The continuum model of twisted bilayers can be derived systematically [1] by assuming that interlayer tunneling amplitudes are non-nocal with a range that is large compared to the honeycomb lattice constant, and leads to an appealing picture in which the tunneling operator has a position-dependent pseudospin dependence that simply reflects the local registry between the two honeycombs. The continuum model twisted bilayer Hamiltonian is therefore periodic, with the periodicity of the moir\'{e} pattern, and insensitive to the incommensurability of the microscopic Hamiltonian. I will discuss the properties of the Bloch bands of this periodic Hamiltonian, which become highly non-trivial at small twist angles. In particular the Dirac velocity crosses zero several times as the twist angle is reduced and vanishes at a discrete set of magic angles. I will also briefly discuss the Hofstadter butterfly spectral patterns [2] created by incommensurability between the moir\'{e} pattern and magnetic lengths when a twisted bilayer is placed in an external magnetic field, and the electronic structure [3] of a single graphene layer that is twisted with respect to a boron nitride substrate.\\[4pt] [1] R. Bistritzer and A.H. MacDonald, PNAS {\bf 108}, 12233 (2011). \hfill \newline [2] R. Bistritzer and A.H. MacDonald, Phys. Rev. B {\bf 84}, 035440 (2011). \hfill \newline [3] A. Raoux and A.H. MacDonald, arXiv:1112.nnnn.   

Anomalies in the magneto-optical conductivity of twisted multilayer epitaxial graphene

The nature of the electronic coupling between carbon layers in twisted multilayer graphene is an intriguing and hot-debated issue. We measured the Faraday rotation and optical absorption spectra of twisted graphene multilayers grown on the carbon face of SiC in the far-infrared range in magnetic fields up to 7 Tesla [1,2]. Multiple spectral components are identified, which include a quasi-classical cyclotron resonance, originating from the highly doped graphene layer closest to SiC, transitions between low-index Landau levels (LLs), which stem from quasineutral outer layers and a broad optical absorption background, which provenance is less obvious. Electron- and hole-type LL transitions are optically distinguished and shown to coexist. The variation of the Fermi velocity is about 10 percent across the layers. Our central observation is an anomalously small optical spectral weight of the individual LL transitions, which is likely caused by the unusual electronic coupling between randomly stacked graphene layers. \\[4pt] [1] I. Crassee \emph{et al.} Nature Phys. \textbf{7}, 48 (2011). \newline\noindent[2] I. Crassee \emph{et al.} Phys Rev B \textbf{84}, 035103 (2011).   

Quantum Hall Effect, Screening and Layer-Polarized Insulating States in Twisted Bilayer Graphene

We present a study of electronic transport in dual-gated twisted bilayer graphene. Despite the sub-nanometer proximity between the layers, we identify independent contributions to the magnetoresistance from the graphene Landau level spectrum of each layer. We demonstrate that the filling factor of each layer can be independently controlled via the dual gates, which we use to induce Landau level crossings between the layers. By analyzing the gate dependence of the Landau level crossings, we characterize the finite inter-layer screening and extract the capacitance between the atomically-spaced layers. At zero filling factor, we observe magnetic and displacement field dependent insulating states, which indicate the presence of counter-propagating edge states with inter-layer coupling.   

Formation of superlattice structures by interlayer bonding in twisted bilayer graphene

We present a computational analysis of carbon nanostructure formation from twisted bilayer graphene, upon creation of interlayer covalent C-C bonds. The analysis is based on a combination of first-principles density functional theory calculations and classical molecular-dynamics simulations. We demonstrate that the resulting configurations constitute a novel class of stable structures and that their features are determined by the relative angle of rotation between the two graphene planes of the bilayer. For small angles of rotation (near 0 degrees), interlayer covalent bonding generates superlattices of diamond-like nanocrystals embedded within the graphene layers; for rotation angles near 30 degrees, superlattices of caged fullerene-like configurations are generated. We calculate the electronic band structure of these superlattices and show that their band gap can be controlled through selective hydrogenation and creation of interlayer bonds. We also show that the linear dispersion around the K point in the first Brillouin zone (Dirac cones), characteristic of single-layer and non-bonded twisted bilayer graphene, is preserved for some of these structures in spite of the introduction of sp3 bonds due to hydrogenation and interlayer C-C bonding.   

Phonon mediated conductance in misoriented graphene bilayers

Electrical transport in a misoriented graphene bilayer is facilitated by umklapp processes whose strength is known to decrease rapidly with the number of atoms in the commensurate cell. As the misorientation angle is reduced, the number of atoms increases, and the umklapp conductance in an ideal (infinitely large and defect free) bilayer becomes negligible. We show that at room temperature coupling to the out-of-plane phonon vibrations leads in a conductance several orders of magnitude larger than that produced by pure electronic umklapp. The most relevant phonons originate from the flexural modes of the monolayer, vibrating out-of-phase in the bilayer, with energies around 80 cm$^{-1}$ near the $\Gamma $-point. These phonon modes disperse nearly quadratically away from the center of the Brillouin zone. As the misorientation angle is reduced, the relevant phonon wavevector connecting the two Fermi surfaces in monolayers is reduced as well, which results in larger phonon mediated conductance. This is the opposite behavior to that expected from the umklapp conductance. We will present calculations of phonon mediated conductance as a function of misorientation angle, doping, temperature, and applied bias, for a tight-binding electron-phonon Hamiltonian.   

Probing interlayer interactions in twisted bilayer graphene with Raman spectroscopy

Chemical vapor deposition (CVD) growth or artificial layer-by-layer assembly of graphene typically produces multi-layer regions in which the layers are twisted with respect to each other, but the electronic and optical properties of this new material are still under investigation. In particular, little is known about how the twist angle affects the Raman signature of this material. We use a combination of dark-field transmission electron microscopy (DF-TEM) and widefield Raman imaging (WRI) to study the Raman signature of bilayer CVD graphene regions with known twist angles. We find that the intensities of the G and 2D peaks vary predictably with twist angle. In particular, we observe a strong G band enhancement at a specific twist angle that depends on our excitation energy. To explain this behavior, we model the electronic band structure of twisted bilayer graphene; the interaction between layers creates new saddle point van Hove singularities, and these energy states can enable a fully resonant G band pathway for a specific angle and excitation energy. This G band resonance feature is a very sensitive probe of twist angle and interlayer interactions.   

Strong Rotational Angle Dependence of Raman Spectroscopy in Rotated Double-Layer Graphene

We perform a complementary Raman spectroscopy and transmission electron microscopy (TEM) study, as well as electronic-structure and Raman calculations, on suspended rotated double-layer graphene. Graphene Raman spectra show a strong dependence on the rotational angles between two stacked layers. For low-angle mis-orientations ($<\sim $ 10 degrees), double-layer graphene exhibits Raman signature closer to AB-stacked bilayer graphene. Double-layers with high rotational angles ($>\sim $ 15 degrees), on the other hand, display Raman spectra similar to monolayer graphene. Rotational angle dependent modifications of the electronic band structure in double-layer graphene can explain this trend and a G peak enhancement at certain middle angles. The computed electronic band structures and key features of the graphene Raman peaks including the blue shift, width and intensity of the 2D peaks agree well with experimental data.   

Effect of stacking on the transport properties of few-layer graphene: NEGF-DFT investigation

We study the effect of the stacking order on the electronic transport properties of few-layer graphene (FLG) by performing ab initio calculations based on the formalism that combines non-equilibrium green's functions and density functional theory. The stacking of the layers - Bernal (ABA), Rhombohedral (ABC) or even a combination between them - have to be considered as an extra degree of freedom and consequently the FLG properties are highly sensitive to the stacking configuration. In particular, the band structures and the transport properties of FLG present a behavior markedly distinct from that for single layer. We consider FLG from trilayer to dodecalayer in both stacks. We show that for FLG, in the Rhombohedral stacking, a simple counting of bands cannot be used to predict the amount of conducting channels. We also show that for FLG, in the Rhombohedral stacking, the outermost layers dominate the contribution to the transmittance whereas for the Bernal stacking the innermost layers also present a significant contribution to the transmittance. Moreover, we investigate the effect of bias voltage and the temperature in the transport properties of FLG. We acknowledge the INCT/CNPq, CAPES and FAPESP for the financial support.   

First principles study of trilayers of graphene-BN-graphene

The stability, electronic structure and electronic transport properties of graphene-BN-graphene (C-BN-C) trilayers are studied in the framework of density functional theory. Different stacking formats, i.e., AAA, ABA and ABC stackings are considered. The ABA stacking is found to be most energetically favorable, followed by ABC and AAA stackings. The interlayer spacing of trilayers are close to those of corresponding C-BN bilayers, while the intralayer bond length can be regarded as the weighted mean of constituent layers. All considered configurations are found to be metallic, independent of stacking formats. When an external electric field is applied perpendicularly, electronic band structures undergo stacking-dependent variations. While both AAA and ABA stackings show good tunability of energy gap, ABC stacking shows less flexibility of gap tuning. We will also present the results of the electronic transport properties which are modeled by sandwiching trilayers between gold contact electrodes.   

Session T12: Focus Session: Graphene: Growth, Mechanical Exfoliation, and Properties - CVD on Metals

Characterization of Few Layer Graphene films Grown on Cu, Cu-Ni and SiC Substrates

The electronic structure of graphene depends on the number of graphene layers and the stacking sequence between the layers. Therefore, it is important to have a non-destructive technique for analyzing the overlayer coverage of graphene directly on the growth substrate. We have developed a technique using angle-resolved XPS to determine the average graphene thickness directly on metal foil substrates and SiC substrates. Since monolayer graphene films can be grown on Cu substrates, these samples are used as a standard reference for a monolayer of graphene. HOPG is used as a standard reference for bulk graphite. The electron mean free path of the C-1s photoelectron can be determined by analyzing the areas under the C-1s peaks of monolayer graphene/Cu and bulk graphite. With the electron mean free path, the graphene coverage of a film of arbitrary thickness can be determined by analyzing the area under the C-1s of that sample. Analysis of graphene coverages for graphene films grown on Cu-Ni substrates and of the thickness of both the graphene overlayer and intermediate buffer layer on SiC will be presented.   

Investigation of large-area graphene synthesized on palladium surface

We present a detailed study of large-area growth of graphene on palladium substrates. By studying the growth at different stages through appropriate variations of the temperature and time intervals of growth, and by investigating the growth at different regions of the metal substrate we have been able to observe a number of important properties of graphene growth on Pd surfaces. We have explored the nature of the as-synthesized graphene through a combination of electron microscopy and Raman spectroscopic analysis. Raman analysis of the graphene enables us to identify different kinds of as-synthesized graphene, including monolayer, turbostratic multi-layer, and mixed Bernal-turbostratic graphene layers. We further demonstrate a systematic study of the evolution of these different types of graphene as a function of temperature and growth-time.   

Crystallographic effects of copper substrate on graphene growth and fluorination

Graphene grown by chemical vapor deposition (CVD) on Cu is appealing due to supposed large-area monolayer growth and the low cost of the Cu foil substrate. However, this Cu substrate is inherently polycrystalline, with low and high index facets, annealing twins, and rough sites. We characterize CVD graphene growth on the Cu surfaces by combining Raman spectroscopy, electron-backscatter diffraction (EBSD), and scanning electron microscopy (SEM). We find that graphene growth on Cu(100) is multilayered and of low-quality, while growth on Cu(111) is monolayer and of high-quality. High index Cu facets containing a high percentage of (111) terraces are more monolayer-like than Cu(100). Graphene has a higher growth rate on (111) surfaces, growing the fastest on Cu(111). At temperatures below 900 \r{ }C, compact islands of graphene form from lowered growth rate. To open a bandgap in graphene, quantum confinement or covalent chemistry must be used. We do the latter by exposing our graphene films to XeF$_{2}$ gas, terminating in an insulating C$_{4}$F stoichiometry and covalent C-F bonds. Rougher facets fluorinate first, which allows possible bandgap engineering by the Cu crystallography. Additionally, film defects assist in fluorination effectiveness. We also show preliminary results on Cu crystallography effects for CVD of hexagonal boron nitride (h-BN).   

Barrier-Guided Growth of Micro- and Nano-Structured Graphene

The patterning of graphene is necessary for tuning its physical and electronic structure and for device-integration. Traditionally, patterning has been achieved via \textit{top-down} chemical or physical etching, which induces defects and disorder that degrades performance. In this work, we overcome these challenges through a fundamentally new \textit{bottom-up} growth method for the rational synthesis of patterned graphene called Barrier-Guided Chemical Vapor Deposition (BG-CVD). We deposit patterned barriers on the Cu surface, using scalable lithography methods, which guide the growth of graphene around them into any desired shape. The barriers locally passivate the surface, (i) preventing the decomposition of the methane, and (ii) blocking the growth of graphene on the barrier. By designing appropriate barrier layers, we have grown arbitrary patterns, nanoribbons, and nanoperforated graphene with features down to 25 nm with high mobility (215 cm$^{2}$/Vs). These materials are highly crystalline with domain size $>$4 $\mu $m and have 2-10x less edge defects than comparable top-down etched materials. The pattern reproducibility is $<$1 nm and thus, ultimately, should enable the bottom-up synthesis of sub-5 nm features. These results indicate BG-CVD as a superior production route to patterned graphene.   

Synthesis of Large-grain, Single-crystalline Graphene by a Novel Chemical Vapor Deposition Method and Electrical properties

Graphene, a two dimensional, honey comb arrangement of carbon atoms has drawn significant attention with its interesting physical and electronic properties. Tremendous efforts have been made to synthesize large-scale, high quality, single-layer graphene (SLG). Based on previous studies, CVD graphene with large grain size (less grain boundaries) and low defect density would show an enhancement of device mobility. Here we report a novel CVD method to synthesize graphene with grain size up to several hundreds of micrometers on copper foil. Raman surface map of individual graphene grain indicated that the large-grain graphene was single-layer and with very low defect density. Selected Area Electron Diffraction (SAED) also confirmed that the each individual graphene island was a single grain. Morphology study was also performed to investigate the relation between the shape of graphene and growth parameters. Furthermore, the large-grain graphene was transferred to SiO$_{2}$/Si for the field effect study, and the device mobility derived from the large-grain graphene was $\sim $ 5,200 cm$^{2}$/V/s. The achieved high device mobility indicates that the large-grain single-crystalline graphene is of great potential for graphene-based nanoelectronics.   

Mesoscale STM Study of Thermally Annealed Copper Foils

The growth of high quality graphene has become a topic of significance. There have been utilized several methods of material growth including the epitaxial growth on SiC, method of exfoliation of graphite, and chemical vapor deposition (CVD). The CVD approach typically utilizes foils of copper or nickel that are exposed to organic compounds at a high temperature. The purpose of the study is to investigate the role of the metal surface morphology during the growth process, relative grain size before and after thermal treatment, and relative flatness of the substrate after annealing. We investigated the effects of thermal annealing of polycrystalline Cu foil at the mesoscale using an ultrahigh vacuum (UHV) scanning tunneling microscope (STM). Prolonged low-temperature and rapid high-temperature annealing of the samples is being carried out and the resulting surface morphology will be reported. The STM observations reveal that the film quality is limited by grain boundaries.   

Graphene Crystal Growth and Device Integration

Graphene has unique electronic, chemical, thermal and physical properties and this is opening many opportunities for its use. However, to date the majority of the experiments have been performed on exfoliated graphene. There is a need to develop high quality, large area single crystal graphene for electronic applications. The discovery of graphene growth copper by chemical vapor deposition (CVD) has led to the growth of polycrystalline large area (square meters) films. The domain size for the baseline process is a few tens of microns in diameter but large ``crystals,'' 0.25 square mm, have been grown. However, even though the films are not yet fully single crystals the transport properties are equivalent to those of exfoliated graphene. The ultimate usefulness of any material for electronics is the ability to integrate it with dielectrics and metals. Graphene is chemically inert and will require special processes to integrate it with dielectrics and metals without interrupting its band structure. The objective of this presentation is to review and present new data on large area graphene crystal growth and integration of dielectrics and metals. Surface analysis of graphene with dielectrics and metals under various processing conditions will also be presented.   

In Situ Characterization of Alloy Catalysts for Low-Temperature Graphene Growth

Chemical vapor deposition (CVD) on transition metal catalysts offers a low-cost method of producing large-area graphene, but due to limited understanding of the underlying mechanism(s), growth control remains rudimentary. We use in situ X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD) to monitor catalytic CVD on Ni based catalysts under typical reactor conditions. We thus develop a coherent model for graphene formation and show that graphene growth occurs during isothermal hydrocarbon exposure and is not limited to precipitation upon cooling. We introduce alloy catalysts to improve graphene growth by tuning reactivity and selectivity. We show that alloying polycrystalline Ni with Au allows low temperature ($<$450\r{ }C) CVD of predominantly monolayer ($>$74{\%}) graphene films with an average D/G peak ratio of $\sim $0.24 and domain sizes in excess of 220$\mu $m$^{2}$ [1]. We suggest that Au decorates a majority of high reactivity Ni surface sites, such as step edges, and lowers the stability of surface C. Au alloying thereby drastically lowers the graphene nucleation density, allowing more uniform and controlled growth at CMOS compatible temperatures. [1] Weatherup et al. Nano Lett. 11, 4154 (2011)   

ACCVD growth of mono- and bi-layer graphene and mechanism study

CVD on metal substrates has been proved to be effective in the synthesis of graphene. But before utilization in graphene electronics, the quality of the consequential graphene needs to be improved, and a reliable method to grow large-scale, high-quality bi-layer graphene is required. Besides, the mechanism of growth is not fully understood. Here we report utilizing Alcohol catalytic CVD (ACCVD) to produce mono- and bi-layer graphene. By applying alcohol as carbon source, we carefully studied how each parameter affects the growth process, and the defects and grain size of graphene. By changing growth conditions we could efficiently control the layer number (1 or 2). Afterwards, we conducted and compared the transfer procedures utilizing three commonly used mediators---PVA, PDMS and PMMA. We also employed $^{12}$C, $^{13}$C, and 2-$^{13}$C ethanol to synthesize graphene, and with the spectroscopy characterization results we are able to explain the growth mechanism on Cu and Ni substrates to a certain extent.   

Synthesis and sensing application of large scale bilayer graphene

We have synthesized large scale bilayer graphene by using Chemical Vapor Deposition (CVD) in atmospheric pressure. Bilayer graphene was grown by using CH4, H2 and Ar gases. The growth temperature was 1050${^\circ}$. Conventional FET measurement shows ambipolar transfer characteristics. Results of Raman spectroscopy, Atomic Force microscope (AFM) and Transmission Electron Microscope (TEM) indicate the film is bilayer graphene. Especially, adlayer structure which interrupt uniformity was reduced in low methane flow condition. Furthermore, large size CVD bilayer graphene film can be investigated to apply sensor devices. By using conventional photolithography process, we have fabricated device array structure and studied sensing behavior.   

CVD growth of graphene at low temperature

Graphene has attracted a lot of research interest owing to its exotic properties and a wide spectrum of potential applications. Chemical vapor deposition (CVD) from gaseous hydrocarbon sources has shown great promises for large-scale graphene growth. However, high growth temperature, typically 1000$^{\circ}$C, is required for such growth. In this talk, I will show a revised CVD route to grow graphene on Cu foils at low temperature, adopting solid and liquid hydrocarbon feedstocks. For solid PMMA and polystyrene precursors, centimeter-scale monolayer graphene films are synthesized at a growth temperature down to 400$^{\circ}$C. When benzene is used as the hydrocarbon source, monolayer graphene flakes with excellent quality are achieved at a growth temperature as low as 300$^{\circ}$C. I will also talk about our recent progress on low-temperature graphene growth using paraterphenyl as precursor. The successful low-temperature growth can be qualitatively understood from the first principles calculations. Our work might pave a way to economical and convenient growth route of graphene, as well as better control of the growth pattern of graphene at low temperature.   

Session T13: Focus Session: Low-Dimensional and Molecular Magnetism - Molecular Ferromagnetism and 2D Magnetism

Magnetic phase diagram of quasi-2D quantum Heisenberg antiferromagnets with XY anisotropy

The magnetic phase diagram of a quasi-2D quantum Heisenberg antiferromagnetic compound Cu(pz)2(Cl$_{\mbox{O4}\mbox{)2}}$ [1] has been determined by experimental measurements; TN shows a strong field dependence. The data reveal the presence of a small (0.5\%) amount of XY anisotropy. QMC simulations have been performed to examine the role of the anisotropy and the interlayer exchange (') upon the phase diagram [2,3]. Comparison of the QMC results with the experimental phase diagram will be presented. \\[4pt] [1] F. Xiao, F. M. Woodward, C. P. Landee, M. M. Turnbull, C. Mielke, N. Harrison, T. Lancaster, S. J. Blundell, P. J. Baker, P. Babkevich, and F. L. Pratt. Phys. Rev. B, 79(13): 134412 (2009) \\[0pt] [2] A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi. Phys. Rev. B, 68(6):060402 (2003). \\[0pt] [3] A. Cuccoli, T. Roscilde, R. Vaia, and P. Verrucchi. Phys. Rev. Lett., 90(16): 167205 (2003).   

Magnetic excitations of the S=1/2 square lattice antiferromagnet CuF$_{2}$(H$_{2}$O)$_{2}$(pyz) (pyz=pyrazine)

We have studied the magnetic structure and excitations of the two dimensional S=1/2 square lattice antiferromagnet deuterated CuF$_{2}$(H$_{2}$O)$_{2}$(pyz). The neutron diffraction measurements show that the antiferromagnetic structure is collinearly arranged with the estimated magnetic moment of 0.60$\pm $0.07 $\mu _{B}$/Cu. This value is much smaller than the single ion magnetic moment, reflecting the presence of strong quantum fluctuations. The spin wave dispersion from magnetic zone center to the zone boundary point ($\pi $/2 $\pi $/2) can be roughly described by a 2d Heisenberg model with a magnetic exchange constant J$_{2d}$=1.099 $\pm $ 0.002 meV and a tiny contribution from an inter-plane interaction (J$_{perp}$ is about 1{\%} of J$_{2d})$. This is close to the first principles DFT calculations while about two times larger than the value extracted by fitting of the magnetic susceptibility. Compared to ($\pi $/2 $\pi $/2), preliminary measurements of the spin excitation at the zone boundary point ($\pi $ 0) shows an obvious suppression of the excitation energy. This suppression is expected on the basis of quantum Monte Carlo and series expansion calculations for the quantum corrections of linear spin wave theory.   

Edge state and its stability of 2D antiferromagnetic quantum spin systems

Topological insulators (TIs) [1] have been of great interest in condensed matter physics. One of the most important points is that TIs are characterized by non-local quantities such as topological quantities of the bulk or gapless surface states [2]. The TI phase and the surface states are quite stable for any time-reversal symmetric perturbations. On the other hand, the Haldane-gap state in quantum spin systems is another class of the topological state [3], because, similarly to TIs, this gapped state has no local order and is characterized by the non-local (string) order parameter or free spins at the edges. In this study, motivated by the recent development of theories for topological phases and surface states, we consider properties of edge states in 2D quantum spin systems by applying the quantum Monte Carlo method. Particularly, we focus on the three points; (1) which spin systems can have gapless edge states, (2) the stability of the gapless edge states, and (3) the difference between the edge modes of TIs and spin systems. \\[4pt] [1] See, for example, M. Z. Hasan and C. L. Kane, RMP82, 3045 (2010). \\[0pt] [2] A. P. Schnyder, et al., PRB 78, 195125 (2008), A. Kitaev, AIP Conf. Proc. 1134, 22 (2009). \\[0pt] [3] F.D.M. Haldane, Phys. Lett. 93A, 464 (1983); PRL50, 1153 (1983).   

Absence of magnetic order in low-dimensional (RKKY) systems

We extend the Mermin-Wagner theorem to a system of lattice spins which are spin-coupled to itinerant and interacting charge carriers. We use the Bogoliubov inequality to rigorously prove that neither (anti-) ferromagnetic nor helical long-range order is possible in one and two dimensions at any finite temperature. Our proof applies to a wide class of models including any form of electron-electron and single-electron interactions that are independent of spin. In the presence of Rashba or Dresselhaus spin-orbit interactions (SOI) magnetic order is not excluded and intimately connected to equilibrium spin currents. However, in the special case when Rashba and Dresselhaus SOIs are tuned to be equal, magnetic order is excluded again. This opens up a new possibility to control magnetism electrically. \\[4pt] References: D. Loss, F. L. Pedrocchi, and A. J. Leggett, Phys. Rev. Lett. \textbf{107}, 107201 (2011).   

Continuous and Discontinuous Quantum Phase Transitions in a Model Two-Dimensional Magnet

The Shasty-Sutherland model consists of a set of spin 1/2 dimers on a 2-dimensional square lattice which are predicted to change from isolated, gapped excitations to a collective, ordered ground state by tuning the ratio of the intra to inter-dimer coupling. We compress the model Shastry-Sutherland material, SrCu2(BO3)2, in a diamond anvil cell at cryogenic temperatures to continuously tune the coupling energies and induce changes in state. High-resolution x-ray measurements exploit a remarkably strong spin-lattice coupling to ascertain the physics of the magnetic transition. The singlet-triplet gap energy is suppressed continuously with increasing pressure, vanishing completely by 2 GPa. This continuous quantum phase transition is followed by a structural distortion at higher pressure corresponding to the onset of long-range order.   

Late-time Domain Growth in the Compressible Triangular Ising Net

We perform large scale Monte Carlo simulations of the long-tme domain growth behavior in a compressible, triangular Ising net. Unlike previous work,\footnote{Mitchell and DP Landau, PRL 97, 025701 (2006)} our model has no bond angle interactions or lattice mismatch. The system is quenched below the critical temperature from a homogenous disordered state to an ordered phase where multiple domains coexist. We include an elastic energy part in the Hamiltonian to adjust the rigidity of the model. Theory expects the domain size $R(t)$ grows as a power law $R(t)=A+Bt^n$, where $t$ is the time after the quench. For the rigid model we find the late-time domain size growth factor $n$ has Lifshitz-Slozov value of $\frac{1}{3}$. For weak flexible models, we get slight reduction from $\frac{1}{3}$. For the strongly flexible model, we get a bimodal distribution of bond lengths and a dramatically reduced value of $n$, which has similar behavior as the mismatch model.\footnote{Ibid.}   

Atomic-scale antiferromagnets with stable Neel states

A macroscopic antiferromagnet is characterized by long-range magnetic order, for example with the spin of neighboring atoms alternating their direction. Here we will discuss how far such concepts can be extended towards the atomic scale. We use low-temperature scanning tunneling microscopy with spin-polarized tips to investigate antiferromagnets consisting of a small number of Fe atoms on a thin Cu2N substrate. As few as 8 Fe atoms show two stable magnetic states in which the spin between neighboring atoms alternates. The STM can be used to switch between these two magnetic states. When heating the spins to about 10K, spontaneous switching occurs from which the switching dynamics is deduced. Small structures show a second switching mechanism that is not dependent on temperature but strongly dependent on the length of the antiferromagnetic chain, suggesting switching by quantum tunneling of magnetization (the Neel vector).   

Contrasting low-dimensional magnetism in the 3D metal-organic frameworks [Cu(VF$_{6})$(pyz)$_{2}$]\textbullet 4H$_{2}$O and [Cu(HF$_{2})$(pyz)$_{2}$]SbF$_{6}$ (pyz = pyrazine)

[Cu(VF$_{6})$(pyz)$_{2}$]\textbullet 4H$_{2}$O (\textbf{1}) and [Cu(HF$_{2})$(pyz)$_{2}$]SbF$_{6}$ (\textbf{2}) form tetragonal frameworks that consist of 2D [Cu(pyz)$_{2}$]$^{2+}$ square lattices that are linked in 3D by bridging VF$_{6}^{2-}$ (\textbf{1}) or HF$_{2}^{-}$ (\textbf{2}) anions. Magnetic susceptibility data shows apparent paramagnetism, although not simple Curie-Weiss behavior, in \textbf{1}. For \textbf{2}, a broad maximum in $\chi (T)$ at 12.5 K and a sharp kink at 4.3 K indicate short- (SRO) and long-range (LRO) magnetic ordering, respectively. Additional experimental data for \textbf{1} (e.g., heat capacity and $\mu ^{+}$SR) however, indicate that a LRO state occurs below 3.6 K whereas pulsed-field magnetization data suggest a superposition of AFM Cu$^{2+}$ layers and fluctuating V$^{4+}$ moments. The structural and magnetic behavior of \textbf{1} and \textbf{2} will be described as well as possible new directions.   

Strong Exchange Anisotropy in Heavy Atom Radical Ferromagnets

The discovery twenty years ago of ferromagnetic ordering in ``light atom'' p-block (N, O based) radicals appeared to provide a major conceptual advance, suggesting the possibility of a new era in non-metal molecular magnetism. However, the weak through-space magnetic exchange interactions present in these early radical-based ferromagnets afforded very low Curie temperatures $T_C$ ($<$ 2 K), and the localization of spin density on light atoms ensured low coercive fields $H_c$ ($<$ 100 Oe). In this context, the observation of ferromagnetic ordering in ``heavy atom'' (Se) radicals, with $T_C$ as high as 17 K and coercive fields $H_c$ up to 1370 Oe (at 2 K), represents a significant improvement in properties. This presentation will provide a theoretical and experimental examination of the source of the large coercive fields reported for these ``heavy atom'' radical ferromagnets. High-field ferromagnetic resonance (FMR) measurements, interpreted in the context of the anisotropic exchange interactions between the radicals in the solid state, leads to the conclusion that spin-orbit effects are responsible for the large observed magnetic anisotropy. This conclusion is supported by detailed analysis of the symmetry and magnitude of the spin-orbit interactions. An interesting discussion is the extent to which these anisotropic exchange terms also contribute to the enhancement of $T_C$. That is, in the field of organic magnetism, where low dimensional magnetic structures are commonly found, long range ordering may depend crucially on such anisotropy. \\[4pt] See \emph{JACS} {\bf 130}, 8414-8425 (2008), \emph{JACS} {\bf 133}, 8126-8129 (2011).   

FMR Study of the Field Dependence of the Ferromagnetic Transition in an Organic Magnet

Organic heterocyclic thia/selenazyl radicals have unique magnetic properties. First and foremost, in their crystalline form, they experience a transition to a ferromagnetic state at temperatures that are the highest for any material containing only non-metallic elements. Second, their low temperature uniaxial anisotropy field is the highest among purely organic ferromagnets [Winter et al., JACS {\bf 133}, 8126 (2011)]. To investigate the effect of a magnetic field on the transition in the mixed Se-S compound ($T_c = 12.5$~K) at zero field, we employ ferromagnetic resonance (FMR) absorption as a measure of the anisotropy field for a single crystal. We also focus on the temperature and field dependence of the FMR linewidth. Our main finding is that the application of a field significantly broadens the ferromagnetic transition, with a noticeable FMR signal observed to as high as $2T_c$ in fields of a few tesla. Meanwhile, the FMR linewidth is relatively insensitive to frequency/field, though it becomes narrower upon decreasing the temperature and saturates below $T_c$. We will discuss the broadening of the ferromagnetic transition within the framework of scaling theory.   

Session T14: Focus Session: Spins in Semiconductors - Spins and Edge States

Controlled coupling of spin-resolved quantum Hall edge states

Spin resolved edge states in quantum Hall systems at filling fraction $\nu $ = 2 posses large coherence [1] and relaxation [2] lengths. They are ideal candidates for the implementation of dual-rail quantum computation architectures [3] by encoding the qubit in the spin degree of freedom of the co-propagating spin resolved edge states. An important element for realization of such architectures is a coherent beam splitter that controllably mixes the two co-propagating spin-resolved edge channels to create any superposition of the two logic states. In this talk we demonstrate a new method to controllably couple spin resolved edge states and induce inter-edge charge transfer associated to spin-flip scattering events [4]. The process exploits the coupling of the electron spin with a spatially-dependent periodic in-plane magnetic field that is created by an array of Cobalt nano-magnets placed at the boundary of the GaAs/AlGaAs modulation doped heterostructure. The maximum charge/spin transfer of 28 $\pm $ 1 {\%} is achieved at 250 mK by fine tuning the perpendicular magnetic field. These results are key steps towards the realization of a scalable quantum interferometric device currently under investigation in our group. \\[4pt] [1] Y. Ji et al. Nature 422 (2003) 415.\\[0pt] [2] G. Muller et al. Phy. Rev. B 45 (1992) 3932.\\[0pt] [3] V. Giovannetti et al., \textit{Phys. Rev. B} 77 (2008) 155320.\\[0pt] [4] B. Karmakar et al., (accepted in PRL).   

Theory of Temperature-dependent Spin Dynamics with Electron-Phonon Interaction

We develop a theory of temperature-dependent spin dynamics in spin-orbit coupled semiconductors that includes the effects of electron-phonon interaction. A set of coupled kinetic equations for the spin density matrix are derived starting from the quantum Liouville equation. The spin-conserving and spin-flipping scattering terms due to electron-phonon interaction in the presence of spin-orbit coupling are derived explicitly using an effective low-energy Hamiltonian for the conduction and valence bands. From the solution of the kinetic equations, we extract the temperature dependence of spin transport and relaxation in various parameter regimes. In particular, we discuss the effect of electron-phonon interaction on the persistent spin helix lifetime.   

Absence of intrinsic spin splitting in 1D quantum wires of tetrahedral semiconductors

The energy bands of 3D, 2D, and 1D structures are generally split at certain wavevector values into spin-components, a spin splitting that occurs even without external magnetic field and reflects the effect of spin-orbit interaction on certain symmetries. We show via atomistic theory that 1D quantum-wires made of conventional zincblende semiconductors have unexpected zero SS for all electron and hole bands if the wire is oriented along (001) (belonging to D2d symmetry), and for some of bands if the wire is oriented along (111) (belonging to C3v symmetry). We find that the predicted absence of Dresselhaus SS in both (001)-oriented and (111)-oriented 1D wires is immune to perturbations lowering their original $D_{2d}$ and $C_{3v}$ structural symmetries, such as alloying of the matrix around the wire or application of an external electric field. Indeed, such perturbations induce only Rashba SS. We find that the scaling of the SS with wavevector is dominated by a linear term plus a minor cubic term.\\[4pt]J.W. Luo, L. Zhang, and A. Zunger, Phys. Rev. B 84, 121303(R) (2011).   

chiral magnon edge mode in a magnonic crystal

A bosonic system with a periodically crystalline potential has a Chern integer associated with its magnetic Bloch wavefunction. As in its fermionic counterpart like integer quantum Hall states, the Chern number thus introduced is defined for each bosonic energy band which is energetically separated from the others. When two bosonic systems having different Chern integers are connected, or when a bosonic system with non-zero Chern integer is terminated with the vaccum, chiral bosonic edge modes appear in their boundaries. We argue that a simple magnonic crystal can realize such magnonic chiral edge modes. Based on this example, we show how to design spin-wave guides in a magnonic crystal and how to channelize, spit and manipulate them.   

Anomalous Hall and Nernst effects in electron and hole-doped semiconductors

Recently it has been proposed that Majorana fermions may exist in a thin film semiconductor with proximity induced s-wave superconductivity. We compute anomalous Hall and anomalous Nernst coefficients for both electron and hole-doped semiconducting systems in the presence of an in-plane magnetic field and Rashba and Dresselhaus spin-orbit coupling. The anomalous Nernst coefficient vanishes and has plateaus as a function of the chemical potential corresponding to carrier densities which realize the topological state.   

The Origin of Dirac Cones for Classical Waves in Periodic Systems

By using a perturbation method, we propose a general theory to understand the origin of Dirac cone dispersions for classical waves in periodic structures. A selection rule for the existence of Dirac cones is established under the group theory analysis, which reveals the relation between the unusual linear dispersions and the symmetry of the degenerate Bloch states at the Dirac point. The theory is capable of accurately predicting the linear slopes at various symmetry points in the Brilliouin zone, independent of frequency and lattice structure. Furthermore, it can be also used to construct the Hamiltonian, which is in consistent with the Berry phase calculations.   

Exactly Solvable Topological Chiral Spin Liquid with Random Exchange

We extend the Yao-Kivelson decorated honeycomb lattice Kitaev model [Phys. Rev. Lett.99, 247203 (2007)] of an exactly solvable chiral spin liquid by including disordered exchange couplings. We have determined the phase diagram of this system and found that disorder enlarges the region of the topological non-Abelian phase with finite Chern number. We study the energy level statistics as a function of disorder and other parameters in the Hamiltonian, and show that the phase transition between the non-Abelian and Abelian phases of the model at large disorder can be associated with pair annihilation of extended states at zero energy. Analogies to integer quantum Hall systems, topological Anderson insulators, and disordered topological Chern insulators are discussed.   

Lie algebras for time-dependent Rashba-Dresselhaus materials

We study the spin dynamics of Rashba and Dresselhaus interactions in systems with unconfined and confined geometries. We show how Lie algebra factorization of the evolution can be used to describe systems with arbitrary time-dependence in the parameters.   

Quantum Spin Holography with Surface State Electrons

Recently Moon et~al. have shown that information can be stored in a fermionic state of a two-dimensional electron gas and have dubbed the proposed concept quantum holographic encoding. They have constructed molecular holograms of CO molecules on a Cu(111) surface, hosting a surface state (SS) [2]. Interference of electron waves scattered at the molecules leads to formation of an electron density pattern representing an information page [1]. This page has then been read out with an STM. It has been also shown that using the innate energy dispersion of SS electrons one can project the hologram not only in two spatial degrees of freedom but also in the energy dimension. In our contribution we expand the concept and show that the spin of the electron can also act as a new dimension for information storage. If the molecules or atoms used for a hologram are magnetic then the scattering of surface state electrons becomes spin-dependent, allowing one to store different information pages in different spin channels. As an example we demonstrate the possibility of simultaneous encoding two different information pages with electrons of the same energy but opposite spins. \\[4pt] [1] C.R. Moon et al., Nature Nano. 4, 167 (2009)\\[0pt] [2] W. Shockley, Phys. Rev. 56, 317 (1939)   

Session T15: Focus Session: Magnetic Nanostructures-Exchange Bias and Exchange-Coupled Systems

Investigation of CoO/Fe/Ag(001) and NiO/Fe/Ag(001) epitaxial thin films X-ray magnetic dichroism

Interfacial coupling at antiferromagnetic(AFM)/ferromagnetic(FM) interface is less understood because of the so-called magnetic frustration and the lack of direct measurement on AFM thin films. These difficulties have been partial overcome by recent development of X-ray Magnetic Dichroism on single crystalline magnetic thin films. In this talk, I will report our study on epitaxial CoO/Fe/Ag(001) system using X-ray Magnetic Circular Dichroism (XMCD) and X-ray Magnetic Linear Dichroism (XMLD). XMCD was used to measure the Fe hysteresis loops and XMLD was used to measure the response of the AFM CoO spins in response to the Fe magnetization reversal. We find that the CoO spins consist of rotatable and frozen spins with respect to the Fe spin rotation, and only the Fe uniaxial magnetic anisotropy follows the CoO frozen spins. By using focused ion beam to pattern the films into microstructures, we also observed vortex state in CoO disk imprinted from the Fe vortex state.   

Mirror symmetry in magnetization reversal and coexistence of positive and negative exchange bias in Ni/FeF$_{2}$ heterostructures

Positively and negatively exchange biased (PEB and NEB) magnetoresistance (MR) loops in Ni/FeF$_{2}$ ferromagnetic/antiferromagnetic (AF) heterostructures proceed through exactly the same reversal mechanisms. The MR curves exhibit striking mirror symmetry: the increasing (decreasing) field branch of the PEB (NEB) loop is identical to the decreasing (increasing) branch of the NEB (PEB) loop. The latter suggests that, on average, similar but opposite sign EB domain configurations are reached for low or high cooling fields, with equal interfacial density of pinned uncompensated AF spins responsible for NEB or PEB. Micromagnetic simulations are in agreement with experimental results and imply the coexistence of EB domains of opposite sign for all cooling fields, which results in a new reversal mechanism not previously reported. The persistence of NEB (PEB) domains even at high (low) cooling fields may be produced by the size distribution and density of pinned uncompensated moments in the bulk of the AF. The support of the Spanish MICINN, Catalan DURSI, IKERBASQUE and the US Department of Energy are recognized.   

Phase separation and giant exchange bias in Mn-based binary alloys

The ability to tailor, control and modify the magnetic properties of Mn-based alloys opens the possibility of developing exchange bias systems for permanent magnet and sensor technologies. Rapid solidification of AgMn, CuMn and AlMn manganese-based alloys, with significant Mn concentration ($\sim $ 30-70 at{\%}), has produced alloys that all exhibit a remarkable exchange bias at $T$ = 10 K, of the order of $\sim $ 10 kOe. Structural characterization confirms the formation of a phase-separated nanostructure (\textit{fcc} for AgMn and CuMn and \textit{hcp} for AlMn) of 40-80 nm in all alloys as characterized by phase-specific crystallographic texture and lattice parameters. The observed exchange bias is highly reduced upon moderate annealing ($T$ = 250 $^{\circ}$C) accompanied by homogenization of the Mn concentrations in the alloys. These results are tentatively attributed to different metastable incorporation of Mn within the two phases, yielding slightly different unit cell volumes, which provides an antiferromagnetic (Mn-rich phase) and ferromagnetic (Mn-poor phase) character in these two phases.   

Exchange Bias and Large Vertical Magnetization Shift in FM/V$_{2}$O$_{3}$ Interfaces

We have investigated exchange bias in different combinations of V$_{2}$O$_{3}$ thin films with ferromagnetic layers. The exchange bias is accompanied by a large vertical shift in the magnetization. These effects are only observed when V$_{2}$O$_{3}$ is grown on top of Ni$_{80}$Fe$_{20}$ permalloy (Py). The magnitude of the vertical shift is as large as 60{\%} of the total magnetization which has never been reported in any system. The exchange bias and the vertical shift are related to the formation of a Fe$_{3}$O$_{4}$ interlayer. We will show evidence that the Fe$_{3}$O$_{4}$ Verwey transition is responsible for the appearance of the exchange bias and the vertical shift in the magnetization.   

Exchange Bias in Ni/Co Multilayers with Perpendicular Anisotropy

We have studied exchange bias in Ta(5nm)/Au(10)/[Ni(t)/Co(0.4)]$\times $5/IrMn(8)/Ta(5) multilayers for Ni thicknesses of 0.8-1.2 nm. The samples were deposited via sputtering and no deposition field was used. The samples were annealed at 200 C in an applied field of 1500 Oe for different durations, then measured by polar Magneto-Optical Kerr Effect at room temperature. We find that the field annealing significantly alters the hysteresis loop shape, giving it more single domain character while simultaneously inducing exchange bias in the direction of the annealing field. After 34 (2 and 32) hrs annealing, the exchange bias of the samples each reach a maximum value ranging from 100 Oe for the thickest Ni to 35 Oe for the thinnest Ni. We find that the samples with the thinner Ni layers approach their exchange bias maximum values for shorter annealing times.   

Electrical measurement of antiferromagnetic moments in exchange-coupled IrMn/NiFe stacks

A great attention is currently focused on the development of new spintronic devices. One crucial technological issue is the coupling phenomena between thin antiferromagnetic (AFM) and ferromagnetic (FM) layers. Despite the exchange coupling was for the first time observed already in 1956, yet the effect is not fully understood. Certainly, the zero macroscopic magnetic moment in the AFM materials hinders the investigation, in contrast to the exhaustive studies on the FM counterpart. Only a very few experiments at large scale facilities explored the status of the AFM layer. Here, we will address the study of both FM and AFM moments in the archetypical IrMn/NiFe exchange-coupled system. Using common laboratory magnetization and transport tools, we found a direct link between reversal of FM moments in NiFe and rotation and pinning of AFM moments in IrMn [1]. We will show that a full rotation of AFM moments in IrMn occurs at high temperatures, in contrast to only partial rotation of AFM at low temperatures. We will discuss the experimental results in the framework of different exchange coupling models. [1] http://arxiv.org/abs/1108.2189   

Exchange bias of conetic thin films

In this work, we study the exchange bias and coercivity of Ni$_{77}$Fe$_{14}$Cu$_{5}$Mo$_{4}$ (Conetic, also known as mu-metal) exchange coupled with FeMn as functions of Conetic thickness and buffer layer material. The samples studied were BL(30nm)/Conetic(9nm-30nm)/FeMn(10nm)/Ta(5nm), where BL = Cu or Ta. All samples were grown by magnetron sputtering in a deposition field of $\sim $150 Oe during growth to set the exchange bias axis. Room temperature hysteresis loops were measured by a magneto-optical Kerr effect magnetometer as a function of applied-field angle. ~For each variety of sample, the exchange bias and coercivity were inversely proportional to Conetic thickness. With Cu buffer layers grown on Si, the H$_{eb}$ decreased from 300 Oe to 62 Oe, and H$_{c}$ decreased from 99 Oe to 9 Oe. ~Similar results were found when the Cu buffer layer was grown on SiOx, though the maximum coercivity was only 67 Oe. For the samples grown on Si(001)/Ta(5nm), the exchange bias decreased from 80 Oe to 14 Oe, while the coercivity increases only slightly from 2 Oe to 10 Oe. These results indicate a trade-off between preserving the softness of the ferromagnet and having a large exchange, which may be useful for tuning the performance of low-field sensing materials   

Effect of Cu Layer on Exchange Bias in FeMn

One of the most important puzzles related to the mechanism of exchange bias is the origin and role of uncompensated magnetization in the antiferromagnet. We study effects of a Cu layer on the uncompensated magnetization and exchange bias in FeMn, the material with a high potential for applications in magnetic recording. The multilayers of Ta(50 {\AA})/[FeMn(50 {\AA} -- 150 {\AA})/Cu(50 {\AA})]$_{10}$/Ta(50 {\AA}) are deposited by UHV DC magnetron sputtering on top of Si/SiO$_{x}$ 3 mm x5 mm substrates. Samples with a single layer of FeMn of the same thickness, Ta(50 {\AA})/FeMn(50 {\AA} -- 150 {\AA})/Ta(50 {\AA}) are used as control samples. The samples are cooled in a field of 7 T and their magnetization is measured using a SQUID magnetometer. All the samples have uncompensated magnetization that exhibits a hysteresis at 10 K. The hysteresis loops for FeMn/Cu multilayers are exchange bias shifted, while FeMn without Cu exhibits no exchange bias. Dependence of coercive field (H$_{c})$, exchange bias (H$_{e})$, and saturated magnetization (M$_{s})$ on the FeMn thickness and on temperature will be discussed. Work is supported by Texas A{\&}M University, TAMU-CONACYT Collaborative Research Program, and by NSF (USF).   

Interface coupling between ferromagnets and random and dilute antiferromagnets

Depth profiles for pinned and unpinned magnetizations were determined across the interface between a ferromagnet (F) and random and dilute antiferromagnets (RAF and DAF) exemplified by Fe$_{0.45}$Ni$_{0:55}$F$_{2}$/Co and Fe$_{0:34}$Zn$_{0:66}$F$_{2}$/Co bilayers, respectively, using polarized neutron reflectivity (PNR). PNR measurements were complemented by magnetometry using applied fields as large as 160 kOe to assure saturation of the entire sample, including magnetic moments that are normally pinned at lower fields. The locations of pinned and unpinned magnetization in the ferro- and antiferromagnets were identified. The origin of exchange bias in the RAF system is noticeably different than that of the DAF system. In the RAF system, a domain wall is formed at the RAF/F interface when the ferromagnet's magnetization is reversed. In the DAF system, some domains within the bulk of the DAF are reversed upon reversal of the ferromagnet with others remaining pinned, while the interface magnetization is entirely reversed. This work was supported by the National Science Foundation.   

A study of the magnetic interlayer coupling between CoO(NiO) and Fe films across MgO spacer layer in CoO(NiO)/MgO/Fe/Ag(001) using MOKE and XMLD

CoO(NiO)/MgO/Fe/Ag(001) films were grown epitaxially and studied by Magneto Optical Kerr Effect (MOKE) and X-ray Magnetic Linear Dichroism (XMLD). The enhancement of the Fe layer coercivity due to its coupling to the AFM (NiO) overlayer was studied as a function of the MgO spacer layer thickness using MOKE. We found that the Fe coercivity enhancement persists to $\sim$2 ML MgO thickness, after which the AFM-FM interlayer coupling becomes too weak to affect the Fe ceorcivity. Below 2ML MgO thickness, the Fe coercivity enhancement depends both on the MgO and NiO thicknesses. To further understand the effect of interlayer coupling, the rotatable CoO spins in CoO/MgO/Fe/Ag(001) after field cooling along the Fe(100) axis were determined using the XMLD measurement as a function of the MgO thickness. We found that 2 ML MgO thickness sets a critical value beyond which the CoO/MgO/Fe interlayer coupling no longer rotates the CoO spins.   

Modification of thickness dependent magnetic properties of perpendicular anisotropy Co/Pd multilayer upon hydrogenation

We have studied the change in saturation magnetization ($M_{S})$ and effective perpendicular anisotropy ($K_{eff}$ ) upon hydrogenation at room temperature and a pressure of one atmosphere in (Co/Pd)$_{25}$ multilayers, with Co thickness \textit{$\le $ }5 {\AA} and Pd thickness ranging from 0 {\AA} to 25 {\AA}. The change in $M_{S}$ and $K_{eff}$ was studied as a function of the x-ray scattering length density profile, generated from the x-ray reflectivity fits. The results show that when the Pd thickness \textit{$\le $ }10 {\AA}, the films were highly interdiffused, resulting in no measurable change in $M_{S}$ and $K_{eff}$ . As the thickness of Pd increases, the contrast between the Co and Pd layers increases, leading to a decrease in $M_{S}$ and an increase in the component of magnetization in the plane of the samples and hence causing $K_{eff}$ to decrease. The results clearly demonstrate that the solubility of hydrogen in the multilayer samples decreases with increasing alloying effects as it decreases the vacancy in the Pd 4$d $band leading to no electronic transfer from the hydrogen atoms to the Pd.   

Momentum transfer resolved memory in a magnetic system with perpendicular anisotropy

We have used resonant, coherent soft x-ray scattering to measure wave vector resolved magnetic domain memory in Co/Pd multilayers. The technique uses angular cross correlation functions and can be applied to any system with circular annuli of constant values of scattering wave vector {\bf q}. In our Co/Pd film, the memory exhibits a maximum at {\bf q}=0.0384 nm$^{\rm -1}$ near initial reversal that decreases in magnitude as the magnetization is further reversed. The peak is attributed to bubble domains that nucleate reproducibly near initial reversal and which grow into a labyrinth domain structure that is not reproduced from one magnetization cycle to the next.   

Measure of magnetization anisotropy by AMR in electrodes of Co/Pd multilayers

We studied the anisotropic magnetoresistance (AMR) properties of multilayered Co/Pd thin film electrodes as function of magnetic field. The perpendicular magnetization anisotropy (PMA) in these films is found to modify the AMR. The magnetoresistance (MR) for fields out-of-plane ($\rho_{op}$) is considerably different than for in-plane fields transverse to current direction ($\rho_{ip}$), although in both cases current is perpendicular to the magnetic field. Moreover, opposed to other thin films, where $\rho_{op}$ is smaller than $\rho_{ip}$, our films show an opposite effect, the origin of which is not clear. We can understand the AMR properties of the electrodes by an expanded Stoner-Wolfarth model, where we introduce an additional energy scale related to the PMA. Through a numerical refinement process, we can extract anisotropic energy constants of the films. This is done by reconstructing the MR behavior of the electrodes, using the linear terms in the dependence of resistivity on magnetization orientation. Our anisotropic constants coincide remarkably with other bulk measurements. Thus, our refinement process is an excellent method to extract anisotropic constants also in nano-scale systems, which cannot be measured otherwise.   

Session T16: Kondo Lattice Theory

A new paradigm for heavy electron materials

Recent experiments on the emergence of heavy electrons that display universal behavior below a characteristic temperature T$^{\ast }$ have shown that the well-known Doniach phase diagram does not apply to most materials. Here we introduce the concept of hybridization effectiveness as the organizing principle and show that it makes possible a consistent and quantitative description of the low temperature emergent behaviors of a number of heavy electron materials. We propose a new phase diagram and predict a delocalization line in the pressure/temperature phase diagram that is to be examined in future experiment.   

Superconductivity in Heavy Fermion Materials

Superconductivity in heavy fermion materials is a complex phenomenon since it often emerges from a strongly entangled state, the Kondo screened heavy Fermi liquid. In this talk, we discuss possible pairing interactions that arises in the heavy Fermi liquid, and the resulting symmetries and momentum dependencies of the superconducting order parameter. In particular, we show that the interplay between the large Fermi surface of the Fermi liquid state and the momentum dependence of the pairing interaction naturally leads to an unconventional symmetry of the superconducting order parameter in general, and a $d_{x^2-y^2}$-symmetry in particular. Moreover, we identify the signatures of unconventional pairing in the differential conductance, $dI/dV$, measured in scanning tunneling spectroscopy as well as in the quasi-particle interference pattern. Finally, we discuss the effects of impurities on the spatial dependence of both the superconducting order parameter and the hybridization.   

Single-particle and optical self-energies of a Fermi liquid revisited

We discuss the conditions under which the imaginary part of the single-particle self-energy at the Fermi surface $\Sigma (\omega, T)$ and the optical scattering rate $1/\tau ( \Omega, T)$ have particular simple scaling forms $\mathrm{Im} \Sigma (\omega, T) \propto \omega^2 + \pi^2 T^2 $ and $1/\tau (\Omega, T) \propto \Omega^2 + 4\pi^2 T^2$. We show that these relations follow from particular analytic properties of the effective fermion-fermion interaction and are only satisfied when the single-particle and optical self-energies are analytic functions of the frequency. When they are not, the scaling forms are more complex even if the system remains a Fermi liquid. We also address recently observed violation of the $\Omega^2 + 4\pi^2 T^2$ form of $1/\tau$ in URu$_2$Si$_2$ and discuss possible mechanisms of this violation.   

Singular Valence Fluctuations at a Kondo Destroyed Quantum Critical Point

Recent experiments on the heavy fermion superconductor $\backslash $beta-YbAlB4 have indicated that this compound satisfies quantum critical scaling [1]. Motivated by the observation of mixed valency in this material [2], we study the Kondo destruction physics in the mixed-valence regime [3] of a particle-hole asymmetric Anderson impurity model with a pseudogapped density of states. In the vicinity of the quantum critical point we determine the finite temperature spin and charge susceptibilities by utilizing a continuous time quantum Monte Carlo method [4] and the numerical renormalization group. We show that this mixed-valence quantum critical point displays a Kondo breakdown effect. Furthermore, we find that both dynamic spin and charge susceptibilities obey frequency over temperature scaling, and that the static charge susceptibility diverges with a universal exponent. Possible implications of our results for $\backslash $beta-YbAlB4 are discussed. [1] Matsumoto et al, Science \textbf{331}, 316 (2011). [2] Okawaet al, Physical Review Letters \textbf{104}, 247201 (2010). [3] J. H. Pixley, S. Kirchner, Kevin Ingersent and Q. Si, arXiv:1108.5227v1 (2011). [4] M. Glossop, S. Kirchner, J. H. Pixley and Q. Si, Phys. Rev. Lett. \textbf{107}, 076404 (2011).   

Kondo Physics in a Rare Earth Ion with well localized {\it 4f } electrons

We observe a rise in the low temperature resistivity of dilute La$_{1-x}$Nd$_x$B$_6$ single crystals. The specific heat data for the same samples show that there is an entropy of $R$ln4 per mole Nd involved in the excess specific heat above that of LaB$_6$. All these features are consistent with a Kondo scale of $T_K$ = 1 K. However, Nd has a well localized {\it 4f }$^{ 3}$ {\it J} = 9/2 Hund's Rule configuration which is not expected to be Kondo coupled to the conduction electrons in LaB$_6$. We conjecture that the unexpected Kondo effect arises via participation of {\it 4f} quadrupolar degrees of freedom of the Nd crystal field ground state quartet. Raman experiments as well as detailed theoretical studies do indicate that one expects strong quadrupolar influence in the properties of NdB$_6$.   

Partial disorder in the periodic Anderson model on a triangular lattice

In Kondo lattice systems, keen competition between the Kondo coupling and RKKY interaction leads to a quantum critical point between a magnetically-ordered state and a Fermi liquid state. This is a source of novel phenomena, such as a non-Fermi liquid behavior and a superconductivity. In the present study, we explore a new quantum phase related to the competition by introducing a new parameter, geometrical frustration of the lattice structure. Especially, we focus on the possibility of a partial disordered (PD) state, in which a magnetically ordered and nonmagnetic sites coexist. We consider a fundamental model for the rare-earth systems, a periodic Anderson model on a frustrated triangular lattice, and investigate the ground-state phase diagram by the Hartree-Fock approximation with assuming three-site unit cell. As a result, we find a PD state at half filling between a noncollinear antiferromagnetic metal and a Kondo insulator [1]. The PD state is stabilized by relaxing the frustration by forming collinear antiferromagnetic order on an unfrustrated honeycomb subnetwork, while leaving remaining sites non-magnetic. We will also discuss the effects of spin anisotropy and carrier doping to the PD state.\\[4pt] [1] S. Hayami, M. Udagawa, and Y. Motome, J. Phys. Soc. Jpn. 80, 073704 (2011).   

Quantum critical Kondo destruction of the Bose-Fermi Kondo model in the presence of a local transverse field

Recent studies of the global phase diagram of quantum critical heavy fermion metals [1] have motivated us to consider the interplay between the quantum fluctuations within the local-moment system and those associated with the Kondo interaction. Towards this goal, we study a Bose-Fermi Kondo model with Ising anisotropy in the presence of a local transverse field. We apply the numerical renormalization group method for the case with a sub-ohmic bosonic bath exponent and a constant conduction electron density of states [2]. Upon increasing the strength of the transverse field in the Kondo screened phase we find a crossover from a fully screened to a fully polarized impurity spin with no transition in between. Increasing the strength of the transverse coupling in the localized phase, on the other hand, we identify signatures for a continuous transition into a partially polarized Kondo phase. We discuss the implications of our results for the global phase diagram of the Kondo lattice system. \\[4pt] [1] Q. Si and F. Steglich, Science 329, 1161 (2010). \\[0pt] [2] M. T. Glossop and K. Ingersent, Phys. Rev. B 75, 104410 (2007).   

A spin-selective Kondo-insulator: Cooperation between Ferromagnetism and Kondo-effect

Taking ferromagnetic heavy fermion compounds as motivation we analyze the mechanism stabilizing the ferromagnetic state in the antiferromagnetically coupled Kondo lattice model. We find that even for this ferromagnetic state Kondo screening plays an essential role in stabilizing the ferromagnetic state at zero temperature leading to very interesting properties: while the majority-spin electrons are metallic, the minority-spin electrons form an insulating state. We clarify that this state is due to partial Kondo screening, so that parts of the local moments are bound to the electrons, resulting in a dynamically-induced commensurability which is essential for producing the gap in the minority-spin electrons. We believe that the mechanism proposed here, the dynamically generated commensurability, is generic for the ferromagnetic phase in the antiferromagnetically coupled Kondo lattice model, thus providing new insights into the zero temperature physics for the Kondo lattice model.   

Phase diagram of half-filled $J_1-J_2$-Heisenberg Kondo lattice model on honeycomb lattice

Recent studies in quantum critical heavy fermion metals have opened up a rich phase diagram. The zero-temperature global phase diagram involves a combination of phases, featuring Kondo screening/destruction and antiferromagnetic order/disorder as the quantum fluctuations of the local moments are tuned relative to their Kondo coupling with the spins of the conduction electrons. Recently, we have studied a one-dimensional Heisenberg-Kondo model to reveal a competition between a Kondo-screened paramagnetic phase with a large Fermi surface and a Kondo-destroyed paramagnetic spin-Peierls phase with a small Fermi surface [1]. To take advantage of the intuitions gained through that work, we study here a half-filled, $J_1-J_2$ Heisenberg-Kondo lattice model on a honeycomb lattice. We have obtained a rich phase diagram as a function of magnetic frustration and Kondo coupling. Apart from antiferromagnetic and Kondo insulators, we also find Kondo-destroyed phases that are semi-metallic with Fermi points. There are also particular critical points which are gapless in both charge and spin sectors. \\[4pt] [1] P. Goswami and Q. Si, Phys. Rev. Lett. {\bf 107}, 126404 (2011).   

Cluster dynamical mean-field study of charge ordering in the Kondo lattice model at quarter filling

The Kondo lattice model is one of fundamental models for heavy-fermion systems, where exchange interactions between itinerant electrons and localized spins play an important role. Among many different phases described by this model, an interesting possibility is a charge-ordered state, in particular when considering the fact that the model does not include any bare repulsive interaction between electrons. The possibility was first pointed out by a perturbation expansion in the strong Kondo coupling limit at quarter filling~[1], and recently examined by the dynamical mean-field theory in infinite dimensions~[2]. However, it remains unclear whether the charge-ordered state still survives in two or three dimensions and what type of magnetic order is accommodated in the charge-ordered state. To clarify these issues, we investigate the quarter-filled Kondo lattice model on a square lattice by using cluster dynamical mean-field theory, which can include both spatial and dynamical correlations. We found that charge-ordered state appears in the intermediate coupling region. We will discuss electronic and magnetic properties in the charge-ordered state in detail.\\[4pt] [1] H. E. Hirsch, Phys. Rev. B {\bf 30}, 5383 (1984).\\[0pt] [2] J. Otsuki {\it et al}., J. Phys. Soc. Jpn. {\bf 78}, 034719 (2009).   

Phase diagram of the non-centrosymmetric Kondo lattice model

Kondo lattice model is prototypical for studying materials with localized f-electrons such as heavy-fermion compounds that exhibit a competition between Kondo screening and magnetism. This competition was argued to be crucial for superconductivity in these systems. We study the effects of spin-orbit interaction (SOI) in the conduction band (due to the lack of inversion symmetry), on the interplay between Kondo, superconducting and magnetic phases by considering the $S=1/2$ 2D Kondo lattice with short-range Heisenberg coupling between localized moments and utilizing a pseudo-fermion hybridization mean-field theory. In particular, we demonstrate that the heavy-fermion state, and hence superconductivity, is suppressed with increasing SOI. Our results are of relevance for ${\rm Ce}$- and ${\rm U}$-based heavy-fermion superconductors without inversion symmetry.   

Simulation of the triangular Kondo-lattice model using the gradient kernel polynomial method

We introduce a method to study systems, such as the Kondo-lattice model, where a classical field is coupled to fermionic degrees of freedom. Such systems are computationally challenging because each change to the classical field requires recalculation of the density of states for the bilinear fermionic Hamiltonian. The kernel polynomial method (KPM) is a useful tool to approximate the density of states at a cost linear in the system size. We extend KPM to approximate the gradient of the density of states at the same cost, allowing fast updates of the entire classical field. Simulations of the triangular Kondo-lattice model indicate phases with exotic non-coplanar spin ordering and spontaneous quantum Hall effect.   

Monte Carlo simulations of magnetic clustering at a quantum critical point

We present the results of Monte Carlo simulations on a percolating magnetic system with relevance to quantum critical point materials. It has previously been shown that, for heavily doped quantum critical point compounds such as Ce(Ru$_{0.24}$Fe$_{0.76})_{2}$Ge$_{2}$, the formation and dynamics of magnetic clusters strongly influences the physical response of the system at low temperature. Our simulation is based on the idea that finite-size effects force small magnetic clusters to order at comparatively high temperatures and, once formed, are impervious to Kondo shielding. Disorder acts to introduce a distribution of Kondo temperatures which, in turn, governs the formation of clusters as the temperature is lowered. We implement a percolation model based on such a distribution-- first introduced by Bernal et al.-- and with a restriction whereby Kondo shielding is allowed to remove moments from the infinite cluster \textit{only}. We investigate how this influences thermodynamic quantities as well as how well the simulations align with our analytic theory that is based on the same restriction.   

Monte Carlo study of a spin-ice type Kondo lattice model on a pyrochlore lattice

Recent experiments on geometrically frustrated metallic oxides, such as pyrochlore oxides R$_2$Mo$_2$O$_7$ and R$_2$Ir$_2$O$_7$, have drawn increasing interest in the effect of geometrical frustration in itinerant electron systems. In these systems, the coupling between electrons and frustrated magnetism leads to various fascinating phenomena. However, much less theoretical studies have been done by treating the interplay of localized spins and itinerant electrons in an unbiased manner. To clarify electronic and magnetic behaviors in such spin-charge coupled systems on frustrated lattice structures, we investigate a spin-ice type Kondo lattice model on a pyrochlore lattice by a real-space Monte Carlo simulation. By employing a sophisticated algorithm, we conduct calculations up to 2048 sites. We show that the system exhibits keen competition between various magnetic phases depending on the spin-charge coupling and electron density. As a consequence, the system shows rich phase diagram with complex magnetic orderings and phase separations between them. Furthermore, in applied magnetic field, we identify a magnetization plateau for one of the novel magnetic phases. In the presentation, the phase diagram and the mechanism of the magnetic orderings will be discussed in details.   

O(3)-symmetric variational wave functions for the Kondo lattice model

We construct and investigate a class of correlated wave functions for the Kondo lattice model. The construction is based on the faithful fermionic representation of the Kondo lattice model that was introduced recently by the author in PRB 83, 235103 (2011). In the limit of small exchange coupling the wave functions allow for both local singlet correlations between the localized moments and the conduction electrons, as well as an essentially arbitrary spin correlation function for the localized moments. We compare and contrast our results with those of previous studies.   

Session T17: Focus Session: Electron, Ion, and Exciton Transport in Nanostructures - Quantum Transport II

AC Bias Spectroscopy of the Kondo Singlet in a Single Electron Transistor

We have measured the nonlinear differential conductance, G, of a single electron transistor in the spin 1/2 Kondo regime in presence of an oscillating source voltage. In two distinct regimes, hf $>$ k$_B$T$_K$ and hf $\ll$ k$_B$T$_K$, where f is the oscillation frequency and T$_K$ is the Kondo temperature, comparison to the static model of Kondo transport reveals agreement at very low frequencies and an increasing systematic departure at high frequencies. When hf > k$_B$T$_K$, the G defined as the derivative of the time averaged current through the device with respect to the average bias drastically differs from the static model. We show that the effect cannot be explained by an increase in the electron temperature.   

Connection between Local moment and Underscreened Kondo effect in parallel double quantum dots

Double quantum dots connected in parallel to a single channel, have been studied theoretically in two disparate limits: (I) Systems in which each dot has strong Coulomb interactions, exhibiting an underscreened spin-1 Kondo effect [1]; (II) An interacting dot 1 and a non-interacting dot 2, showing a quantum phase transition between Kondo phase and non-Kondo local-moment [2]. In this work, we use the numerical renormalization group approach to study a strongly interacting ``quantum dot 1'' and a weakly interacting ``dot 2'' connected in parallel to metallic leads. Gate voltages can drive the system between Kondo-quenched and free-moment phases separated by Kosterlitz-Thouless quantum phase transitions. As interactions in dot 2 become stronger relative to the dot-lead coupling, the free moment evolves from an isolated spin-1/2 in dot 1 to a many-body doublet arising from an underscreened Kondo effect. These limits, which feature very different entanglements between dot and lead electrons, can be distinguished by conductance measurements at finite temperatures. \\[4pt] [1] D. E. Logan, C. J. Wright, and M. R. Galpin, PRB 80, 125117 (2009).\\[0pt] [2] L. G. G. V. Dias da Silva et al., PRL 97, 096603 (2006).   

Temperature Dependence of a Double Quantum Dot Kondo Effect

Lateral quantum dots are highly tunable experimental systems ideal for exploring the interplay of orbital, spin, and charge correlations. We present studies of a double quantum dot system in a GaAs/AlGaAs heterostructure where transport through each dot may be measured independently. In the limit of negligible inter-dot tunneling, the conductance through both dots is enhanced along inter-dot charge degeneracy lines, where the energy cost for an electron to be on either dot is the same [A. H\"{u}bel, et al. PRL 101, 186804 (2008)]. With spin degeneracy, there are expected to be four or five-fold degenerate states, depending on the parity of the electron occupation number of each dot. We attribute the enhanced conductance to a double-dot Kondo effect that screens these localized, degenerate states. The temperature dependence of this Kondo effect is studied as a function of the coupling strength of each dot to its leads and the parity of the electron occupation numbers.   

Phase-dependent coherence and transport effects in a double-dot Aharonov-Bohm interferometer

We study coherence dynamics between two sites comprising a double-dot interferometer attached to non-equilibrium leads. We demonstrate via numerical simulation that a magnetic flux passing through the interferometer results in phase-dependent decoherence in the case of degenerate dots. The precise details of these effects relies on an interplay between Markovian and non-Markovian dynamics. We employ various methods to further investigate these effects analytically, including the derivation of a quantum Langevin equation and a direct calculation of the relevant correlation functions. In addition, we investigate multi-particle scattering states in the same system.   

Electrostatic modulation of periodic potentials in a two-dimensional electron gas: from antidot lattice to quantum dot lattice

We use a dual gated device structure to introduce a gate-tunable periodic potential in a GaAs/AlGaAs two dimensional electron gas (2DEG). Using a suitable choice of gate voltages we can controllably alter the potential landscape in the 2DEG, thereby inducing either a periodic array of antidots or quantum dots. Antidots are artificial scattering centers, and therefore allow for a study of electron dynamics. On the other hand, a quantum dot lattice provides the opportunity to study correlated electron physics. We use a variety of electrical measurements such as magneto-resistance, thermo-voltage and current-voltage characteristics to probe these two contrasting regimes.   

Universal out-of-equilibrium transport in Kondo-correlated quantum dots: a renormalized superperturbation theory on the Keldysh contour

The non-linear conductance of semiconductor heterostructures and single molecule devices exhibiting Kondo physics has recently attracted attention [1,2]. We address the observed sample-dependence across various systems by considering additional electronic contributions present in the effective low-energy model underlying these experiments. To this end we develop a novel version of the superperturbation theory [3] in terms of dual fermions on the Keldysh contour. We analyze the role of particle hole asymmetry on the transport coefficients. Our approach [4] systematically extends the work of Yamada and Yosida and others to the particle-hole asymmetric Anderson model and reproduce the exactly solvable resonant level model and the special case considered in [5]. It correctly describes the strong coupling physics and is free of internal inconsistencies that would lead to a breakdown of current conservation. \\[4pt] [1] M. Grobis et al., Phys. Rev. Lett. 100, 246601 (2008).\\[0pt] [2] G. D. Scott et al., Phys. Rev. B 79, 165413 (2009).\\[0pt] [3] H. Hafermann et al., EPL 85, 27007 (2009).\\[0pt] [4] Enrique Munoz, C.J. Bolech, and Stefan Kirchner, submitted (2011).\\[0pt] [5] K. Yamada, Prog. Theo. Phys. 62, 354 (1979).   

Muli-state operation in quantum dot channel FETs incorporating spatial wavefunction-switching

Three-state behavior has been demonstrated in Si and InGaAs quantum dot gate (QDG) field-effect transistors\footnote{S. Karmakar, \textit{et al.}, J. Electronic Materials, 40, 1746, 2011.}$^,$\footnote{F Jain, J. Electronic Materials, 40, 1717, 2011.} (FETs). Recently, spatial wavefunction switched\footnote{Ibid.} (SWS) and quantum dot channel\footnote{F. Jain et al., Proc. II-VI Workshop, Oct.2011.} (QDC) FETs have been reported to exhibit four-state operation. This paper presents simulations of versatile combinations of SWS features in QDC channels to optimally design multi-state transport in FETs that have the potential of scaling to sub-12nm regime. A QDC-FET channel is modeled as having superlattice-like mini-energy bands where the carrier wavefunctions are transferred across the channel as drain voltage is changed, producing step-like multi-state electrical characteristics. This behavior is analogous to that of single electron transistors.\footnote{S. J. Shin, et al., Appl. Phys. Lett. 97, 103101, 2010.} The difference is that QDC devices use more than a few electrons and operate at room temperature. The SWS feature additionally provides carrier transfer from lower to upper dot layer(s) in a QDC having more than one layer of quantum dots.   

Tunneling in double quantum dots and rings: search for chaos assistance

Semiconductor heterostructures as quantum dots (QD) or quantum rings (QR) demonstrate discreet atom-like energy level structure. In the case of double QD (DQD) or double concentric QR (DCQR), a single electron spectrum is composed of a set of quasi-doublets [1]. We study influence of these specific spectrum properties on electron tunneling related to the electron transport through DQD (DCQR). The double InAs/GaAs quantum dots (rings) are considered within three dimensional single sub-band effective approach [2]. Tunneling between dots (rings) is evaluated by effect of inter-dot distance and QD (QR) geometry. We show that the quasi-doublets of the electron spectra define tunneling properties of the DCQR. Violation of symmetry of the DCQR geometry leads to increase of tunneling. Discussed will be also the chaos assisted tunneling in the double QD (DCQR). \\[4pt] [1] I. Filikhin, S. G. Matinyan and B. Vlahovic, Phys. Lett. A 375, 620 (2011); I. Filikhin, S. G. Matinyan, J. Nimmo and B. Vlahovic, Physica E 43, 1669 (2011). \\[0pt] [2] I. Filikhin, V. M. Suslov and B. Vlahovic, Phys. Rev. B 73, 205332 (2006).   

First-principles study of orbital-dependent quantum confinement in Si/Ge nanowire superlattices

We study electronic structures of H-passivated Si/Ge nanowire superlattices (NWSLs) oriented along [110] direction, using an \textit{ab-initio} pseudopotential density-functional method with the local density approximation. Obtained electronic structures of the Si/Ge NWSLs show both dispersive and non-dispersive bands in conduction and valence bands due to band-selective quantum confinement: the highest valence band and the lowest conduction band are not confined in either the Si- or Ge-nanowire segment but they are extended throughout the whole NWSLs, while there exist non-dispersive bands confined in either Si- or Ge-nanowire segment below the top of the valence band and above the bottom of the conduction band. This feature originates from strong orbital-dependence of quantum confinement of electronic states, making conventional band-offset diagrams for superlattices invalid in Si/Ge NWSLs. Effects of atomic geometries on the confinement are studied with different diameters and superlattice periodicities. This work was supported by NRF of Korea (Grant Nos. 2009-0081204 and 2011-0018306). Computational resources have been provided by KISTI Supercomputing Center (Project No. KSC-2011-C3-05).   

One-dimensional physics in transition-metal nanowires

One atom wide transition-metal nanowires can now be fabricated on Cu step edges. We present a theoretical study of the electronic properties of such systems. While the systems fall within the broad class of Luttinger liquids, about which much is known, characteristic features of transition metals including orbital degeneracy and interactions which favor locally high-spin configurations lead to new physics. Density functional calculations indicate that Co nanowires on Cu surfaces are half metals and are not electronically isolated from the substrate material. The multi-orbital and local high-spin physics are elucidated by Hartree-Fock approximations and bosonization calculations of the multi-orbital Hubbard model.   

Detection of spin states in a quantum dot by random telegraph signal analysis with the hidden Markov model

A lateral GaAs quantum dot with an adjacent quantum point contact charge sensor was tuned so that its chemical potential is close to the Fermi level of an adjacent electron reservoir. In this configuration electrons tunnel back and forth between the quantum dot and the reservoir due to thermal fluctuations, characteristic switching known as a random telegraph signal (RTS). The charge state of the quantum dot is directly observable, but spin and orbital state information is not. Such extra states may reveal themselves in the statistics of the timing of tunneling events. We present a statistical analysis approach based on the Hidden Markov Model (HMM) for extracting information about the internal structure of the quantum dot from RTS data, particularly focusing on determining the electronic spin state. We demonstrate on simulated and experimental data that this technique can detect electron spin states and measure their tunneling rates individually when the energy level difference is less than or comparable to the thermal energy scale. This opens a new regime for studying quantum dot spin physics because other experiments require a Zeeman energy difference greater than the thermal energy in order to distinguish the spin states.   

Impact of adsorbed organic monolayers on vacuum electron tunneling contributions to electrical resistance at an asperity contact

Electrical Contact Resistance measurements are reported for RF MEMS switches situated within an ultrahigh vacuum system equipped with \textit{in situ} oxygen plasma cleaning capabilities. Measurements were preformed on Au/Au permanently adhered switches, and functioning Au/RuO$_{2}$ switches in the presence and absence of adsorbed monolayers of pentane and dodecane. The data are analyzed to explore how adsorbed molecules in regions close to the contact may impact vacuum tunneling contributions to the experimentally measured resistance: (1) The resistance associated with direct contact in parallel with a vacuum tunneling path, which upon uptake of the monolayer is replaced by the molecular resistance, and (2) A series connection of the direct contact resistance with the molecular layer after adsorption occurs, with the vacuum tunneling path assumed to be negligible. The results favor scenario (1), whereby uptake of the molecular layer effectively shuts down the vacuum tunneling path, which in this case is effectively $\sim $30 Ohms in the absence of an adsorbed film. The methods constitute a new and original approach to documenting vacuum tunneling levels in regions of close proximity. Funding agencies: NSF, AFOSR MURI, DARPA. \\[4pt] [1] D. Berman, M. Walker, C. Nordquist, J. Krim, \textit{J. Appl. Phys.,} in press   

Dependence of Conductance Resonanoces and Modulations on Channel Length in Asymmetric Quantum Point Contacts (QPCs)

Transport features below $2e^2/h$ show resonance peaks in highly asymmetric QPCs. As we increace the channel length, the number of peaks observable also increases. We characterize the number of peaks and/or oscillations as a function of channel length, when the QPC is tuned to or below the first quantum channel. The the number of peaks/oscillations appears to increase on average as the channel length increases. In addition, we find preliminary evidence that there is a correspondence between the resonance peaks and the zero-bias anomaly(ZBA) in the differential conductance. These behaviors are consistent with an interpretation based on the formation of quasi-bound-states within the QPC channel in the single-mode limit.   

New scenario of shuttling mechanism in magnetic nano-electromechanical single-electron tunneling systems

We investigate a new shuttling scenario in the electro-mechanics of a movable quantum dot between a nonmagnetic lead and a magnetic lead. In this device, the quantum dot has two energy levels due to the Zeeman energy splitting under magnetic field with Coulomb blockade. The electromechanical instability is shown to depend on the external voltage when the vibrating energy overcomes the dissipation energy of the system. In addition to the normal shuttling behavior, the shuttling current can be suppressed and then recovered depending on the external voltage. It is also found that the nano-electromechanical oscillation significantly improves the spin polarized current compared with one in the fixed quantum dot due to the interplay between the spin polarized transport and mechanical degree of freedom.   

Session T18: Focus Session: Interfaces in Complex Oxides - Superconductivity and Magnetism at Interfaces

Local imaging of the superfluid density at the LAO/STO interface as a function of gate voltage

The interface between two insulating oxides, LaAlO$_{3}$ and SrTiO$_{3}$, exhibits a two-dimensional electron system with high mobility, magnetism, superconductivity at low temperatures, and an electric-field-tuned superconductor-insulator transition. This interface has been studied extensively using transport and magnetization, which do not directly probe potential variation on a local length scale. We use a scanning SQUID microscope to locally probe superconductivity and magnetism in LAO/STO heterostructures. We measure the local diamagnetic susceptibility and critical temperature of as a function of position and gate voltage. Our local susceptibility measurement is related to the density of superconducting carriers which gives us a map of superfluid density. We find that the superfluid density is inhomogeneous, showing regions of susceptibility that varies over a large fraction of the total response while the critical temperature remains relatively uniform across the sample. Tracking the evolution of both of these parameters as a function of gate voltage and position enables investigation of the local onset of the superconductor-insulator transitions on both sides of the dome.   

Magnetism and superconductivity at LAO/STO-interfaces: the role of Ti 3d interface electrons

Ferromagnetism and superconductivity are in most cases adverse. However, recent experiments reveal that they coexist at interfaces of LaAlO$_{3}$ and SrTiO$_{3}$ [1]. We analyze the ferromagnetic state within density functional theory and provide evidence that it is also generated by Ti 3d interface electrons, as is the two-dimensional electron liquid at the interface which gives rise to superconductivity [2]. We demonstrate that oxygen vacancies in the TiO$_{2}$ interface layer enhance the tendency for ferromagnetism considerably. This allows for the notion that areas with increased density of oxygen vacancies produce ferromagnetic puddles and account for the previous observation of a superparamagnetic behavior in the superconducting state [3].\\[4pt] [1] Lu Li, C.Richter, J.Mannhart, and R.C.Ashoori, Nature Physics 7, 762 (2011).\\[0pt] [2] N. Reyren et al., Science 317, 1196 (2007).\\[0pt] [3] N.Pavlenko, T.Kopp, E.Y.Tsymbal, G.A.Sawatzky, and J.Mannhart, cond-mat/arXiv:1105.1163 (2011)   

Superconductivity and magnetism in the presence of interface-induced Rashba spin-orbit coupling

Two dimensional electron systems at oxide interfaces are often influenced by a Rashba type spin-orbit coupling (SOC), which is tunable by a transverse electric field. Ferromagnetism at the interface can simultaneously induce strong local magnetic fields. This combination of SOC and magnetism leads to anisotropic two-sheeted Fermi surfaces, on which superconductivity with finite-momentum pairing is favored. The superconducting order parameter is derived within a generalized pairing model realizing both, the FFLO superconductor in the limit of vanishing SOC and a mixed-parity pairing state with zero pair momentum if the magnetism vanishes. The nature of the pairing state is discussed in the context of interface superconductivity and ferromagnetism at LAO-STO interfaces [1,2]. \\[4pt] [1] Lu Li, C. Richter, J. Mannhart, and R. C. Ashoori, Nature Physics \textbf{7}, 762 (2011) \\[0pt] [2] J. A. Bert, B. Kallisky, C. Bell, M. Kim, Y. Hikita, H. Y. Hwang, and K. A. Moler, Nature Physics \textbf{7}, 767 (2011)   

Superconductivity and magnetism in a three-band model of the LAO/STO interface from a weak-coupling perspective

Recent experiments on LAO/STO interfaces have shown the occurrence of both superconductivity and magnetism in this system. Motivated by these experiments, we analyze various Fermi-liquid instabilities in a three-band model of the LAO/STO interface with purely repulsive interactions by calculating susceptibilities for superconducting, magnetic and nematic orders. In light of recent transport experiments proposing a Lifshitz transition between d orbitals, we particularly study how the susceptibilities depend on the chemical potential. Further, we investigate the interplay of these different orders.   

Magnetism of LaAlO$_3$/SrTiO$_3$ Heterostructure Interface

The LaAlO$_3$/SrTiO$_3$ heterostructure is a potential candidate for a high mobility two-dimensional electron system with novel electronic and magnetic properties. Magnetic ordering has been proposed to arise from d-shell electrons transferred by the polarization discontinuity at the interface. However the magnetization of this system cannot easily be detected with standard techniques due to the small volume of the interfacial region. Using torque magnetometry, we measure the magnetic moment of the interface system directly. Our results indicate the existence of a magnetic ordering at the two-dimensional conductive interface. The ferromagnetic-like ordering state persists up to 200 K. Such a state is hardly explained by ion-exchange at the interface, since LaTiO$_3$ is antiferromagnetic. Moreover, the same magnetic behavior persists even when the sample is superconducting, which suggests an unconventional two-dimensional superconducting phase.   

Signatures of local superconducting islands at elevated temperatures in LaAlO$_3$/SrTiO$_3$ Heterostructure Interface

Superconductivity has been observed in LaAlO$_3$ /SrTiO$_3$ heterostructures below 300 mK in resistivity measurements and later confirmed with Meissner effect. Our detailed magnetization measurements in several LaAlO$_3$/SrTiO$_3$ samples indicate a quasi superconducting state persisting up to 4 K. In these samples, we discovered large nonreversible magnetization vs. field curves. Moreover, the magnitude of the nonreversible loop is proportional to sweep rates, suggesting that it is caused by local magnetic moments generated by eddy currents. Based on this eddy current picture, the inferred conductance is found to be 7 orders of magnitude larger than the conductance across the whole interface. This contrast suggests the existence of small local quasi superconducting regions at a temperature of 4 K, well above the long range superconducting transition temperature.   

Superconductivity and Ferromagnetism in Oxide Interface Structures: Possibility of Finite Momentum Pairing

We present a model that captures the physical properties of the interface between two oxides, LaAlO$_3$ and SrTiO$_3$. Despite extensive experimental studies of these systems, no clear theoretical picture has emerged so far. The model that we suggest for the interface electrons explains the main experimental observations. In particular, we address one of the most intriguing phenomena observed in these system: the coexistence of ferromagnetism and superconductivity. Ordinarily this ferromagnetism would destroy superconductivity, but due to strong spin-orbit coupling near the interface, the magnetism and superconductivity can coexist by forming an FFLO-type condensate of Cooper pairs at finite momentum. Surprisingly, this unconventional superconducting state survives even at strong disorder.   

Tuning the ferromagnetism in LaAlO$_{3}$/SrTiO$_{3}$

The interface of LaAlO$_{3}$/SrTiO$_{3}$ heterostructures exhibits both conductivity and magnetism. Significant effort has been invested researching the details and characteristics of the conductivity, such as conductance only above a critical LaAlO$_{3}$ thickness. However, reports of ferromagnetism differ in a variety of details requiring further investigation into the material properties that control magnetism. In this study we use a scanning SQUID microscope to locally image the landscape of ferromagnetism as a function of several tuning parameters including the LaAlO$_{3}$ thickness, back gate voltage, local strain and surface treatment. We find that the ferromagnetism is inhomogeneous within each sample, varies considerably between samples, and appears only in samples whose LaAlO$_{3}$ layer is thicker than a threshold value, similar to the conductance critical thickness. The ferromagnetism changes with local strain, surface treatment with polar solvents and applied field. However it is not affected by changing the gate voltage or cycling the temperature up to 300K. These results provide experimental input for determining and controlling the mechanisms of magnetism in engineered complex oxide interfaces.   

Strong magnetic interaction in localized two-dimensional electron gas in LaAlO$_3$/SrTiO$_3$/NdGaO$_3$ heterostructures

Via reducing the thickness of SrTiO$_3$ layer, strong localization of two-dimensional electron gas is artificially introduced at LaAlO$_3$/SrTiO$_3$ interface grown on NdGaO$_3$ (110) substrates. This localization is characterized by the low carrier density, robust insulating ground state and variable range hopping behavior at low temperature. Given the spatially-limited conducting channel in the thin SrTiO$_3$ layer, the degeneration of Ti 3d orbitals at the interface should be responsible for this strong localization. Moreover, the typical butterfly-like hysteresis loop and unusual anisotropic features in magnetoresistance observed in the thinner SrTiO$_3$ samples indicate the enhanced magnetic interaction in this strongly localized two-dimensional electron gas.   

Investigation of electric field induction of superconductivity at complex oxide interfaces

We examine the modified electronic states and change in carrier density at the interfaces of complex oxide films produced by an external electric field. Using a Ginzburg-Landau formalism and ab-initio calculations, we show that linear coupling of an electric potential can influence the superconducting order parameter and induce a transition to a superconducting phase. Further, we examine the correlation between carrier density and the superconducting critical temperature $T_c$ by investigating capacitance and density of states with changing electric potential. We will discuss implications of this work in the context of interfaces formed by LaAlO3 and SrTiO3 thin films. This approach points to an alternative path to superconducting devices with tunable transition temperature. Work was carried out under the help and support of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under Contract No. DE-AC52-06NA25396.   

Evidence for charge-vortex duality at the LaAlO$_3$-SrTiO$_3$ interface

The conducting gas formed at the inteface between LaAlO$_3$ and SrTiO$_3$ undergoes a superconductor to insulator transition (SIT) on the application of a back gate voltage, $V_g$. The system also shows evidence of ferromagnetic order coexisting with superconductivity.\footnote{Dikin \textit{et al}, PRL \textbf{107}, 056802 (2011)} The juxtaposition of the ferromagnet with the conducting gas allows for the observation of a novel manifestation of charge-vortex duality. The field due to the magnetization dynamics in the ferromagnet causes a sharp \textit{increase} in resistance on the superconducting side of the transition, in the magnetoresistance measurements, and a sharp \textit{decrease} in resistance on the insulating side. The system can be modeled as an array of Josephson junctions, with two characteristic energy scales: a Josephson coupling energy $E_J$, and a Coulomb charging energy $E_c$. $V_g$ then tunes the ratio, $E_J/E_c$, to cause the transition. We will present external field sweep-rate dependent magnetoresistance data on both sides of the transition to elucidate the nature of the superconducting and insulating states.   

Single-Mode Cooper Pair Channel in LaAlO$_3$/SrTiO$_3$ Nanowires

The conducting LaAlO$_{3}$/SrTiO$_{3}$ interface becomes superconducting\footnote{N. Reyren, \textit{et al.}, Science \textbf{317}, 1196-9 (2007).} below a critical temperature T$_{c}\sim$100-400~mK. Here, we investigate the transport characteristics of LaAlO$_{3}$/SrTiO$_{3}$ structures formed from $\sim$10 nm-wide nanowire segments produced by a conductive atomic force microscope lithography technique\footnote{C. Cen, S. Thiel, K. E. Andersen, C. S. Hellberg, J. Mannhart, and J. Levy, Nature Materials \textbf{7}, 2136 (2008).}. Above T$_{c}\sim$200~mK we find a characteristic four-terminal conductance $G\sim e^{2}/h$ that is independent of the channel length. Below T$_{c}$ we find that the conductance increases to $G\sim 4e^{2}/h$. This increase is attributed to the formation of Cooper pairs that propagate in a single mode. We also discuss the interactions between Cooper pairs and spin-polarized transport in these structures. This work is supported by AFOSR (FA9550-10-1-0524).   

Two doped holes with different distributions in $\rm Sr_{2}CuO_{4-\delta}-La_{2}CuO_{4}$ superlattices

X-ray absorption in $\rm Sr_{2}CuO_{4-\delta}-La_{2}CuO_{4}$ (SCO-LCO) superlattices shows a variable occupation with doping of two hole states. In addition to the holes doped for $x [Preview Abstract]

Highly Spin-Polarized Conducting State at the Interface between Nonmagnetic Band Insulators: LaAlO3/FeS2 (001)

Interface engineering of complex oxide heterostructures allows creating interfaces with properties and functionalities distinct from those typical for the respective bulk constituents. In the spirit of the well known conducting LaAlO3/SrTiO3 interface we study a similar interface with the added functionality of being unambiguously ferromagnetic. Our first-principles density functional calculations demonstrate that such a spin-polarized two-dimensional conducting state can be realized at the (001) interface between the two non-magnetic band insulators FeS2 and LaAlO3. The (001) surface of FeS2(pyrite), a diamagnetic insulator, supports a localized surface state deriving from the Fe d-orbitals near the conduction band minimum. We find that, similar to the LaAlO3/SrTiO3 system, the deposition of a few unit cells of the polar perovskite oxide LaAlO3 leads to electron transfer into these surface bands, thereby creating a conducting interface. The occupation of these narrow bands leads to an exchange splitting between the spin sub-bands, yielding a highly spin-polarized conducting state quite distinct from the rest of the non-magnetic, insulating bulk. [Ref: J. D. Burton and E. Y. Tsymbal, Phys. Rev. Lett. 107, 166601 (2011).]   

Session T19: Kavli Foundation Special Session: Emergent Physics at the Mesoscale

Mesoscopic Lawlessness

Whether physics will contribute significantly to unraveling the secrets of life, the grandest challenge of them all, depends critically on whether proteins and other mesoscale objects exhibit emergent law. By this I mean quantitative relationships among their measured properties that are always true. The jury is still out on the matter, for there is evidence both for and against, but it is spotty, on account of the difficulty of measuring 100 nm - 1000 objects without damaging them quantum mechanically. It is therefore not clear that history will repeat itself. Physics contributed mightily to 20th century materials science through its identification and mastery of powerful macroscopic emergent laws such as crystalline rigidity, superconductivity and ferromagnetism, but it cannot do the same thing in biology, regardless of how powerful computers get, unless nature cooperates. The challenge before us as physicists is therefore not to amass more and more terabytes of data and computational output but rather to search for and, with luck, find operating principles at the scale of life greater than those of chemistry, which is to say, greater than a world ruled by nothing but miraculous accidents.   

Ultracold, trapped atomic gases as material systems

Laser cooling and evaporative cooling of neutral atomic gases has led to the creation of quantum degenerate Bose and Fermi gases that constitute a new class of material systems. Many of the features of the Hamiltonians governing the behavior of these systems can be controlled and manipulated in experiments. The necessarily finite sizes of such systems are often mesoscopic in the sense that they are large enough that collective effects are important, yet small enough that the size plays a role in determining the systems' behavior. Among the experimental tools available are optical lattices, synthetic fields, and the ability to change the size and dimensionality of the system. Ultracold gases can realize some of the idealized Hamiltonians used to model condensed matter systems, creating a quantum simulation of such models, which may be calculationally intractable. Atomic gases can also provide new condensed-matter-like systems that have no analogs in real condensed matter.   

Session T20: Invited Session: Advanced Characterization of Transistor Gate Stacks and Interfaces

Directions in High-k Gate Stacks: From Silicon Chips to Carbon Nanomaterials

The successful implementation of high-k/metal gates for silicon CMOS has culminated a decade of research on metal-oxide interactions with silicon. The ability to profile materials on a nanometer length scale has greatly assisted our ability to tailor electrical properties to create functional devices. Initial concerns addressed with composition profiling (e.g. Si content, Hf diffusion, thermal stability) have been replaced by more advanced questions. For example, gate-first technologies often use threshold-modifying layers, whose electrical properties are closely linked with their depth distribution. Oxygen diffusion is another complex problem of current concern, where physical characterization by isotopic tracing has given valuable insights. A similar set of challenges will confront us in creating carbon-based devices. Much effort is focused on nucleation of dielectrics, along with stability and interactions with the channel. This parallels work in the early development of high-k/Si. This talk will review some important lessons from the past decade, and discuss how we can apply this knowledge to creating improved graphene-channel devices.   

Nanometer-scale properties of metal/oxide interfaces and ``end-on'' metal contacts to Si nanowires studied by ballistic electron emission microscopy (BEEM)

BEEM is a hot-electron (HE) technique based on scanning tunneling microscopy that can probe buried metal/semiconductor and metal/dielectric interfaces with nm-scale spatial resolution and energy resolution of a few meV. BEEM is a three-terminal technique, so the HE energy and interface electric field can be varied independently. I will discuss two studies of interest for future transistor technologies. The first concerns the band structure and alignments in a 20 nm-thick film of the high-k dielectric material Sc$_{2}$O$_{3}$ grown epitaxially on Si(111). Sc$_{2}$O$_{3}$ and related rare-earth/transition metal oxide films on Si were found to have similar band alignments and bandgap, and also ``tailing'' conduction band (CB) states extending $\sim $1 eV below the primary CB. We combined BEEM with internal photoemission to measure the band alignment and to study electron transport through these ``tail'' states.\footnote{W. Cai, S. E. Stone, J. P. Pelz, L. F. Edge, and D. G. Schlom, Appl. Phys. Lett \textbf{91}, 042901 (2007).} Surprisingly, these tail states were found to form a robust band of extended states that supports elastic hot-electron transport even \textit{against} an applied electric field. The second study concerns HE injection and transport through ``end-on'' metal contacts made to $\sim $100 nm diameter vertical Si nanowires (NWs) embedded in a SiO$_{2}$ dielectric. At low HE flux, We observed \textit{lateral variations} of the local Schottky Barrier Height (SBH) across individual end-on Au Schottky contacts, with the SBH at the contact edge found to be $\sim $25 meV lower than at the contact center. Finite-element electrostatic simulations suggest that this is due to a larger interface electric field at the contact edge due to positively charged Si/native-oxide interface states near the Au/NW contact, with this (equilibrium) interface state charge induced by local band bending due to the high work function Au contact. We also observed a strong \textit{suppression} of the hot-electron transmission efficiency at larger HE flux, likely due to (non-equilibrium) \textit{steady-state negative charge accumulation} in metastable traps at the Si/oxide interface located near the injecting metal contact. Ongoing BEEM measurements of metal contacts to SrTiO$_{3}$ substrates and films may also be discussed.\\[4pt] In collaboration with W. Cai, Y. Che, L. F. Edge, D. G. Schlom, E. R. Hemesath, and L. J. Lauhon.   

Metropolis Prize Talk: Defects in Al$_{2}$O$_{3}$ and their impact on III-V/Al$_{2}$O$_{3}$ MOS-based devices

As the dimensions of conventional silicon devices continue to shrink, novel approaches are required to achieve increasing performance demands. Recently Intel announced the implementation of a 3-D MOSFET geometry known as the tri-gate transistor for their 22 nm technology. In addition to different geometries, new materials will also be needed for future technologies. In this talk, we will consider the use of III-V channel materials, and novel gate dielectrics. Al$_{2}$O$_{3}$ is a promising dielectric for III-V devices. However, the presence of deep levels and fixed charge in the Al$_{2}$O$_{3}$ layer is a concern, with native defects being a potential source of traps, leakage, and fixed charge. We will present the results of hybrid density functional calculations for such defects. The energetic positions of defect-induced levels will be discussed in the context of the III-V/ Al$_{2}$O$_{3}$ interface. We find that native defects are a source of border traps, and fixed charge in the dielectric. We will also discuss the interaction of hydrogen with such defects, in the context of passivation. Our results indicate that hydrogen is effective at removing border traps, and helps to alleviate the problem of fixed charge. This work was performed in collaboration with A. Janotti and C. G. Van de Walle.   

Charge Traps at and near High-K Oxide/III-V Interfaces

The effort to achieve higher performance metal-oxide-semiconductor (MOS) devices prompts interest in new semiconductor channel materials such as indium gallium arsenide that can achieve larger drive currents than state-of-the-art Si field effect transistors, at low operating voltages. In order for InGaAs-channel transistors to approach their performance limits, however, high permittivity (high-k) metal oxide gate dielectrics must be prepared on the III-V surface in a manner that produces a minimal areal density of charge-trapping defects. This presentation will review different experimental approaches to prepare relatively passive interfaces between deposited oxides and GaAs or InGaAs. Both pre-oxide deposition and post-deposition methods will be summarized. It will also describe the influence of near-interface defects in the oxides (border traps) and why these particular defects are so significant for arsenide MOS devices. An attempt will be made to associate electrically-active traps detected at different energies in the III-V semiconductor bandgap with specific surface and point defects, based on prior reported experimental and computational observations. The difficulty of quantifying trap densities using typical capacitance-voltage and conductance-voltage methods developed for silicon MOS will be discussed.   

Electrical characterization of interfacial defects

Aggressive transistor scaling to achieve better chip functionality calls for the introduction of new dielectric and metal materials into traditional device gate stacks. The advanced gate stacks represent multilayer structures, the materials of which may strongly interact (primarily during high temperature processing), generating structural defects in these layers. These complex structures pose new challenges in interpreting electrical measurements, which are sensitive to even extremely small concentrations of electrically active defects. The critical task is, thus, to link the structural and electrical characteristics of these multicomponent gate stacks in order to identify and control defects affecting device performance. In this presentation, we focus on analyzing interfacial defects affecting electrical characteristics of the metal/high-k (HK) gate stacks, which are of major interest to the semiconductor industry. We first developed models of the physical processes governing the measurements of the electrical techniques we used that allowed us to extract the structural parameters of the defects from the electrical data. By comparing the extracted parameters to those obtained by ab initio calculations of the material structures, we identified the nature of the contributing defects. A recently proposed model for random telegraph noise (RTN) and frequency-dependent charge pumping (CP) measurements that takes into consideration the multi-phonon lattice relaxation induced by charge trapping/detrapping at the defect sites was employed to extract characteristics of the traps in the interfacial SiO2 layer in HfO2-based HK devices. Our results indicate that the electron capture/emission times are controlled by the lattice re-arrangement (caused by the trapped electrons) rather than by electron tunneling to/from the trap as generally assumed. The strong dependency of the measured values on defect relaxation and ionization energies allows these values to be extracted; the values can then be used as a defect identifier. Complementary modeling of the gate leakage current in HK devices during electrical stress using the same approach yields characteristics of the traps in the interfacial SiO2 layer contributing to trap-assisted tunneling (TAT). Based on the values obtained by RTN, CP, and TAT measurements, the electrically active defects were tentatively assigned to oxygen vacancies in various charged states. In all cases, stress-induced traps were generated exclusively in the interfacial layer of the HK stacks, consistent with earlier findings that HK dielectrics are more resistant to defect generation than SiO2. Based on these findings, as well as an earlier TEM/EELS study of the elemental composition of the breakdown path, we proposed that the breakdown path formation/evolution in the interfacial layer is associated with the growth of an oxygen-deficient filament facilitated by the grain boundaries in the overlaying high-k film. This model successfully describes the temperature-dependent evolution of interfacial layer degradation through various breakdown phases.   

Session T21: Magnetic Ordering and Dynamics in Cuprates

Two Dimensional Incommensurate and Three Dimensional Commensurate Magnetic Order and Fluctuations in $La_{2-x}Ba_{x}CuO_{4}$

We present neutron scattering measurements on single crystals of $La_{2-x}Ba_{x}CuO_{4}$, with $0 \leq x \leq$ 0.035. These experiments reveal the evolution of the magnetism: from a three dimensional (3D) commensurate (C) antiferromagnet, with a relatively high T$_{N}$, to a two dimensional (2D) incommensurate (IC) antiferromagnet with finite range static correlations, with relatively low effective T$_{N}$s. At low temperatures, the 2D IC magnetism co-exists with the 3D C magnetism for Ba concentrations as low as x = 0.0125. We find that 3D C magnetism disappears by x = 0.025; consistent with the limit of x $\sim$ 0.02 observed in the sister family of doped Mott insulators $La_{2-x}Sr_{x}CuO_{4}$. We construct a phase diagram based on magnetic order parameter measurements, which displays much of the complexity of standard high temperature superconductivity phase diagrams discussed in the literature. Analysis of high energy-resolution inelastic neutron scattering shows the low energy dynamic susceptibility to fall off with temperature on a scale much higher than the effective 2D IC T$_{N}$s in the sample. This effect is such that appreciable dynamic 2D IC magnetic fluctuations inhabit much of the ``pseudogap'' regime of the phase diagram.   

Novel magnetic excitations in the high-temperature superconductor HgBa$_{2}$CuO$_{4+ \delta }$

We report on the observation of novel magnetic excitations in the pseudogap phase of the cuprate superconductor HgBa$_{2}$CuO$_{4+\delta }$ (Hg1201) using neutron scattering, and on their relationship with antiferromagnetic (AF) fluctuations. Following polarized neutron diffraction experiments that demonstrated a novel (q=0) magnetic order in the pseudogap phase [B. Fauqu\'{e} \textit{et al.} PRL 96, 197001 (2006); Y. Li \textit{et al.}, Nature 455, 372 (2008)], our inelastic measurements revealed two weakly-dispersive magnetic excitation branches in Hg1201 [Y. Li \textit{et al.}, Nature 468, 283 (2010), and preprint]. These excitations are observed in the pseudogap phase and appear to be associated with the q=0 magnetic order. In our optimally-doped sample, the magnetic resonance occurs at the dispersion maximum of the higher-energy branch. In under-doped Hg1201, the two excitation branches exhibit local intensity maxima at q$_{AF}$, and we find evidence for an hourglass dispersion associated with the lower branch. These results reveal a profound connection between the novel excitations and the conventional AF fluctuations.   

Stripe order in La$_{2-x}$Ba$_{x}$CuO$_{4}$ in high magnetic fields

The observation of enhanced spin stripe order in the vortex cores of La$_{2-x}$Sr$_{x}$CuO$_{4}$ has been a landmark experiment that revealed the intimate connection between superconductivity and incommensurate antiferromagnetism. Only recently we have observed a corresponding field dependence of the spin and, more importantly, of the charge stripe order in La$_{2-x}$Ba$_{x}$CuO$_{4}$. Here we present our recent results from neutron diffraction, x-ray diffraction, and torque measurements in high magnetic fields. These helped us to establish the field versus temperature and doping phase diagrams for spin and charge order, and to further corroborate the stripe model as the more appropriate description than for example spiral and vortex states.   

Pressure study of local tilts and their correlation to stripe order in single crystal La$_{1.875}$Ba$_{0.125}$CuO$_{4}$

The strong Tc suppression in LaBaCuO at x=0.125 is widely believed to be related to formation of static stripes, at least partially driven by a strong electron-lattice coupling in a low temperature tetragonal (LTT) phase (Tranquada et al., Nature 375, 561 (1995)). A recent high-pressure experiment appears to challenge this view as it was observed that static stripe order persists to pressures higher than required to induce LTT to HTT transition (Hucker et al., PRL 104, 057004 (2010)). We carried out high-pressure La K-edge polarized XAFS measurements in LaBaCuO (x=0.125) single crystals in a diamond anvil cell to probe local CuO6 tilts. We observe that the local tilts remain LTT-like at high pressure, even though the macroscopic structure is HTT. The results suggest a significant order-disorder component to this pressure-induced phase transition, whereby the local LTT tilts remain present in the local scale but disorder over long range resulting in HTT symmetry seen by diffraction. The result may help explain why the stripe order is largely unaffected by the LTT to HTT pressure-induced transition. Work at Argonne (BNL) is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357 (DE-AC02-98CH10886).   

Gutzwiller Charge and Magnetic Phase Diagrams of Cuprates

We extend our previous analysis of the magnetic phase diagram of the cuprates to look for charge instabilities, either purely electronic or involving electron-phonon coupling, employing Gutzwiller approximation GA+RPA calculations of the Hubbard model. In the absence of phonons we find an overscreening instability for large doping at $(\pi ,\pi)$. In the presence of electron-phonon coupling, we find a rich response to Fermi surface nesting, very similar to the magnetic case, and in this case the instability criterion can be formulated as a generalized Stoner criterion. In the hole-doping regime, where evidence exists for a nonmagnetic (stripe) pseudogap, we find competing instabilities. Since the same susceptibility peaks are present for both spin and charge excitations, differences in preferred $q$-vectors arise from the $q$-dependence of the interaction $U_{eff,q}$.   

The impact of incommensurate bond centered density waves in underdoped cuprates

We study the particle-particle channel and the particle-hole channel of the valence bond fluctuations away from half filling in cuprates. Based on strong-coupling analysis of the t-J model, we argue that the superexchange interaction J induced incommensurate bond centered density wave order is the driving mechanism for the pseudogap state. We show that the interplay between the incommensurate bond centered density wave instability and the intrinsic electronic inhomogeneity in real cuprates materials is responsible for the observed pseudogap phenomena.   

Two-component electron fluid and pseudogap asymmetry in underdoped high-Tc cuprate superconductors

Evidence from NMR of a two-component spin system in the cuprate high-Tc superconductors is shown to be paralleled by similar evidence from the total electronic entropy so that a two-component quasiparticle fluid is implicated. We propose that this two-component behavior arises from reconstruction of the energy-momentum dispersion into two branches in the pseudogap regime. If correct then it follows that single-component electronic behavior will be recovered when the pseudogap closes in the overdoped regime. We illustrate this by calculating the spin susceptibility using the resonating valence bond spin liquid model developed by Yang, Rice and Zhang, finding excellent agreement with the NMR results. In addition, we find that the particle-hole asymmetric pseudogap of this model accounts for both the large thermoelectric power, and the downturn in resistivity observed in underdoped cuprates.   

Spin excitations in a layered antiferromagnetic metal

The proximity of antiferromagnetic order in high-temperature superconducting materials is considered a possible clue to the electronic excitations which form superconducting pairs. Here we study the transverse and longitudinal spin excitation spectrum in a one-band model in the pure spin density wave (SDW) state and in the coexistence state of SDW and superconductivity. We start from a Stoner insulator which is similar to the case of cuprate parent compounds. By changing the chemical potential and the SDW order parameter, we study the evolution of the spectrum with different Fermi surfaces, such as the one with only hole pockets, with only electron pockets and with pockets of both types. We also compute the spin excitations in the coexistence of the AF and d-wave superconductivity, motivated by electron-doped cuprates.   

Coexistence of Superconductivity and Magnetic Order in RuGd$_2$Sr(Cu$_{1-x}$Fe$_x$)$_2$O$_8$ probed by $^{99}$Ru and $^{57}$Fe M\"{o}ssbauer Effects

RuGd$_2$Sr$_2$Cu$_2$O$_8$ develops magnetic order at about 137K and becomes a superconductor at lower temperatures(T$_{SC} \sim$ 40K). T$_{SC}$ decreases with increasing Fe doping in RuGd$_2$Sr$_2$(Cu$_{1-x}$Fe$_x$)$_2$O$_8$ and is zero by $x=.03$. We measure the $^{99}$Ru and $^{57}$Fe M\"{o}ssbauer Effects for x=0, 0.1, 0.2, and 0.3. The $^{57}$Fe M\"{o}ssbauer spectra(MS) show that there are two different Fe sites at 4.2K with very similar hyperfine magnetic fields, $H_{hyper}\sim 48$ T. However $H_{hyper}$ goes to zero at $\sim$half the Fe sites in a temperature range between 30K and 40K in superconducting and non-superconducting samples. There is no significant change in $H_{hyper}$ in the $^{99}$Ru MS in this temperature range. We conclude that the Fe sites whose $H_{hyper}$ does not change are in the magnetically ordered RuO planes. We assume that the Fe's which see the transition between 30K and 40K are in the CuO planes and investigate how this transition arises.   

NMR Studies of the pseudogap in BSCCO-2212

We present O-17 NMR measurements on a single crystal of overdoped BSCCO-2212 (T$_{c}$= 82K). As a function of temperature we measure the planar oxygen's: resonance linewidths, Knight shift (K), electronic field gradient (EFG), and spin lattice relaxation rate (1/T1) along each principle axis. Our analysis shows that their temperature dependence can be explained by a suppression of the density of states in the pseudogap region T $<$ T$^{\ast }$ = 94K.   

$^{17}$O and $^{199}$Hg NMR measurements of HgBa$_2$CuO$_{4+y}$ single crystals

The high superconducting transition temperature and the simple tetragonal structure of HgBa$_2$CuO$_{4+y}$ (Hg1201) makes this material an ideal candidate to study unconventional superconductivity in the cuprates[1]. Nuclear magnet resonance has been performed on Hg1201 single crystals which have been annealed in an $^{17}$O atmosphere to various dopings. Preliminary results of the NMR spectra and relaxation of both $^{17}$O and $^{199}$Hg are presented. Narrow linewidths allow for the resolution of both $^{17}$O lattice sites and a doping dependent $^{199}$Hg spectral splitting[2]. This work is supported by \textbf{DOE/BES: DE-FG02-05ER46248} and the NHMFL by NSF and the State of Florida.[1] N. Bari\u{s}i\'{c} \textit{et al}, PRB \textbf{78}, 054518 (2008) [2] J. Haase \textit{et al}, arXiv:1110.601v1 (2011)   

Magnetic susceptibility analysis on Zn-doping in the high $T_{c}$ superconductor YBa$_{2}$Cu$_{3}$O$_{7}$

Localized magnetic moments are known to destroy superconductivity in conventional superconductors. In the case of YBa$_{2}$Cu$_{3}$O$_{7}$ (YBCO), the nonmagnetic ion Zn has a very strong impact on suppressing the superconducting transition temperature ($T_{c})$. YBCO loses all superconductivity when only 10\% of the Cu is substituted with Zn.\footnote{R. E. Walstedt et al. Phys. Rev. B, \textbf{48}, 10646 (1993)} In this project, we have investigated the magnetic susceptibility for a number of Zn doping levels in samples with the nominal composition YBa$_{2}$(Cu$_{1-x}$Zn$_{x}$)$_{3}$O$_{7}$. We observe the development of Curie-Weiss paramagnetism for some Zn compositions, and will address whether the associated paramagnetic moments might cause magnetic pair-breaking.   

Observable NMR signal from orbital current order in YBCO

Assuming, as suggested by recent neutron scattering experiments, that a broken symmetry state with orbital current order occurs in the pseudo-gap phase of the cuprate superconductors, we show that there must be associated equilibrium magnetic fields at various atomic sites in the unit cell, which should be detectable by NMR experiments.   

Numerical study of magnetic excitations probed by photon spectroscopies in families of high-temperature superconductors

Magnetic excitation in high-temperature superconductors has been a topic of cutting edge research for many years. In photon spectroscopies, single- and two-magnon excitations can be created and measured efficiently using techniques such as resonant inelastic x-ray scattering and optical Raman scattering. We present numerical studies of the magnetic excitations for different families of high-temperature superconductors, including both copper and iron based superconductors. These magnetic excitations and their dispersions provide important information in understanding the magnetic properties of these materials.   

Session T22: Focus Session: Fe-based Superconductivity - Properties of 122 phases

Combined effects of chemical doping and pressure on physical properties of CaFe$_{2}$As$_{2}$

The AFe$_{2}$As$_{2}$ compounds (A = alkaline earth) are the most extensively studied materials among the FeAs-based superconductors, and CaFe$_{2}$As$_{2}$ is the most pressure sensitive among them. The structural/magnetic phase transition near 170K is suppressed rapidly under pressure and a nonmagnetic, collapsed tetragonal phase is stabilized. Depending on the hydrostaticity of the pressure medium, the superconducting phase may or may not be induced. In this talk we will present the combined effects of chemical doping and pressure on the structural/magnetic phase transition as well as the collapsed tetragonal structure phase transition in an attempt to better understand the interactions between these phases.   

First Principles Calculations of the Pnictide CaFe$_{2}$As$_{2}$ under Pressure

We carry out first principles calculations of the effects of pressure on the structural and magnetic properties of the pnictide CaFe$_{2}$As$_{2}$ and compare with experiments. Our PBE-GGA calculations accurately reproduce the experimentally observed structural and magnetic ordering at zero pressure. Enthalpic considerations show that antiferromagnetic orthorhombic phase is favored over the non-magnetic tetragonal phase at pressure P=0, while the ``collapsed'' tetragonal phase is favored for pressures greater than 0.4 GPa, in good agreement with experiments. The calculated pressure dependences of the lattice parameters and the Fe-As bond lengths agree with experimental trends. We will discuss the nature of bonding and antibonding orbitals near the Fermi surface and we will evaluate the interplanar magnetic exchange interaction J.   

Evidence for domain wall superconductivity in antiferromagnetic CaFe2As2

$^{75}$As nuclear magnetic resonance (NMR), resistivity, and magnetization measurements in the antiferromagnetic state of the iron-based superconductor parent compound CaFe$_2$As$_2$ exhibit anomalous features consistent with the collective freezing of domain walls. Below T* $\approx$ 10 K, the $^{75}$As NMR measurements reveal the presence of slow fluctuations of the hyperfine field, the resistivity shows an enhancement and subsequent suppression, and the bulk magnetization shows a sharp increase. These features in both the charge and spin response are strongly field dependent, are fully suppressed by H* $\approx$ 15 T, and suggest the presence of filamentary superconductivity nucleated at the antiphase domain walls.   

Local atomic structure of BaFe$_2$As$_2$ by neutron powder diffraction

All structures of iron-based superconductors (FeSC) have planar layers of iron, tetrahedrally coordinated by pnictogens or chalcogens, and the structural details of this layer impact the superconducting and magnetic properties. Local structural studies of the iron-coordinated layer show evidence for local distortions resulting from models that allow for overall reductions in local symmetry. BaFe$_2$As$_2$, a parent compound of several families of FeSC, undergoes a transition at T $\approx=$ 140K, resulting in the onset of AFM ordering following a small lattice distortion. Here we report the results of a by time of flight neutron diffraction study on BaFe$_2$As$_2$, analyzed using Rietveld and pair distribution function techniques. This work produces a comprehensive view of the local structure of BaFe$_2$As$_2$ as a function of temperature. The results are consistent with previous work showing stratification of the As-As bond length, and show that models accounting for an overall reduction in local symmetry provide the best fit to the experimental data. Further, the results show that local distortions are present up to room temperature. Details of the experiment and implications for the paramagnetic and magnetic states will be discussed.   

First principles study of uniaxial pressure-induced phase transitions in CaFe$_2$As$_2$ and BaFe$_2$As$_2$

We consider density functional theory methods to determine the equilibrium structures of CaFe$_2$As$_2$ and BaFe$_2$As$_2$ under the effect of uniaxial pressure. We compare the results with calculations for hydrostatic pressure as well as with available experimental results. In CaFe$_2$As$_2$, we observe a unique phase transition from a magnetic orthorhombic phase to a nonmagnetic collapsed tetragonal phase for both pressure conditions and no indication of a tetragonal phase at intermediate uniaxial pressures. In contrast, for both uniaxial and hydrostatic pressure, BaFe$_2$As$_2$ shows two phase transitions from a magnetic orthorhombic to a collapsed tetragonal phase through an intermediate nonmagnetic tetragonal phase. We predict the critical transition pressures under uniaxial conditions to be much lower than those under hydrostatic conditions which implies that the systems are highly sensitive to uniaxial stress. We compare our results to available experimental measurements.   

Temperature-Pressure Phase Diagram of Lightly Hole-doped BaFe$_2$As$_2$

Chemical doping and application of pressure are the two common tools to tune the electronic structure of a material. Although electron-doping on Fe-site in BaFe$_2$As$_2$ gives superconductivity up to $\sim$ 22 K, it is puzzling that hole-doping does not. For this reason, we decided to carry out pressure studies on a few lightly Cr- or Mo-doped crystals of BaFe$_2$As$_2$. We have applied pressures of up to 2~GPa using a cylinder cell, and Fluorinert as pressure medium. Our preliminary findings reveal the shift of antiferromagnetic ordering temperatures to lower with pressure, and a down-turn in resistivity at low temperatures and pressures, which may be attributed to superconductivity.   

Magnetism, superconductivity, and the volume collapse transition in (Ca$_{0.67}$Sr$_{0.33})$Fe$_{2}$As$_{2}$ under pressure

The alkaline earth site of CaFe$_{2}$As$_{2}$ can be chemically substituted with Sr, forming a homogeneous solid solution series ending with SrFe$_{2}$As$_{2}$. It is found that (Ca$_{0.67}$Sr$_{0.33})$Fe$_{2}$As$_{2}$ exhibits a pressure-temperature phase diagram intermediate between the two end members of the series, shifting the phase lines for the suppression of magnetism, the development of superconductivity, and the occurrence of a volume collapse transition to higher pressures. The overall shift in the pressure-temperature phase diagram permits the study of each phase field, yielding valuable information about the correlations between local atomic structure, magnetism, superconductivity, and the volume collapse transition. Lawrence Livermore National Laboratory is operated by Lawrence Livermore National Security, LLC, for the U.S. Department of Energy, National Nuclear Security Administration under Contract DE-AC52-07NA27344.   

Inducing structural collapse and superconductivity in CaFe$_{2}$As$_{2}$ by systematic substitutions of rare earths

Recently, we have reported structural collapse and 47 K superconductivity in CaFe$_{2}$As$_{2}$ by aliovalent rare earth substitutions for Ca atoms [1]. We will present the evolution of structural and superconducting properties in single crystals of CaFe$_{2}$As$_{2}$ by systematic substitutions of R (=La, Ce, Pr, and Nd) for Ca, causing electron doping that is indirect to FeAs layer. Effect of annealing, growth method, etching, and pressure on Ca$_{1-x}$R$_{x}$Fe$_{2}$As$_{2}$, indicating the intrinsic nature of this high Tc superconductivity, the highest in 122 Fe-based materials, will be discussed. Ref. [1] S. R. Saha \textit{et al}. arXiv:1105.4798.   

Defect-Associated Superconductivity in (Pr,Ca)Fe$_{2}$As$_{2}$

The superconductivity in rare earth doped CaFe$_{2}$As$_{2}$ remains puzzled. As reported before, there are two distinguishable superconductive transitions at 20 K and 49 K, respectively, and the 49 K superconductivity can be better modeled as Josephson-Junction-Arrays (JJA). The H- and T-dependencies of the ac/dc magnetization are further explored here. The data suggest that the effective lower-critical-fields at both $c$- and \textit{ab}-directions are below 1 Oe down to 5 K, in agreement with previous JJA assumption. The \textit{ac} susceptibility below the critical field is highly anisotropy, suggesting a thin-disk-like morphology of the JJA's. The associated weak-links, however, appear to be broken above 20 K by a \textit{dc} bias as small as 10 Oe. The \textit{ac} response at higher bias fields, therefore, will be dominated by the isolated superconducting islands of JJA. It is interesting to note, therefore, that the \textit{ac} susceptibility remains highly anisotropic at high fields, but is much weaker than that expected from the field-cooled magnetization. We interpret this as the result of sub-micron size, thin-disk-like local superconductivity, $i.e.$ Defect-associated superconductivity.   

Rare Earth Doping in the (Sr,Ca)Fe2As2 System

The (Sr,Ca)Fe2As2 system shows an unusual persistence of the Neel ordering temperature of $\sim $200 K up to a concentration of 70{\%} calcium. We present electrical transport, magnetic susceptibility and structural characterization data as a function of rare earth substitution into Sr0.3Ca0.7Fe2As2 single crystals, focusing on the resultant phase diagram and the comparisons of solubility limit of rare earth substitution as compared to end members SrFe2As2 and CaFe2As2.   

Microstructure and the non-bulk superconductivity up to 49K in electron-doped Rare-earth (Ca, R)Fe$_{2}$As$_{2}$ (R=La, Ce, Pr and Nd) Single Crystals

In an attempt to raise the Tc in the 122 family, we have carried out electron-doping and observed an onset Tc up to 49K in the single crystalline (Ca, R)Fe$_{2}$As$_{2}$ (R=La, Ce, Pr and Nd). The single crystals up to 5 x 5 mm size are grown from self-flux technique and the optimal doping parameters for different rare-earth elements will be reported. Magnetic and resistivity data suggest possible existence of two superconducting transitions in all the rare-earth electron doped (Ca, R)Fe$_{2}$As$_{2}$ samples: one starts at $\sim $40s K, and the other at $\sim $20K, with drastically different response to the field. Detailed single crystals diffraction analysis show that there are no significant difference in terms of atomic position, bond distances, angles and lattice parameters upon different rare earth doping; the defect-related local structure might be responsible for the observed high Tc in this system. The unusual superconducting phase appears to be filamentary or interfacial in nature, and the possible mechanism will be discussed.   

Codoping -- A way to enhance the upper critical field in iron-arsenic superconductors

Technological key features of iron-based superconductors are the high critical temperature $T_{c}$ of up to 55 K and the high tolerance against magnetic fields, which led so far to upper critical fields in the range of 75 T. Furthermore, the small $H_{c2}$-anisotropy between field applied along the $c$-direction and in the \textit{ab}-plane, in particular for the FeSe and \textit{AE}Fe$_{2}$As$_{2}$ (\textit{AE} = Ca, Sr, Ba) materials, is a prerequisite for several technical applications. Currently, different approaches (chemical substitutions, processing) are discussed how to increase $H_{c2}$ further. Here, we show a feasibility study for codoping of polycrystalline Sr- or BaFe$_{2}$As$_{2}$ samples, namely the simultaneous substitution of K on the Sr/Ba layer and of Co on the FeAs layer. The upper critical field was investigated by magnetoresistance in high pulsed magnetic fields up to 64~T. We find, that the extrapolated critical field $H_{c2}(T\to $0) is enhanced by 15{\%} for Ba$_{0.55}$K$_{0.45}$Fe$_{1.95}$Co$_{0.05}$As$_{2}$ in comparison to Ba$_{0.55}$K$_{0.45}$Fe$_{2}$As$_{2}$, although $T_{c}$ is almost identical in both materials. These results suggest that codoping is a promising route for the systematic optimization of iron-arsenic based superconductors for high-magnetic field and high-current applications.   

Influence of random point defects introduced by proton irradiation on the vortex pinning and dynamics of superconducting $122$ iron arsenides

Vortex matter in iron-arsenide superconductors exhibits a rich phenomenology that is still largely unexplored. One way to understand and manipulate the pinning mechanisms and the vortex dynamics in superconductors is by the artificial introduction of additional defects. In this work we explore the influence of the random point defects introduced by proton irradiation on the vortex dynamics and critical currents of 122 iron arsenide superconductors. Our comparison includes Ca1-xNaxFe2As2 and Co-doped BaFe2As2 single crystals. We find that the influence of random point defects on the creep rate (S) and the elastic to plastic crossover of the vortex dynamics show a strong dependence with intrinsic superconductor parameters such as the coherence length. We analyze the magnetic field -- temperature (H-T) vortex phase diagrams for the as-grown single crystals and the changes produced by the random point defects.   

Upper critical and irreversible fields of polycrystalline CeFeAsO$_{1-x}$F$_{x}$ superconductors

We have investigated the upper critical ($H_{c2})$ and irreversible ($H_{irr})$ fields of polycrystalline samples of Ce oxypnictide at different doping levels. $H_{c2}$ was obtained from temperature dependent resistivity measurements with increasing applied magnetic field. Critical field values as high as 150 Tesla were observed with a decreasing trend as the doping level shifts from a slightly under-doped state to the highly over-doped region. The irreversible fields were lower in this superconductor compared with other rare-earth oxypnictides, with values below 3 Tesla at 20 K. However, $H_{irr}$ was found to increase with increasing doping, opposite to that of $H_{c2}$. The origin of $H_{irr}$ was studied by determining the exponent `n' extracted from plots of log$_{10}(H_{irr})$ versus log$_{10}$(1-$T$/$T_{c})^{n}$. We found that $H_{irr}$ follows a 3D vortex lattice-melting model similar to the other low anisotropic iron-based superconductors.   

Session T23: Actinides and Transport Magnetism in Metals

A quantum Monte Carlo study of thorium halide molecules

We present electronic structure calculations of thorium halide molecules, namely, a series of $ ThCl_n $ and $ ThBr_n $ (n=1,2,3,4) systems. We calculate the bond dissociation energies for the sequence of the following dissociation reactions: $ ThCl_n -> ThCl_{n-1} + Cl $ and $ ThBr_n -> ThBr_{n-1}+Br $. We apply both large core and small core energy-consistent pseudopotentials for thorium atom and we employ DFT GGA and hybrid functionals for energies and geometry calculations. For high accuracy energies we use the fixed-node diffusion Monte Carlo (DMC) method. In DMC calculations we employ both single- and multi-reference trial wave functions in order to test the quality of the nodal surfaces. We study the dissociation energies with regard to different multiplicities of the $ ThX_{n} $ molecules and the different behavior of the bromides with respect to chlorides. We compare our results with hybrid DFT methods and experimental values. Supported by DOE and NSF.   

Electron binding energy of uranium-ligand and uranyl-ligand anions

Electron binding energies of the early actinide element uranium in gas-phase anion complexes are calculated by relativistic density functional theory (DFT) with two different exchange-correlation functions (RPBE and B3LYP) and also in the Hartree-Fock (HF) approximation\footnote{ADF2010.02, SCM.com}. Scalar and spin-orbit calculations are performed, and the calculated energies are compared to available experimental measurements and shown to disagree by energies of order 1 eV. Strong correlations that are poorly treated in DFT and HF can be included by a hybrid approach in which a generalized Anderson impurity model is numerically diagonalized. Reduction-oxidation (redox) potentials of aqueous actinide ions show improved agreement with measured values in the hybrid approach\footnote{S. E. Horowitz and J. B. Marston, J. Chem. Phys {\bf 134} 064510 (2011).}. We test whether or not similar improvements are found in the gas-phase.   

Electronic structure of Pu metal and intermetallics as determined by ARPES and XPS

We exploit our unique capability in angle resolved photoemission (ARPES) measurement for plutonium materials to compare the electronic structure of delta Pu, PuCoIn5 and PuCoGa5. We present a systematic study for polycrystalline delta Pu metal as well as the first photoemission measurements on single crystals of the superconductor PuCoIn5. These first results for PuCoIn5 are compared to results for PuCoGa5 and variations in the electronic structure are attributed to differences in 5f hybridization with conduction states based on differences in lattice values. Laser ablation was used to clean the surface of Pu materials and cleanliness was monitored through O 1s and Pu 4f core levels as well as valence band features. Observation of these spectra provides better insight into the differentiation of contaminant features versus the strong correlation effects within Pu metal.   

Elastic moduli of nearly pure polycrystalline plutonium

We measure elastic moduli of microalloyed poly-crystalline cylindrical specimen of Pu-239. We observe $\alpha \rightarrow \beta \rightarrow \gamma \rightarrow \delta$ phase transitions and find that the elastic moduli of nearly pure plutonium are the same as those of Ga-stabilized plutonium.   

Magnetization at 1 Mbar Near the Tricritical Point in the Ce(0.9-$x)$La($x)$Th(0.10) System

The gamma to alpha isostructural transition in the Ce(0.9-$x)$La($x)$Th(0.10) system is measured as a function of La alloying and external pressure up to 1 Mbar using magnetic susceptibility. We probe a line of discontinuous transitions, as indicated by the change in volume, decreasing exponentially from 118 K to close to 0 K with increasing La doping, and the transition changes from being first order to continuous at a critical concentration close to $x$ = 0.14. At the tricritical point, the magnetic susceptibility increase rapidly near the critical concentration and approaches large values at $x$= 0.35 signifying that a heavy Fermi-liquid state evolves at large doping near the critical concentration. The Wilson ratio reaches a value above two for a narrow range of concentrations where the specific heat and susceptibility vary most rapidly with the doping concentration.   

Actinide oxides under pressure

We use the self-interaction corrected local spin density approximation to investigate the oxidation of actinide dioxides under pressure. The methodology enables us to determine the ground state valency configuration of the actinide 5f electrons and to study the localization/delocalization transition that occurs under pressure. We argue that this delocalization facilitates the oxidation of the actinide dioxides and present results for the estimated transition pressures.   

Dephasing due to electron interactions in inhomogeneous systems

At sufficiently low temperatures, the dephasing time $\tau_\varphi$ of mesoscopic samples is governed by so-called Johnson-Nyquist (electronic) noise. We study the spatial dependence of the corresponding noise correlation function (NFC) in inhomogeneous systems. Using the fluctuation-dissipation theorem and the random-phase approximation, we derive a real-space integro-differential equation for the NCF and show that it reduces to a diffusion equation in the case of strong screening. In particular, using a method based on the spectral determinant, we evaluate the NCF for arbitrary networks of quasi-1D disordered wires with boundary conditions. As an application, we construct a realistic quantum dot model via a set of parallel wires connected at contacts to leads, and calculate the temperature dependence of $\tau_\varphi$ as well as the quantum corrections to the conductance. Furthermore, we analyze the observability of the elusive 0D regime (reached at $T < E_{\rm Thouless}$ with the characteristic $\tau_\varphi \propto T^{-2}$ behavior) in such systems, and discuss alternative scenarios of its observation.   

Does aluminum conduct better than copper at the nanoscale? A first-principles study of metallic nanowires

From first-principles, we present a theoretical and comparative investigation of the role of quantum confinement in altering the electronic, transport, and phonon properties of linear, single-atom thick chains, i.e. nanowires, of metallic (Au, Ag, Cu, and Al) atoms. Our results for the ballistic quantum transport properties and electronic structure are in perfect agreement with those previously published. Motivated by this, we also consider electron-phonon interactions in such devices, where we report an order of magnitude reduction in the electron-phonon coupling constant for Al, whereas an enhancement is predicted for Au, Ag, and Cu.   

Quantum oscillations and low-T resistivity of the 5s delafossite PdCoO$_2$

We report dHvA torque and resistivity data on the highly conductive delafossite PdCoO$_2$. Quantum oscillations confirm electronic structure calculations in showing a single, highly 2D Fermi surface with almost exactly half filling. However the cyclotron masses and the details of the warping are consistent with PdCoO$_2$ being a 5s metal, rather than the 4d metal indicated in most electronic structure papers. The room temperature resistivity is $\rho_{ab}=2.6 \pm 0.2$~$\mu\Omega$-cm, lower than all elemental metals apart from the noble metals. The low-T residual resistivity of our samples is 0.008~$\mu\Omega$-cm, corresponding to an extremely long mean free path of 20~$\mu$m, surprising for a flux-grown material. The temperature dependence of the electron-phonon contribution to the resistivity is exponential rather than $T^5$, indicating phonon drag, and the only observation of phonon drag in resistivity outside the alkali metals.   

Dielectric function of Ni-Pt alloys from 0.6 to 6.6 eV by spectroscopic ellipsometry

The complex dielectric function of different Ni-Pt alloys (10{\%} to 25{\%} Pt concentration, 10nm thickness) was determined using spectroscopic ellipsometry over a broad photon energy range from 0.6 to 6.6eV. The films were deposited on a thick SiO$_{2}$ layers using Si as a substrate. The data were fitted using previously determined optical constants for Si and SiO$_{2}$. Optical constants of the Ni-Pt alloys were described using a Drude model (free carrier term), a pole due to d-intraband transition, and 2 to 3 Lorentz oscillators due to interband transitions. Data were compared with the calculated band structure of Nickel and Platinum. Results showed only small changes with the variation of Pt concentration or with annealing at 500\r{ }C for 30s.   

The Role of $d$-Orbitals in the Rashba Splitting on Au(111) and Ag(111)

We investigate the Rashba-type spin splitting in $sp$-derived Shockley surface states on (111) surfaces of noble metals, such as Au(111) and Ag(111), based on first-principles calculations including the spin-orbit interaction. By turning on and off $l$-dependent spin-orbit coupling one by one, we find that although the surface states on Au(111) have predominantly $p$-orbital character, the spin splitting in energy originates mainly from $d$-orbital character of the surface states. We also demonstrate that the spin splitting in surface states of both metallic surfaces of Au(111) and Ag(111) can be controlled by varying the sizes of $d$-orbital parts of the surface-state wave functions. These results show that in addition to difference in the atomic spin-orbit strength in Au and Ag, difference in $d$-orbital contributions to the surface states makes substantial difference in the sizes of the Rashba-type spin splitting in their surface electronic structures. This work was supported by the NRF of Korea (Grant Nos. 2009-0081204 and 2011-0018306) and KISTI Supercomputing Center (Project No. KSC-2011-C2-04).   

Effects of Co doping on the metamagnetic states in fcc Fe$_{1-x}$Co$_{x}$

It is well known that fcc-Fe have shows metamagnetism, with a low-spin state (LS) at small volume and and a high-spin state (HS) at large volume in the total-energy vs volume curve. In this work, we have studied the evolution of the metamagnetic states in the Fe$_{1-x}$Co$_{x}$ alloy as a function of Co concentration by means of first principles calculations. The ground state properties were obtained using the Full-Potential Linear Augmented Plane Waves method and the Generalized Gradient Approximation for the exchange-correlation functional. The alloying was modeled using the self-consistent virtual crystal approximation. The magnetic states are obtained from the total-energy as a function of the spin moment calculations, obtained using the Fixed Spin Moment methodology. For fcc-Fe, we found that the ground state corresponds to the LS state. Increasing the Co concentration the HS state decrease in energy. Thus, for $x=0.05$ the energy of the LS and HS states is practically the same, corresponding to a spin-glass state. The LS state is substituted by a paramagnetic state for $x>0.3$ of Co concentration. Interestingly, for the alloy with $x\sim0.35$ the total-energy vs volume curve shows ``effective symmetry,'' which is expected to exhibit invar behavior.   

Investigation of Possible Phase Separation in Rapidly Quenched Fe$_{1-x}$Co$_x$ Alloys with Cluster Expansion Model

Recently, experiments observed phase separation in rapidly quenched Fe$_{1-x}$Co$_x$ alloy in the ordered $\alpha'$ phase [ J. Alloys Compd. 424, 145 (2006) ]. It is also believed that this is not an equilibrium result because of phase rule violation in the published phase diagram. To clarify this situation, we calculate the phase diagram of the system using cluster expansion in combination with a genetic algorithm. We calculated free energy of the system using super-cells up to 32 atoms with compositions ranging from 35 to 100 at. \% Fe. Possible explanations for the experimental observations will be discussed.   

Atomic Structures and Magnetic Properties of Fe-rich Fe$_{1-x}$Co$_x$ Alloys: A Genetic Algorithm Search

Using genetic algorithm with first-principles calculations, we performed a broad global search for low-energy crystal structures of Fe-rich Fe$_{1-x}$Co$_x$ alloys. We found that Fe-rich Fe$_{1-x}$Co$_x$ alloys are highly configurationally degenerate and there are many additional off-stoichiometric stable structures to the well-known stoichiometric FeCo - B$_2$ structure, giving a possibility for atomistic manipulation of the alloys. The Co-Co nearest-neighbor pair is strongly unfavorable in Fe-rich Fe$_{1-x}$Co$_x$ alloys. The magnetic moment of Fe atom is increasing with Co concentration while that of Co atom is almost constant, inducing a Slater-Pauling curve for magnetic moment per atom. The magnetic moment of Fe atom is strongly dependent on the number of Co nearest-neighbors and it increases with this number.   

Session T24: Fractional Quantum Hall Effect III

Evolution of 7/2 fractional quantum Hall state in two subband systems

We report the evolution of the fractional quantum Hall state (FQHS) at total Landau level (LL) filling factor $\nu=7/2$ in wide GaAs quantum wells in which electrons occupy two electric subbands. The data reveal subtle and distinct evolutions as a function of density, magnetic field tilt-angle, or symmetry of the charge distribution. At intermediate tilt angles, for example, we observe a strengthening of the $\nu=7/2$ FQHS. Moreover, in a well with asymmetric change distribution, there is a developing FQHS when the LL filling factor of the symmetric subband $\nu_S$ equals 5/2 while the antisymmetric subband has filling $1<\nu_A<2$.   

Observation of reentrant quantum Hall states in the lowest Landau level

Measurements in very low disorder two-dimensional electrons confined to relatively wide GaAs quantum well samples with tunable density reveal reentrant $\nu=1$ integer quantum Hall states in the lowest Landau level near filling factors $\nu=4/5$ and 6/5. These states are not seen at low densities and become more prominent with increasing density and in wider wells. Our data suggest that these reentrant phases are (bubble) Wigner crystal states, stabilized here in the lowest Landau level thanks to the large electron layer thickness.   

Spin waves in the second Landau level: Probing the spin-polarization enigma

The physics in the second Landau level (SLL) is governed by competing phases resulting in striking phenomena. We use resonant inelastic light scattering experiments to explore collective excitation modes with the focus on low lying spin excitation modes in the SLL. The intensity of the small momentum spin-wave at the bare Zeeman energy (E$_{Z})$ collapses for filling factors away from integer filling factor $\nu <$3 and are dominated by a continuum of modes. We find that at the fractional filling factors 14/5, 8/3, 5/2, 7/3, 11/5 the continuum coexists with a weak but distinct signal at E$_{Z}$, a long wavelength spin-wave that suggests a degree of spin polarization. In addition, at 5/2 an intriguing well developed sharp mode is observable below E$_{Z}$, which is unique for the even-denominator filling factor. Modes at energies larger than E$_{Z}$ merge additionally at odd-denominator states in ILS spectra, most pronounced for 7/3, in a manner that is similar to that of the 1/3 state. This observation could be evidence that the CF framework could be applicable to these states.   

Ballistic transport of (001) GaAs two-dimensional holes and hole-flux composite fermions through a lateral strain-induced superlattice

The addition of a unidirectional superlattice on the surface of high-mobility two-dimensional carrier systems leads to a potential modulation signaled by the observation of magnetoresistance commensurability oscillations. We present measurements in high-mobility, two-dimensional (001) GaAs systems patterned with strain-induced surface superlattices of periodicity 100 to 250 nm. The data exhibit pronounced commensurability oscillations of holes near zero magnetic field and of hole-flux composite fermions near filling factor v = 1/2, allowing us to probe the Fermi contours of these quasi-particles.   

Microscopic Disorder-Based model for non-Abelian Quasi-Particles in $\nu=5/2$ FQH states

The detection of non-Abelian quasiparticles remains an outstanding experimental problem in the $\nu=\frac{5}{2}$ fractional quantum Hall (FQH) state. The presence of non-Abelian statistics would lead to additonal low energy states in the system, and hence an additional low-temperature entropy. One approach to test for non-Abelian quasiparticle statistics uses thermodynamic measurements to detect this entropy contribution~[1,2]. We present a microscopic model for quasiparticles in the $\nu=\frac{5}{2}$ FQH state with a disorder potential that fluctuates on the order of several magnetic lengths, and attempt to determine the feasibility of the experiments proposed in~[1], based on local probe measurements of incompressibility~[3]. \\ \ [1] Cooper, N.R., Stern, A. PRL. {\bf 102}, 176807 (2009). \\ \ [2] Yang, K., Halperin, B.I. PRB {\bf 79}, 115317 (2009). \\ \ [3] Venkatachalam, V., Yacoby, A., Pfeiffer, L., West, K. Nature {\bf 469}, 185 (2011).   

Correlating scattering times with the strength of the $\nu $=5/2 fractional quantum Hall state

There is widespread interest in the fractional quantum Hall effect at $\nu $=5/2. Theory predicts that the state at $\nu $=5/2 may possess non-Abelian braiding statistics. Experimental interrogation remains difficult due to the fragility of the excitation gaps requiring both high quality samples and examination at low temperatures. Mounting evidence suggests that the strength of the most fragile fractional quantum Hall states in the 2$^{nd}$ Landau level including $\nu $=5/2 are poorly correlated with the scattering time extracted from zero-field mobility measurements at higher temperatures. It is also unclear if the quantum scattering time derived from analysis of the low-field Shubnikov de-Haas oscillations provides any additional information relevant to prediction of the strengths of the observed fractional states. We report on a systematic attempt to correlate the T=0.3K behavior of the mobility lifetime, quantum scattering time, and an effective high field mobility lifetime evaluated at $\nu $=5/2 with the measured activation gap. We will present results from a number of heterostructure designs over a wide span of zero-field mobility ranging from $\sim $10x10$^{6}$cm$^{2}$/Vs to greater than 20x10$^{6}$cm$^{2}$/Vs.   

``Perfect'' Coulomb Drag in a Bilayer Quantum Hall System

We report Coulomb drag measurements in Corbino geometry which reveal that equal but oppositely directed electrical currents can freely propagate across the insulating bulk of the bilayer quantized Hall state at $\nu_T =1$ even when the two 2D layers are electrically isolated and interlayer tunneling has been heavily suppressed by an in-plane magnetic field. This effect, which we dub ``perfect'' Coulomb drag, reflects the transport of charge neutral excitons across the bulk of the 2D system. The equal magnitude of the drive and drag currents is lost at high current and when either the temperature or effective separation between the two 2D layers is increased. In each of these cases, ordinary quasiparticle charge transport across the annulus has grown to dominate over exciton transport.   

Topological order, quasi-particle statistics and braiding from ground state entanglement

Topologically ordered phases are gapped states, defined by the properties of excitations when taken around each other. By calculating Topological Entanglement Entropy (TEE) of a disc shaped partition using a Monte Carlo technique, we establish the existence of topological order in $SU(2)$ symmetric gapped spin liquids and lattice Laughlin states obtained by the Gutzwiller projection technique. On the other hand, the TEE of partitioning the torus into two cylinders is generally different and depends on the chosen ground state. We demonstrate a method to extract the statistics and braiding of excitations, given just the set of ground state wave-functions on a torus. Central to our scheme is the identification of groundstates with minimum entanglement entropy, which reflect the quasi-particle excitations. We demonstrate our method by extracting the modular$\mathcal{S}$ matrix of an $SU(2)$ symmetric chiral spin liquid, and prove that its quasi-particles obey semionic statistics. This method offers a route to a nearly complete determination of the topological order in several cases.   

Paired Quantum Hall States at Weak Coupling: Phenomenology

Paired quantum Hall states such as the Pfaffian exhibit a weak-coupling regime much like that of BCS superconductivity. In this regime their lowest energy excitations are neutral fermions -- Bogoliubov quasiparticles constructed from the composite fermions -- and not the charged vortices which generally govern the behavior of quantum Hall states. We discuss a rich set of phenomena which follow from this observation. At finite temperatures of order the pairing scale these include (i) an almost sharp phase transition (ii) a new finite-temperature length scale for the penetration of longitudinal electric fields, and (iii) the existence of a new collective excitation in paired QH states which is a cousin to the well known Artemenko-Volkov-Carlson-Goldman-Schmid-Schon mode in conventional superconductors. At lower temperatures, we find (i) a proximity effect between the paired states and their ancestor metals, which in turn mediates (ii) `Josephson' couplings between paired QH droplets separated by metallic regions and leads to (iii) a distinctive response of such states to disorder; and finally, we also comment on (iv) an analog of Andreev reflection in these systems.   

From Luttinger liquid to non-Abelian quantum Hall states

We formulate a theory of non-Abelian fractional quantum Hall states by considering an array of coupled interacting one dimensional wires, each described by a Luttinger liquid theory. This coupled wire construction provides a solvable Hamiltonian formulated in terms of electronic degrees of freedom, and provides a direct route to characterizing the quasiparticles and edge states in terms of conformal field theory. It also leads to a simple interpretation of the coset construction of conformal field theory, which is a powerful method for describing non-Abelian states. The level-$k$ Read-Rezayi state at filling $\nu=k/(2+qk)$ is constructed by an uneven but periodic magnetic field configuration that organizes the wires into bundles. Gapless degrees of freedom in each bundle are decomposed into conformal sectors, which acuire energy gaps independently by intra-bundle and time reversal breaking inter-bundle interactions.   

A comparative study of the reentrant integer quantum Hall states in the second and third Landau levels

In the two-dimensional electron gas competing electron-electron interactions and disorder effects give rise to many-body ground states such as the fractional quantum Hall and the reentrant integer quantum Hall states (RIQHS). The latter are not yet well understood, but they are believed to be Wigner crystal-like electron solids with one or more electrons at each lattice nodes. We have recently shown that for the RIQHS in the second Landau level one can extract their onset temperature from the temperature-dependent magnetoresistance. We report similar studies of the RIQHS in the third Landau level. To our surprise, the onset temperatures of the RIQHSs in the third Landau level are about a factor of 3 larger than those in the second Landau level. This result clearly shows that the RIQHSs in the second and third Landau level have vastly different cohesion energies and may indicate different internal symmetries for these states. This work was supported by the DOE grant DE-SC0006671.   

Pomeranchuk Instability driven by Coulomb interaction in half-filled Landau levels

We study the Coulomb interaction driven Pomeranchuk instability as a mechanism for observed electronic nematic phases at high Landau levels. Such a mechanism will be signaled by the instability of the Fermi surface to quadripolar deformations: $F_2<-1$, where $F_2$ is the Fermi liquid parameter for the angular momentum $L=2$ channel. We compare the Fermi Liquid parameters for the lowest three half-filled Landau levels ($\nu=1/2, 5/2 and 9/2$). We calculate the Fermi liquid parameters by evaluating energies of eight independent particle-hole pair excitation configurations using a quantum Monte Carlo algorithm through correlated sampling. We used composite fermion many-body wave functions for $37$ electrons on a toroidal geometry that are interacting through the Coulomb potential. We find $F_2$ to become increasingly negative as we go to higher Landau levels. This is consistent with experimental observations.   

Bulk-edge correspondence and entanglement spectra of quantum Hall trial wave functions

We construct edge states wave functions for quantum Hall trial states built out of conformal blocks (e.g. Laughlin, Moore-Read or Read-Rezayi wave functions). We then compute the overlaps between these edge states in the thermodynamic limit. The result is that the Hilbert space of the edge theory is isomorphic to the one of the conformal field theory (CFT) which defines the quantum Hall state. This is a microscopic derivation of the bulk/edge correspondence for trial states given by conformal blocks. Our result definitely rules out the use of non-unitary theories for the construction of quantum Hall states. We obtain this result by analysing the quantum Hall droplet in the thermodynamic limit, under the assumption that all correlations are short-range inside the droplet. We argue that one is then left with a CFT in the domain outside the droplet, with a perturbed conformal boundary condition along the edge. We show that the entanglement spectra of these states can be tackled analytically with the same techniques.   

Finite-size studies of the $\nu=5/2$ quantum Hall state in wide quantum wells: the effect of subband mixing and breaking of particle-hole symmetry

A number of theoretical studies have argued that the quantized plateau at half filling of the second Landau level is described by the Pfaffian wavefunction of Moore and Read, or by its particle-hole conjugate, the anti-Pfaffian. The two wavefunctions are difficult to compare in finite-size systems due to their different shifts in the spherical geometry, or because of their high mutual overlap on the torus. Here we propose a way to circumvent these problems by envisioning systems with periodic boundary conditions, for which the Pfaffian and anti-Pfaffian become orthogonal to each other due to their different symmetry properties under discrete rotations. Furthermore, we show that periodic boundary conditions can be used to study the Moore-Read ground state, as well as the collective excitation spectrum, in finite systems in a ``quartered'' Brillouin zone scheme. To demonstrate the utility of this method, we provide a realistic, two-component model of a wide quantum well that can unambiguously distinguish between the Pfaffian and anti-Pfaffian state in finite-sized systems. These results describe the recent experiments that probed the stability of the $\nu=5/2$ state by tuning the mixing between electronic subbands and Landau levels in a wide quantum well.   

Quantitative analysis of the disorder broadening and the intrinsic gap for the $\nu $=5/2 fractional quantum Hall state

We analyze several different methods of extracting intrinsic gaps of fractional quantum Hall states (FQHS) of the second Landau level from experimental data. Because of the discrepancy between these methods, we introduce a new way of estimating the disorder broadening in the second Landau level based on scaling of the gaps of the major odd denominator states. The results of our technique are in good agreement with a previously used method utilizing only the gaps of the even denominator states. We successfully apply this technique to several samples of high quality and find an excellent agreement between the estimated intrinsic gap and results of numerical simulations. We also report, for the first time, the dependence of the intrinsic gap of $\nu $=5/2 FQHS on Landau level mixing. This work was supported by the NSF grant DMR- 0907172.   

Quantum Topology of Lattice Dislocations in Fractional Chern Insulators

An exciting prospect in condensed matter physics is the possibility of realizing fractional quantum Hall (FQH) states in simple lattice models without a large external magnetic field. Here we find a remarkable consequence of the interplay between the lattice translation symmetry and topological properties of these fractional Chern insulators. When the partially filled flat band has a Chern number N, it can be mapped to an N-layer quantum Hall system. We find that lattice dislocations can act as wormholes connecting the different layers and effectively change the topology of the space. Lattice dislocations become defects with non-trivial quantum dimension, topological degeneracy, and non-Abelian statistics, even when the FQH state being realized is a conventional Abelian FQH state.   

Session T25: High Pressure: Theory

Nanoshells as a high-pressure gauge

Nanoshells, consisting of multiple spherical layers, have an extensive list of applications, usually performing the function of a probe. We add a new application to this list in the form of a high-pressure gauge in a Diamond Anvil Cell (DAC). In a DAC, where high pressures are reached by pressing two diamonds together, existing gauges fail at higher pressures because of calibration difficulties and obscuring effects in the diamonds. The nanoshell gauge does not face this issue since its optical spectrum can be engineered by altering the thickness of its layers. Furthermore their properties are measured by broad band optical transmission spectroscopy leading to a very large signal-to-noise ratio even in the multi-megabar pressure regime where ruby measurements become challenging. Theoretical calculations based on the Maxwell equations in a spherical geometry combined with the Vinet equation of state show that a three-layer geometry (SiO$_2$-Au-SiO$_2$) indeed has a measurable pressure-dependent optical response desirable for gauges.   

Pressure-induced phase transitions and superconductivity in platinum hydride

The transition metal hydrides have attracted much attention from the scientific community due to their promising properties from both fundamental and practical points of view. Here we present our recent work about platinum hydride under pressure. Structural phase transitions and superconducting properties of platinum hydride under pressure are explored through the first-principles calculations based on the density functional theory. Three new low-pressure phases (Pm-3m, Cmmm, and P4/nmm) are predicted, and all of them are metallic and stable relative to decomposed cases. Two high-pressure phases are close-packed structure with hydrogen atoms occupying the octahedral interstices. The superconducting critical temperature of two high-pressure phases correlates with the electron-phonon coupling. The presence of soft modes induced by Kohn anomalies and the hybridization between H and Pt atoms result in the strong electron-phonon coupling. Our results have great implications for other transition metal hydrides under pressure.   

The hard-disk melting transition

Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed upon after 50 years of studies. A recent Monte Carlo algorithm [1] allows us to thermalize systems large enough to access the thermodynamic regime. I will show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first order [2]. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational, and experimental research. 1. Bernard, E. P.; Krauth, W. {\&} Wilson, D. B. \textit{Phys. Rev. E., }\textbf{2009}$, 80$, 056704 2. Bernard, E. P. {\&} Krauth, W. \textit{Phys. Rev. Lett., }\textbf{2011}$, 107$, 155704   

Electric Field Induced Phase Transitions

A novel theory of phase transitions that are driven by strong, symmetry-breaking electric fields is presented. The underlying mechanism is based on the formation of needle-shaped, metallic embryos that acquire strong dipole moments in the applied field. It is shown that the electrostatic contribution to the free energy can be so significant that it dominates the nucleation process and elongated metallic particles can form even in cases where they would be otherwise unstable in the bulk. As such, the theory predicts that any insulator will eventually form metallic inclusions when immersed in a sufficient electric field. Materials can thus be synthesized by the controlled application of a dc or laser field. In this work, the general mechanism is described and closed form expressions are presented for the field-dependent nucleation barrier and the effective field range as functions of material parameters. Overall, the theory presents a new parameter space to explore phase transitions and opens the venue of Field Induced Materials Synthesis (FIMS). As a provocative example, the potential for FIMS of metallic hydrogen at standard pressure is discussed; the effective field range is estimated to be $10^7 < E\ll 10^9$ V/cm (laser intensity $10^{12}< I \ll 10^{16}$ W/cm$^2$).   

Consistent first-principles pressure scales for diffraction experiments under extreme conditions

Diamond anvil cell (DAC) diffraction experiments are fundamental in geophysics and materials science to explore the behavior of solids under very high pressures and temperatures. A factor limiting the accuracy of DAC experiments is the lack of an accurate pressure scale for the calibration materials that extends to the ever-increasing pressure and temperature limits of the technique. In this communication, we address this problem by applying a newly developed technique that allows the calculation of accurate thermodynamic properties from first-principles calculations [Phys. Rev. B 84 (2011) 024109, 84 (2011) 184103]. Three elements are key in this method: i) the quasiharmonic approximation (QHA) and the static energies and phonon frequencies obtained from an electronic structure calculation ii) the appropriate representation of the equation of state by using averages of strain polynomials and iii) the correction of the systematic errors caused by the exchange-correlation functional approximation. As a result, we propose accurate equations of scale for typical pressure calibrants that can be used in the whole experimental range of pressures and temperatures. The internal consistency and the agreement with the ruby scale based on experimental data is examined.   

Low-temperature phases of dense hydrogen and deuterium by first-principles path-integral molecular dynamics

The low-temperature phases of dense hydrogen and deuterium have been investigated using first-principles path-integral molecular dynamics, a technique that we have recently implemented in the ABINIT code and that allows to account for the quantum fluctuations of atomic nuclei. A massively parallelized scheme is applied to produce trajectories of several tens of thousands steps using a 64-atom supercell and a Trotter number of 64. The so-called phases I, II and III are studied and compared to the structures proposed in the literature. The quantum fluctuations produce configurational disorder and are shown to systematically enhance the symmetry of the system: a continuous gain of symmetry in the angular density of probability of the molecules is found from classical particles to quantum D2 and finally to quantum H2. Particular emphasis is made on the ``broken-symmetry'' phase (phase II).   

Predictive equation of state method for heavy materials based on the Dirac equation and density functional theory

Density functional theory (DFT) provides a formally predictive base for equation of state properties. Available approximations to the exchange/correlation functional provide accurate predictions for many materials in the periodic table. For heavy materials however, DFT calculations, using available functionals, fail to provide quantitative predictions, and often fail to be even qualitative. This deficiency is due both to the lack of the appropriate confinement physics in the exchange/correlation functional and to approximations used to evaluate the underlying equations. In order to assess and develop accurate functionals, it is essential to eliminate all other sources of error. In this talk we describe an efficient first-principles electronic structure method based on the Dirac equation and compare the results obtained with this method with other methods generally used. Implications for high-pressure equation of state of relativistic materials are demonstrated in application to Ce and the light actinides. Sandia National Laboratories is a multi-program laboratory managed andoperated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Requirements for Predictive Density Functional Theory Methods for Heavy Materials Equation of State

The difficulties in experimentally determining the Equation of State of actinide and lanthanide materials has driven the development of many computational approaches with varying degree of empiricism and predictive power. While Density Functional Theory (DFT) based on the Schr\"{o}dinger Equation (possibly with relativistic corrections including the scalar relativistic approach) combined with local and semi-local functionals has proven to be a successful and predictive approach for many materials, it is not giving enough accuracy, or even is a complete failure, for the actinides. To remedy this failure both an improved fundamental description based on the Dirac Equation (DE) and improved functionals are needed. Based on results obtained using the appropriate fundamental approach of DFT based on the DE we discuss the performance of available semi-local functionals, the requirements for improved functionals for actinide/lanthanide materials, and the similarities in how functionals behave in transition metal oxides. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

High pressure/temperature equation of state of gold silver alloys

Gold-silver alloys crystallize in face centered cubic structures, like their constituent pure elements [McKeehan -- Phys.Rev. 20, 424 (1922)]. The cell parameter of the alloys does not scale linearly with the ratio of Ag/Au. In this work we investigate the high-pressure/temperature behavior of gold-silver alloys with different Au/Ag ratios. Powder x-ray diffraction experiments performed at HPCAT/Advanced Photon Source confirm the stability of the alloy's fcc structure to pressures/temperatures exceeding 100 GPa/1000 K. We will present isothermal EOS of the alloys from ambient temperature up to 1000 K, discuss the thermal expansion and its variation with pressure.   

Persistence of Covalent Bonding in Liquid Silicon Probed by Inelastic X-ray Scattering

Metallic liquid silicon at 1787K is investigated using x-ray Compton scattering. An excellent agreement is found between the measurements and the corresponding Car-Parrinello molecular dynamics simulations. Our results show persistence of covalent bonding in liquid silicon and provide support for the occurrence of theoretically predicted liquid-liquid phase transition in supercooled liquid states. The population of covalent bond pairs in liquid silicon is estimated to be 17{\%} via a maximally-localized Wannier function analysis. Compton scattering is shown to be a sensitive probe of bonding effects in the liquid state.   

Effects of the Structure of the Confinement Matrix on Liquid-Liquid Phase Transition and Density Anomaly

We investigate using molecular dynamics the effect of geometrical order in nanoconfinement of liquids with water-like anomalies that display liquid-liquid coexistence at low pressure and low temperature. Our studies using both a ramp and a shoulder interaction potentials show that regularly structured confinement matrices preserve the anomalies, while the phase diagram is shifted to lower temperatures, higher pressures and higher densities with respect to bulk. On the contrary, if the confinement matrices have no geometrical order, we find a drastically different phase diagram: the liquid-liquid coexistence region shrinks significantly and the anomalies are washed out. To understand this effect we calculate the changes in the system at the microscopic level. In the vicinity of the confining nanoparticles we observe that the liquid has a dramatic increase of density that we interpret as an entropic effect. We explain the macroscopic effect of confinement as a consequence of the amount of disorder that is introduced through the configuration of the confining nanoparticles.   

First-principles calculations for pressure-induced transition of Sr2CuO3

One-dimensional cuprate, Sr$_{2}$CuO$_{3}$ has attracted much attention from the theoretical and material research. Recently, it is found that Sr$_{2}$CuO$_{3}$ exhibits the pressure-induced structural transition with the space group change. In this work, we perform the first-principles calculations in order to investigate the mechanism for the pressure-induced structural transition of Sr$_{2}$CuO$_{3}$. The calculation results are in good accordance with the experimental ones. The structural transition of Sr$_{2}$CuO$_{3}$ are related with the ionic interaction between strontium and oxygen atoms. We also discuss the electronic and magnetic structure of Sr$_{2}$CuO$_{3}$.   

Magnetic Phase Transition in Rare Earth Metal Holmium at Low Temperatures and High Pressures

The heavy rare earth metal Holmium has been studied under high pressures and low temperatures using a designer diamond anvil cell and neutron diffraction using a Paris-Edinburgh Cell at the Spallation Neutrons and Pressure (SNAP) Diffractometer. The electrical resistance measurement using designer diamond shows a change in slope at the Neel temperature as the temperature is lowered at high pressures. At atmospheric pressure TN=120 K and decreases with a slope of -4.7 K/GPa as pressure is increased, until reaching 9 GPa, at which pressure the magnetic ordering is lost. This correlates to the pressure at which there is a structural change from an hcp phase to an $\alpha $-Sm structure. Neutron diffraction measurements made above and below the Neel temperature at increasing pressures show the reversibility of the change between the paramagnetic and antiferromagnetic states. The parameters of the low temperature incommensurate magnetic phase will be reported at various pressures.   

Session T26: Focus Session: Computational Frontiers in Quantum Spin Systems II

Cubic Interactions and Quantum Criticality in Dimerized Antiferromagnets

Dimerized quantum antiferromagnets can be driven through a quantum phase transition from a dimerized phase into a magnetically ordered state upon tuning the exchange parameters. In recent years, the critical properties in such dimerized antiferromagnets were examined in detail, based on large-scale quantum Monte Carlo simulations, which reported deviations from O(3) universality for specific two-dimensional geometries, in particular for the staggered-dimer antiferromagnet. Symmetry arguments and microscopic calculations exhibit that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, related to three-particle interactions among the triplet excitations within the paramagnetic phase of this model. The consequences of such cubic terms are explored using a combination of analytical and numerical methods. Complemented by finite-temperature quantum Monte Carlo simulations, these results lead to the conclusion that critical exponents in dimerized antiferromagnets are identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling for these specific dimerization geometries.   

Computational Studies of $T=0$ Neel-Valence bond solid transitions in two dimensional quantum antiferromagnets

We use Quantum Monte Carlo techniques to study a direct quantum phase transition in two dimensional quantum antiferromagnets between a collinear Neel ordered state and a valence bond solid ordered singlet state. We contrast the strongly first order behavior of the transition in cases where the valence bond solid order is of a ``staggered'' type with the deconfined critical behavior seen in cases where the valence-bond solid order is of a columnar type. In the deconfined case, we find evidence for weak, apparently logarithmic violations of scaling. [References: preprint; Phys. Rev. B 83, 235111 (2011); Phys. Rev. B 83, 134419 (2011); Phys. Rev. B 82, 155139 (2010)]   

Velocities of Goldstone and critical modes in SU(2) symmetric quantum spin systems

The low-energy excitations of many interesting quantum spin systems are gapless and linearly dispersing. Examples include Goldstone modes in the N\'eel phase and critical modes at a z=1 quantum critical point. We calculate the velocities of such modes for a variety of SU(2) symmetric S=1/2 systems using quantum Monte Carlo (QMC) methods. We use two complementary approaches:a)The lowest triplet gap from the singlet ground state is calculated using T=0 projector QMC by measuring appropriate imaginary-time correlation functions. The velocity is obtained from extracted momentum dependent gaps.b)We use a method based on tuning the system to the cubic regime by varying its temperature to equate the variance of spatial and temporal winding numbers, which was recently used by Jiang [1] for a system with Goldstone modes. We find that this method can also be applied to a z=1 critical point (the critical point of an S=1/2 Heisenberg bilayer) and to the 1D Heisenberg spin chain, where there are no Goldstone modes. We also extract the velocity of the critical modes of the J-Q model. It agrees very well with the velocity obtained from a phenomenological approach [2] based on a spinon gas picture. [1] Jiang, Phys. Rev B 83, 024419 (2011) [2] Sandvik et al., Phys. Rev. Lett. 106, 207203 (2011)   

Unconventional versus conventional destruction of square lattice SU(N) magnetism

Recently we have found SU($N$) symmetric square lattice spin models of quantum anti-ferromagnets, which have quantum phase transitions between magnetic and non-magnetic phases for arbitrary $N$, and which are nonetheless free of the ``sign-problem'' of quantum Monte Carlo. The absence of the notorious sign-problem allows detailed unbiased numerical simulations of two-dimensional magnetic quantum phase transitions on lattices containing in excess of 10$^4$ spins. Depending on the absence or presence of uncompensated Berry phases in our microscopic models we find evidence for both conventional first order phase transitions and unconventional continuous quantum phase transitions at which both N\'eel- and valence bond solid-order (VBS) are {\em simultaneously} quantum critical. A detailed quantitative study of the N\'eel and VBS scaling dimensions as a function of $N$ provides compelling evidence that the long-wavelength description of these quantum critical points may be found in the CP$^{N-1}$ gauge theory, as predicted by the deconfined quantum criticality scenario. R. K. Kaul and A. W. Sandvik, http://arxiv.org/abs/1110.4130. R. K. Kaul (forthcoming).   

Neel to valence-bond solid transitions in generalized amplitude-product states with correlated weights

An amplitude-product state is a superposition of valence-bond states with the expansion coefficients being products of individual bond amplitudes that depend only on the bond shape. In two dimensions, these states have Neel order or are spin liquids, but they never have any valence-bond solid order. We construct generalized amplitude-product states on the square lattice which include correlated weights for short-range bonds. Using these states, we explore phase transitions between Neel phase, valence-bond solid phases, and spin liquid. We also study the Neel-VBS transition in the standard amplitude-product states in one dimension.   

Emergent U(1) Symmetry in Square Lattice Quantum Dimer Models

We report an exact diagonalization study of Rokhsar-Kivelson quantum dimer models on square lattice. Using a finite-size scaling analysis of excited energy levels, we are able to identify a regime of length scales where the the quantum dimer model exhibits a $U(1)$ symmetry. Dimer order parameter histograms confirm this remarkable symmetry. Beyond this crossover length, columnar dimer order emerges at least for $v/t \la 0.6$. Our interpretation is supplemented with field-theory analysis as well as large-scale quantum Monte-Carlo simulations.   

A round-trip from spin to quantum dimer models

Short-range valence bonds wave-functions are often used as a paradigm for non-magnetic states (such as spin liquids or valence bond crystals). Recently, two local S=1/2 spin Hamiltonians which admits nearest neighbor valence bond wave-function(s) as ground-state(s) on the square lattice have been proposed by Cano and Fendley [Phys. Rev. Lett. {\bf 105}, 067205 (2010)]. We present a numerical study, by means of exact diagonalizations and diagonalizations restricted in the subspace spanned by nearest neighbor valence bond states, of the ground state and excitations of these models. We show that it corresponds to a new type of spin liquid state, with gapped spin but gapless non-magnetic excitations. Mixing the two models is shown to stabilize valence bond crystal ground states that are very reminiscent of the phases present in the Rokhsar-Kivelson quantum dimer model phase diagram. Using a generic mapping scheme [Phys. Rev. B {\bf 81}, 214413 (2010)] of spin hamiltonians to generalized quantum dimer models we show how this correspondence between the phase diagram of a local S=1/2 spin hamiltonian and the Rokhsar-Kivelson quantum dimer model can be understood.   

Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal Formation

We present a comprehensive computational study of the phase diagram of the frustrated $S=1/2$ Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest $(J_2)$ and third-neighbor $(J_3)$ couplings. Using a combination of exact diagonalizations of the original spin model, of the Hamiltonian projected into the nearest neighbor short range valence bond basis, and of an effective quantum dimer model, we determine the boundaries of several magnetically ordered phases in the region $J_2,J_3\in [0,1]$, and find a sizable magnetically disordered region in between. We characterize part of this magnetically disordered phase as a {\em plaquette} valence bond crystal phase.   

Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice

We have precisely determined the ground state phase diagram of the quantum spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice using the tensor renormalization group method. We find that the ferromagnetic, ferroquadrupolar, and a large part of the antiferromagnetic phases are stable against quantum fluctuations. However, around the phase where the ground state is antiferro-quadrupolar ordered in the classical limit, quantum fluctuations suppress completely all magnetic orders, leading to a plaquette order phase which breaks the lattice symmetry but preserves the spin SU(2) symmetry. The quantum phase transition between the antiferromagnetic phase and the plaquette phase is found to be a direct second order transition, being the first candidate of the deconfined quantum critical point for the spin-1 quantum systems.   

Three-sublattice order in the SU(3) Heisenberg model on the square and triangular lattice

We present a numerical study of the SU(3) Heisenberg model on the triangular and square lattice by means of the density-matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS). For the triangular lattice we confirm that the ground state has a three-sublattice order with a finite ordered moment which is compatible with the result from linear flavor wave theory (LFWT). The same type of order has recently been predicted also for the square lattice. However, for this case the ordered moment cannot be computed with LFWT due to divergent fluctuations. Our numerical study clearly supports this three-sublattice order, with an ordered moment of m=0.2-0.4 in the thermodynamic limit.   

Zero- vs. finite-field transition in S=1 Heisenberg antiferromagnet with single-ion anisotropy

We use large scale quantum Monte Carlo simulation on finite size lattices to study the ground state and finite temperature transitions in a $S=1$ Heisenberg antiferromagnet (HAFM) with single-ion anisotropy ($D$) in the presence of an external magnetic field ($h_z$). The ground state phase diagram (in the $h_z-D$ plane) is characterized by a quantum paramegnetic phase (QPM) at large $D$ and small $h_z$ and an XY-AFM phase at small $D$ and/or large $h_z$ separated by a continuous transition. We show that the QPM to XY-AFM transition belongs to the XY universality class at $h_z=0$ (driven by varying $D$) whereas it belongs to the BEC universality class at $h_z\neq 0$ (driven by either varying $D$ at constant $h_z$ or varying $h_z$ at constant $D$). This has important implication in the behavior of the specific heat at the transition point which can be verified experimentally. Finally, we discuss the experimental relevance of our results in the case of DTN.   

Ferronematic order in a spin-1 Heisenberg antiferromagnet

We study the field-induced ground-state phase transition of a spin-1 Heisenberg antiferromagnet with large easy-axis single-ion anisotropy $D$. Direct spin-wave treatment predicts a single first-order phase transition from an antiferromagnetic N\'{e}el phase at low magnetic fields to a fully polarized state at high magnetic fields. Mean field arguments, based on an effective spin-1/2 model that is exact in the $D\rightarrow\infty$ limit, show that this transition is preempted by an intermediate phase with double-spin-flip correlations. We call this phase the {\em ferronematic} phase, as the effective spin model for large (negative) $D$ is a spin-1/2 XXZ model with {\em ferromagnetic} transverse exchange. Using exact diagonalization and quantum Monte Carlo, we confirm the presence of the ferronematic phase. Long range order is observed in the equal-time Green's function $\langle S_{i}^{+}S_{i}^{+}S_{j}^{-}S_{j}^{-}+H.c.\rangle$, which is the correlation function for ferronematic order. We also show the rapid convergence to the effective model for large values of $D$.   

Monte Carlo study of a $U(1)\times U(1)$ system with $\pi$-statistical interaction

We study a $U(1)\times U(1)$ system with two species of loops with mutual $\pi$-statistics in (2+1) dimensions. We are able to reformulate the model in a way that can be studied by Monte Carlo and we determine the phase diagram. In addition to a phase with no loops, we find two phases with only one species of loop proliferated. The model has a self-dual line, a segment of which separates these two phases. Everywhere on the segment, we find the transition to be first-order, signifying that the two loop systems behave as immiscible fluids when they are both trying to condense. Moving further along the self-dual line, we find a phase where both loops proliferate, but they are only of even strength, and therefore avoid the statistical interactions. We study another model which does not have this phase, and also find first-order behavior on the self-dual segment.   

Session T28: Semiconductors

Interaction-driven versus disorder-driven transport in ultra-dilute GaAs two-dimensional hole systems

It is well-known that the insulating behavior in the two-dimensional metal-to-insulator transition demonstrates a finite temperature conduction via hopping. Recently, however, some very strongly interacting higher purity two-dimensional electron systems at temperatures $T\rightarrow 0$ demonstrate certain nonactivated insulating behaviors that are absent in more disordered systems. Through measuring in dark the $T$-dependence of the conductivity of ultra-high quality 2D holes with charge densities down to $7\times10^{8}$ $cm^{-2}$, an approximate power-law behavior is identified. Moreover, for the lowest charge densities, the exponent exhibits a linearly decreasing density-dependence which suggests an interaction-driven nature. Such an electron state is fragile to even a slight increase of disorder which causes a crossover from nonactivated to activated conduction. The non-activated conduction may well be an universal interaction-driven signature of an electron state of strongly correlated (semiquantum) liquid.   

Abruptness improvement of the interfaces of AlGaN/GaN superlattice by cancelling asymmetric diffusion

Interface abruptness has been an important issue in the construction of quantum wells as active layer in optoelectronic devices, which is extremely crucial in achieving stronger quantum confinement and consequently higher emission efficiency. The interfacial sharpness is highly associated with the crystal structure as well as the elemental transition. However, few studies have been done focusing on the elemental diffusion effect at the interface. In this work, the accurate determination was approached to the elemental inter-diffusion depth across the GaN/Al$_{0.5}$Ga$_{0.5}$N interfaces by using transmission electron microscopy, Auger electron microscopy, and X-ray diffraction. The GaN/Al$_{0.5}$Ga$_{0.5}$N superlattice was grown by metalorganic chemical vapor deposition (MOCVD) at high growth temperature (1070 $^{\circ}$C). The results showed that the Al diffusion at the upper and lower interfaces of Al$_{0.5}$Ga$_{0.5}$N barrier appears an asymmetric behavior, which is 0.62 and 0.99 nm, respectively. Such will lead to the gradient interfacial region and asymmetric quantum well, affecting the carrier quantum confinement. To improve the abruptness of the interface and to modify the asymmetric diffusion, self-compensation pair technique was proposed and introduced to the growth of the lower Al$_{0.5}$Ga$_{0.5}$N/GaN interface, blocking the Al downward diffusion. Fist-principles simulations also showed that the structural relaxation at the strained heterointerface influences the electronic structure as well as elemental diffusion.   

Local Structure of Amorphous GaNAs Alloys Across the Composition Range

Typically only dilute (up to $\sim$10\%) highly mismatched alloys (HMAs) can be grown due to the large differences in atomic size and electronegativity of the host and the alloying elements. Recently, we overcame the miscibility gap of the GaN$_{1-x}$As$_{x}$ system using low temperature molecular beam epitaxy (LT-MBE) and successfully synthesized alloys over a wide composition range. In the intermediate composition range (0.10 $<$ x $<$ 0.75) the resulting alloys are amorphous. To gain a better understanding of the amorphous structure, the local environment of the As and Ga atoms was investigated using extended x-ray absorption fine structure (EXAFS). The EXAFS analysis shows a high concentration of dangling bonds compared to the crystalline binary endpoint compounds of the alloy system. The disorder parameter was larger for amorphous films compared to crystalline references, but comparable with other amorphous semiconductors. By examining the Ga local environment, the dangling bond density and disorder associated with As-related and N-related bonds could be decoupled. The N-related bonds had a lower dangling bond density and lower disorder. The significant dangling bond density may help explain the difficulty of doping the material.   

Characterization of GaN grown on Si substrate with sputtering AlN buffer layer by molecular beam epitaxy

This study reports the characterization of GaN grown on Si substrate with sputtering AlN buffer layer by plasma-assisted molecular beam epitaxy. Structural properties were measured by X-ray diffraction measurement and transmission electron microscopy. XRD spectrum showed the sputtering buffer layer which was mainly (100)$_{AlN}$ and followed by the GaN epilayer which contained poly \textbf{\textit{M}}-plane GaN and other structural planes such as (002)$_{GaN}$ (\textbf{\textit{c}}-plane), and (101)$_{GaN}$. In TEM analysis, we demonstrated GaN of \textbf{\textit{c}}- and \textbf{\textit{A}}-plane grains. The pure \textbf{\textit{M}}-plane GaN was also found in the form of grain and the high-resolution images showed clear atomic arrangement. Besides, the diffraction pattern with multi \textbf{\textit{M}}-plane GaN was attributed to several \textbf{\textit{M}}-plane GaN crystals which were grown in different orientations on in-plane surface. In addition, optical properties measured by photoluminescence and cathodoluminescence measurement both showed two main peaks at 3.2 eV and 3.4 eV, indicated that zinc-blende and wurtzite structure exist in the GaN layer at the same time.   

Characterization of InGaN/GaN Quantum Well grown on GaN microdisk using $\gamma $-LiAlO$_{2}$ substrate by Plasma-assisted Molecular Beam Epitaxy

The InGaN/GaN quantum wells grown on GaN microdisks by plasma-assisted molecular beam epitaxy (PAMBE) have been investigated. The optical properties and micro-structure of InGaN/GaN quantum wells were studied by Cathodoluminescence (CL) and transmission electron microscope (TEM). According to the observation of high-resolution TEM, we obtained the high quality of InGaN/GaN quantum wells grown on GaN micro-disk. The In-ratio (x) of In$_{x}$Ga$_{1-x}$N is $\sim $8{\%} determined by the measurement of energy-dispersive X-ray spectroscopy (EDX). The optical gap of In$_{0.08}$Ga$_{0.92}$N was measured to be $\sim $3eV determined by CL measurement, which is consistent with the calculation of bowing parameters and the measurement of EDX.   

Unraveling the Atomic Structure of GaN(0001) Pseudo-1$\times $1: Surface-Electron-Gas Mediated Dimer Ordering

Gallium nitride based light emitting devices have seen a steep rise of attention in recent years because of their potential in revolutionizing the current lighting industry. Of great importance in advancing the material technology is the understanding of the GaN(0001) surface, onto which most of the commercial devices are grown. We report a novel dimer-based model for Ga-rich GaN(0001), which exhibits an intriguing reconstruction known as the pseudo-1$\times $1. To unravel its atomic structure, we have cooled the surface to cryogenic temperatures while monitoring the reconstruction by reflection high-energy electron diffraction and scanning tunneling microscopy. Upon cooling, the pseudo-1$\times $1 phase transforms into a new phase consisting of buckled Ga-dimers on the surface. This observation then strongly suggests the existence of Ga dimers also at the room-temperature surface, although only partially ordered compared to the low temperature case. Combined with first-principles calculations, we propose a new model for the pseudo-1$\times $1 consisting of dimers that are spaced $\sim $1.9 nm (6a) apart along $<$11\underline {2}0$>$ azimuths, while being randomly distributed along other directions. The mechanism of this partial ordering is identified to be through the surface electron gas residing within the bulk band-gap.   

The electrical properties of epitaxial p-type ZnO films grown on GaAs (001)

Wurtzite ZnO epitaxial layers with both p-type and n-type characteristics are grown on n-type GaAs(001) substrates by pulsed laser deposition (PLD). The local electrical properties of the ZnO layers were investigated by electrostatic force microscope (EFM), Kevin force microscopy (KFM), and conducting atomic force microscopy (CAFM). Local work function difference of $\sim $125.5 meV was observed on p-type ZnO layer from KFM and EFM measurements due to the un-uniform diffusion of As atoms from the GaAs substrate upon thermal annealing. We also found the work function of p-type ZnO is larger than that of n-type ZnO layer, in which the difference varied from 368.4 to 493 meV. The rectifying junction under p-ZnO/n-GaAs configuration and Ohmic contact under metal probe (Ti)/p-ZnO configuration were both observed by CAFM.   

Mapping the band profile across the Gd$_{2}$O$_{3}$/GaAs(100) hetero-interface by using scanning tunneling microscopy

Direct measurements of atomic-scale electronic structure at nm-thick epitaxial Gd$_{2}$O$_{3}$ gate oxides on GaAs have been performed using cross-sectional scanning tunneling microscopy and spectroscopy. Both scanning tunneling spectroscopy and analysis of the local electronic states across the gate oxides suggest the Ga-O terminated hetero-interface. In addition, along with the theoretical modeling, the band offsets for both conduction and valence states are identified. A unique combination of STM and STS successfully provides direct information on the interfacial band profile and band offsets across the model high-$\kappa$/III-V system in the work.   

Phase-dependence and manipulation of coherent oscillations of a single-electron wavefunction in a dynamic quantum dot

Surface acoustic waves (SAWs) in a GaAs heterostructure generate dynamic quantum dots, each capable of carrying a single electron through a gated potential landscape. At the SAW velocity (~2800 m/s), the change in potential due to a 100nm surface gate will occur in a period of 40ps in the rest frame of the dot. This high-speed modulation of the potential, far beyond the experimental limit of fast gate-switching, allows for the observation of coherent single-electron dynamics. Previous work has shown that an abrupt shift in dot confinement will cause an electron to oscillate unitarily from side to side. This excitation was measured non-invasively via a tunnel barrier, and good agreement was found between measurements and simulations of the dot dynamics. We present here the results of further work in which we examine the coherence length and phase-dependence of the single-electron oscillations. Through the use of a time-dependent model we also study surface-gate arrangements which may be used to manipulate the electron dynamics mid-stream.   

Equi-spin-splitting distribution near the minimum-spin-splitting surface under biaxial strains in bulk wurtzite materials

The spin-splitting energies in biaxially strained bulk wurtzite materials are calculated using the linear combination of atomic orbital method, and the equi-spin-splitting distributions in $k$-space near the minimum-spin-splitting (MSS) surfaces are illustrated. These data are compared with those derived analytically using the two-band \textbf{k} $\mathbf{\cdot}$ \textbf{Dp} (2KP) model. It is found the results from these two methods are in good agreement for small $k$. However, the ellipsoidal MSS surface under compressively biaxial strain predicted by the 2KP model does not exist, due to the data points are far from the $\Gamma $ point in this case. As a result, from compressively to tensilely biaxial strain, only three types of shapes of the MSS surface exist in the wurtzite Brillouin zone; that is, a hyperboloid of two sheets, a hexagonal cone and a hyperboloid of one sheet.   

How Hydrogen Terminated Diamond Acquires a Negative Electron Affinity Surface

Electron emission from the negative electron affinity (NEA) surface of hydrogen terminated, boron doped diamond in the [100] orientation is investigated using angle resolved photoemission spectroscopy (ARPES). ARPES measurements using 16 eV synchrotron and 6 eV laser light are compared and found to show a catastrophic failure of the sudden approximation. While the high energy photoemission is found to yield little information regarding the NEA, low energy laser ARPES reveals for the first time that the NEA results from a novel Franck-Condon mechanism coupling electrons in the conduction band to the vacuum. The result opens the door to the development of a new class of NEA electron emitter based on this effect.   

Laser Phase Separation of Si Rich Oxides: The Role of Composition

Continuous-wave laser annealing of Si-rich oxide thin films with varying Si content were performed in order to obtain Si nanocrystals (Si$_{nc}$) embedded in silica. The composition, irradiation times and power densities were investigated as well as the role of hydrogen in phase separation. Si$_{nc}$ in SiO$_{2}$ appear to be very promising for the realization of optical function as light emission or optical memory. Nanocrystaline Si finds also important utility in photovoltaics thanks to quantum confinement in the nanostructures offering a wider bandgap material which, in a tandem configuration, can allow a better use of the solar spectrum. Conventional techniques utilize high-temperature processing to obtain Si-SiO$_{2}$ phase separation. These processes are not compatible with mass production methods. An alternative approach capable of avoiding high temperature processing is the laser annealing of SiO$_{x}$ films. The structural effect due to annealing were investigated by Raman and photoluminescence spectroscopy. It has been shown that the size and amount of Si$_{nc}$ depends both on the oxygen content and on the laser power density. PECVD grown hydrogenated SiO$_{x}$ films were compared with sputtered films without hydrogen to identify its role for the phase separation.   

A Novel Technique for Detecting Trace Residues of Contamination on GaAs Surfaces before MBE Growth

To prepare a GaAs substrate for molecular beam epitaxial (MBE) growth, the nominal $\sim $ 3 nm native oxide is typically thermally desorbed in vacuum. To test the completeness of this desorption, we describe a technique, which combines MBE, thermal desorption, atomic force microscopy (AFM), reflection high-energy electron diffraction (RHEED), and secondary ion mass spectroscopy (SIMS), for detecting trace residues of contamination on (100) GaAs surfaces before MBE growth. At all desorption temperatures in the range 600 \r{ }C to 665 \r{ }C, our RHEED measurements show that the native oxide is largely desorbed within 2 min. However, the SIMS and AFM data indicate that a residue of sub-monolayer oxide invariably remains on the GaAs (100) surface, and tenaciously resists all further attempts at its removal by thermal desorption. Since thermal desorption of the native oxide has long been the standard technique before MBE growth, we suggest that all MBE growth of GaAs heterostructures has been through a partial monolayer of native oxide. We believe that this is the likely reason for the failure of high quality attempts at MBE growth of GaAs after lithographic patterning on a previously grown MBE structure.   

High-performance substrate-emitting quantum cascade ring lasers

An InP based mid-infrared quantum cascade laser with a ring-shaped cavity is demonstrated in room temperature continuous wave operation. The light is coupled out with a second order distributed feedback grating buried inside the cavity. The device is epilayer-down bonded to a heat spreader and the light is emitted through the substrate. The emission wavelength is around 4.85 $\mu $m with a high power output of 0.51 W. Single mode operation persists up to 0.4 W. Far field exhibits concentric ring features. Modal behavior is analyzed using the coupled mode theory, which suggests that the device operates in an extremely high order mode. Polarization measurement indicates that the beam is azimuthally polarized. This unique polarization state with high power output may find applications in tight focusing, optical tweezers, and material processing.   

3D Simulation of the Growth of Alloy Semiconductor Quantum Dots Considering Morphological and Compositional Coupling

Fabrication of quantum dots (QDs) with high density may be realized by self-assembly via heteroepitaxial growth of thin films. Since the electronic and optoelectronic properties of QDs are sensitive to size, morphology, strain and especially composition, it is of great importance to control their composition profiles and morphology, and engineer the strain in them. Since the growth is a dynamic process, which carries out via surface diffusion driven primarily by strain relaxation and entropy change due to chemical intermixing, a strong coupling between morphological and composition evolutions during this process leads to a rather complex dynamics, which has not been fully understood. In this work, a 3-D finite element model is developed, which is capable of modeling the formation, self-assembly and coarsening of hetero-epitaxial alloy islands by considering the coupling of morphological and compositional evolution. Several interesting experimental observations, such as fast coarsening kinetics; asymmetries in composition profile and island shape; lateral motion of alloy islands have been observed in our simulations. Our model predictions have painted a rather complete picture for the entire dynamic evolution during the growth of nanoscale heteroepitaxial islands.   

Session T29: Focus Session: Semiconductor Qubits - Coherent Control, Decoherence, and Relaxation

Electrical control of single spin dynamics

Over ten years ago, Daniel Loss and David DiVincenzo proposed using the spin of a single electron as a quantum bit. At the time of the proposal, it was not possible to trap a single electron in a device and measure its spin, let alone demonstrate control of quantum coherence. In this talk I will describe recent progress in the field, focusing on two new methods for single spin control that have been developed by my group at Princeton. The first method is based on quantum interference and implements spin-interferometry on a chip. The second method utilizes the strong spin-orbit coupling of InAs. By shifting the orbital position of the electronic wavefunction at gigahertz frequencies, we can control the orientation of a single electron spin and measure the full g-tensor, which exhibits a large anisotropy due to spin-orbit interactions. Both methods for single spin control are orders of magnitude faster than conventional electron spin resonance and allow investigations of single spin coherence in the presence of fluctuating nuclear and spin-orbit fields. I will also describe recent efforts to transfer these methods to silicon quantum dots, where the effects of fluctuating nuclear fields are much smaller.   

Harmonic Generation in InAs Nanowire Double Quantum Dots

InAs nanowires provide a useful platform for investigating the physics of confined electrons subjected to strong spin-orbit coupling. Using tunable, bottom-gated double quantum dots, we demonstrate electrical driving of single spin resonance.\footnote{S. Nadj-Perge {\it et al.}, Nature {\bf468}, 1084 (2010)}$^,$\footnote{M.D. Schroer {\it et al.}, Phys. Rev. Lett. {\bf107}, 176811 (2011)} We observe a standard spin response when the applied microwave frequency equals the Larmour frequency $f_{0}$. However, we also observe an anomalous signal at frequencies $f_n = f_0 / n$ for integer n up to n $\sim$5. This is equivalent to generation of harmonics of the spin resonance field. While a $f_0/2$ signal has observed,\footnote{E.A. Laird {\it et al.}, Phys. Rev. Lett. {\bf99}, 246601 (2007)} we believe this is the first observation of higher harmonics in spin resonance. Possible mechanisms will be discussed.\footnote{E.I. Rashba, arXiv:1110.6569 (2011)} Acknowledgements: Research supported by the Sloan and Packard Foundations, the NSF, and Army Research Office.   

Composite pulse sequences for Z-rotations robust against small magnetic field gradient in singlet-triplet qubits

We design piecewise composite pulse sequences of the exchange interaction in singlet-triplet qubits, suitable for achieving a Z-rotation along the Bloch sphere of arbitrary angle under the influence of a small stray magnetic field gradient. We explicitly show that upon appropriately choosing the pulse parameters, the error arising from the magnetic field gradient can be canceled at least to the third order. Examining the error as a function of the magnetic field gradient, we estimate the magnitude of fluctuation in the magnetic field gradient that can be tolerated under certain quantum error correction threshold.   

Composite pulse sequences for robust universal control of singlet-triplet qubits

We consider composite pulse sequences for the exchange interaction in singlet-triplet qubits, in the presence of a finite magnetic field gradient (producing a term in the Hamiltonian similar in magnitude to the exchange interaction). We find pulse sequences achieving arbitrary rotations on the Bloch sphere, for which there is no first-order term in the error arising from fluctuations of the magnetic field gradient. We quantify the range of experimental parameters where our composite sequences can outperform naive uncorrected sequences.   

Analytically solvable pulses for spin qubit rotations

The hyperbolic secant pulse is a well known pulse shape for which the time dependent Schrodinger equation of a two-level system is analytically solvable. It has in the past been proposed [1] for optical spin rotations in quantum dots, and used experimentally to that end [2]. In this talk, a family of pulses will be introduced which can be viewed as the generalization of the sech pulse. These pulses may have skewed temporal profiles and frequency modulation (``chirping''). I will present results for the fidelity of spin rotations using some of these pulses and show that in the case of ``Raman-type'' control, where an auxiliary excited state is used, it can be advantageous to replace the usual 2$\pi$ sech pulse. \\[4pt] [1] Economou et al., Phys. Rev. B \textbf{74}, 205415 (2006), Economou and Reinecke, Phys. Rev. Lett. \textbf{99}, 217401 (2007) \\[0pt] [2] Greilich et al., Nature Physics \textbf{5}, 262 (2009)   

Universal set of single-qubit gates based on geometric phase of electron spin in a quantum dot

The electron spin in a single quantum dot is one of the perspective realizations of a qubit for the implementation of a quantum computer. During last decade several control schemes to perform single gate operations on a single quantum dot spin have been reported. We propose a scheme that allows performing ultrafast arbitrary unitary operations on a single qubit. We demonstrate how to use the geometric phase, which the Bloch vector gains along the cyclic path, to prepare an arbitrary state of a single qubit. It is shown that, the geometrical phase is fully controllable by the relative phase between the external fields. Using the analytic expression of the evolution operator for the electron spin in a quantum dot, we propose a scheme to design a universal set of single-qubit gates based solely on the geometrical phase that the qubit state acquires after a cyclic evolution in the parameter space. The scheme is utilizing ultrafast linearly-chirped pulses providing adiabatic excitation of the qubit states and the geometric phase is fully controlled by the relative phase between pulses.   

A fast ``hybrid'' silicon double quantum dot qubit

We propose a quantum dot qubit architecture that has an attractive combination of speed and fabrication simplicity. It consists of a double quantum dot with one electron in one dot and two electrons in the other. The qubit itself is a set of two states with total spin quantum numbers $S^2$ = 3/4 (S = 1/2) and $S_z$ = -1/2, with the two different states being singlet and triplet in the doubly occupied dot. The architecture is relatively simple to fabricate, a universal set of fast operations can be implemented electrically, and the system has potentially long decoherence times. These are all extremely attractive properties for use in quantum information processing devices.   

Theory of Spin Relaxation in Two-Electron Lateral Coupled Quantum Dots

We present a global picture of the phonon-induced spin relaxation of two-electron lateral double quantum dots. The analysis covers a wide range of tuning parameters, such as the magnetic field, the exchange coupling, and the electric field (detuning). Our examples cover experimentally important scenarios. Quantitative results were obtained with a highly accurate numerical technique for the two most relevant host materials--GaAs and silicon. We find that in the presence of spin-orbit coupling, the rate becomes anisotropic and its maxima and minima are generated with an in-plane magnetic field parellel or perpendicular to the dots' alignment dependent on specifics, such as spectral (anti-)crossings (spin hot spots), or the detuning strength. For all regimes, we give qualitative explanations of our observations. By understanding the spin lifetimes ($T_1$), this work marks a crucial step to the realization of two-electron semiconductor qubits.   

Dephasing in lateral double quantum dot systems due to evanescent-wave Johnson noise

Lateral double quantum dots suffer decoherence due to coupling to the environment. Previous theoretical calculations of dephasing time based on the phonon bath model (Vorojtsov et al. PRB 71, 2005) and gate-voltage fluctuations (Valente et al. PRB 82, 2010) are insufficient to explain the short dephasing time observed in experiment with a charge-based double quantum dot system (Petta et al. PRL 93, 2004). Here we analyze the effect of fluctuating electromagnetic fields in the vicinity of conducting gates on the dephasing rate of charge-based double quantum dot systems.   

Spin relaxation times and spin-dependent transport of silicon 2DEG and donors in high magnetic fields

We measured the spin-lattice relaxation ($T_1$) and spin coherence ($T_2$) times of the two-dimensional electron gas (2DEG) and neutral donors in a silicon field-effect transistor by pulsed electrically detected magnetic resonance at $\approx3.4\:$T. The 2DEG $T_1$ varies between $\approx200-800\:$ns depending on the carrier density with an in-plane magnetic field configuration, but remains constant at $\approx400\:$ns with an out-of-plane field configuration. On the other hand, $T_2\approx50-150\:$ns for all carrier densities and both field orientations. The neutral donor $T_1$ and $T_2$ are found to be similar to that of the 2DEG. At even higher out-of-plane magnetic fields of $8-12\:$T, Landau levels are clearly resolved in transport measurements and both the 2DEG and donor EDMR signals show corresponding oscillatory behavior as the carrier density is varied. We attribute this behavior to the alignment of the Fermi level with spin-split and different indexed Landau levels.   

Two-electron dephasing in a single silicon quantum dot

We study the dephasing of two-electron states in a single silicon quantum dot. Specifically, we consider dephasing due to the electron-phonon coupling and charge noise, treating orbital, valley, and mixed valley-orbit excitations. For phonon-induced dephasing, the intervalley processes are most important and lead to a dephasing rate of about 1 MHz. In an ideal system, dephasing due to charge noise is strongly suppressed due to a vanishing dipole moment. However, introduction of disorder or anharmonicity leads to large effective dipole moments, and hence possibly strong dephasing.   

Long Spin Relaxation and Coherence Times of Electrons In Gated Si/SiGe Quantum Dots

Single electron spin states in semiconductor quantum dots are promising candidate qubits. We report the measurement of 250 $\mu $s relaxation (T$_{1})$ and coherence (T$_{2})$ times of electron spins in gated Si/SiGe quantum dots at 350 mK. The experiments used conventional X-band (10 GHz) pulsed electron spin resonance (pESR), on a large area (3.5 x 20 mm$^{2})$ dual-gate undoped high mobility Si/SiGe heterostructure sample, which was patterned with 2 x 10$^{8}$ quantum dots using e-beam lithography. Dots having 150 nm radii with a 700 nm period are induced in a natural Si quantum well by the gates. The measured T$_{1}$ and T$_{2}$ at 350 mK are much longer than those of free 2D electrons, for which we measured T$_{1}$ to be 10 $\mu $s and T$_{2 }$to be 6.5 $\mu $s in this gated sample. The results provide direct proof that the effects of a fluctuating Rashba field have been greatly suppressed by confining the electrons in quantum dots. From 0.35 K to 0.8 K, T$_{1}$ of the electron spins in the quantum dots shows little temperature dependence, while their T$_{2}$ decreased to about 150 $\mu $s at 0.8 K. The measured 350 mK spin coherence time is 10 times longer than previously reported for any silicon 2D electron-based structures, including electron spins confined in ``natural quantum dots'' formed by potential disorder at the Si/SiO$_{2}$\footnote{S. Shankar \textit{et al}., Phys. Rev. B 82, 195323 (2010)} or Si/SiGe interface, where the decoherence appears to be controlled by spin exchange.   

Creation of entangled exciton states in coupled quantum dots

Quantum state preparation through external control is fundamental to established methods in quantum information processing and in studies of dynamics. In this respect, systems such as excitons in semiconductor quantum dots (QDs) are of particular interest since they can be easily driven to a particular state through the coherent interaction with a tuned optical field such as an external laser pulse. Here we propose to use adiabatic rapid passage (ARP) to excite entangled states in an ensemble of coupled quantum systems. The ARP protocol makes use of optical pulses with both frequency and temporal modulation and it is an efficient method to achieve population inversion in quantum dot ensembles as it is robust with respect to fluctuations in coupling and detuning. We explore this problem using a generalized t-J Hamiltonian to model an interacting many-dot system described in terms of hard-core bosons. Our quantitative analysis shows that ARP can be successfully implemented to create entangled states in a realistic ensemble of inhomogeneously distributed QDs.   

Session T30: Quantum Algorithms

Adiabatic Surface Code Quantum Computing

There are many approaches to constructing a quantum computer. In addition to the numerous different physical substrates available, there are a plethora of different underlying computational architectures from which to choose. Two major classes of architectures can be distinguished: those requiring a substantial external active control system to suppress errors, and those whose underlying physical construction eliminates much, if not all, of the need for such a control system. Here we focus on the latter class of architectures and address the question: ``How does one fault-tolerantly quantum compute on a system protected from decoherence by a static Hamiltonian?'' We present a solution that adiabatically interpolates between static Hamiltonians, each of which protects the quantum information stored in its ground space. Since each of these ground spaces can be described as a quantum error-correcting codespace, we call this process adiabatic code deformation. After describing a particular surface code (the toric code) and the way to encode information in code defects, we give explicit adiabatic interpolations that effect braids between defects, allowing for a CNOT gate between encoded qubits. We finish by describing how to extend our procedures to allow for universality.   

Quantum Random Walks and the Graph Isomorphism Problem

We investigate the quantum dynamics of particles on graphs (``quantum walk''), with the aim of developing quantum algorithms for determining whether or not two graphs are isomorphic. We investigate such walks on strongly regular graphs (SRGs), a class of graphs with high symmetry. We explore the effects of particle number and interaction range on a walk's ability to distinguish non-isomorphic graphs. We numerically find that both non-interacting three-boson and three-fermion continuous time walks have the same distinguishing power on a dataset of 70,712 pairs of SRGs, each distinguishing over 99.6\% of the pairs. We also find that increasing to four non-interacting particles further increases distinguishing power on this dataset. While increasing particle number increases distinguishing power, we prove that any walk of a fixed number of non-interacting particles cannot distinguish all SRGs. We numerically find that increasing particle number and increasing interaction range both result in increased distinguishing power of non-SRGs that are designed to be indistinguishable to the hard-core two-boson walk.   

Hamiltonian Simulation Using Linear Combinations of Unitary Operations

We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation algorithms based on product formulas and, most notably, scales better with the simulation error than any known Hamiltonian simulation technique. Our main tool is a general method to nearly deterministically implement linear combinations of similar unitary operations, which we show is optimal among a large class of methods.   

Measurement-Based Quantum Computation with Thermal States and Always-on Interactions

Quantum computation can be achieved by single-qubit measurements on an initial entangled state. It is often implicitly assumed that the interactions between spins can be switched off so that the dynamics of the measured spins does not affect the computation. We propose a model spin Hamiltonian so that measurement-based quantum computation can be accomplished on a thermal state with always-on interactions. Moreover, computational errors induced by thermal fluctuations can be corrected and thus the computation can be executed fault tolerantly if the temperature is below a threshold value.   

Quantum Computational Universality of the 2D Cai-Miyake-D\"ur-Briegel Quantum State

Universal quantum computation can be achieved by simply performing single-qubit measurements on a highly entangled resource state, such as cluster states. Cai, Miyake, D\"ur, and Briegel recently constructed a ground state of a two-dimensional quantum magnet by combining multiple Affleck-Kennedy-Lieb-Tasaki quasichains of mixed spin-3/2 and spin-1/2 entities and by mapping pairs of neighboring spin-1/2 particles to individual spin-3/2 particles [Phys. Rev. A {\bf 82}, 052309 (2010)]. They showed that this state enables universal quantum computation by constructing single- and two-qubit universal gates. Here, we give an alternative understanding of how this state gives rise to universal measurement-based quantum computation: by local operations, each quasichain can be converted to a one-dimensional cluster state and entangling gates between two neighboring logical qubits can be implemented by single-spin measurements. Furthermore, a two-dimensional cluster state can be distilled from the Cai-Miyake-D\"ur-Briegel state.   

Algorithmic Quantum Cooling

Efficient methods of cooling are essential for exploring the fundamental properties of low temperature physics. A remarkable cooling method is known as the evaporative cooling (or ``coffee'' cooling), where energetic particles are filtered away so as to lower the mean energy of the rest of the system. Inspired by the idea of evaporative cooling, we developed a method called algorithmic quantum cooling (AQC) for achieving the goal of cooling for any physical system which is simulable by a quantum computer. The novel feature of AQC is that the evolution of the state of the system is modeled as the movement of a one-dimensional classical random walk; the walker plays the role of the motion of the gas particles in an ordinary evaporative cooling. The implementation of this method is analogous to the setting of Maxwell's demon, where the experimentalist can monitor the heat-up or cool-down of the system, and apply feedback control to the resulting states. Here we cover the results of the connection of AQC with quantum non-demolition measurement, a scaling analysis of AQC, and the application of amplitude amplification to achieve quantum speedup. Experimental realization of AQC can be accomplished with currently available technologies.   

Progress on exploring practical applications of quantum annealing and D-Wave One

A D-Wave One quantum optimizer is currently being installed at the newly created USC-Lockheed Martin Quantum Computing Center. This chip implements quantum annealing at finite temperature as a computational resource, with 90 working qubits. Quantum annealing is a particularly simple branch of adiabatic quantum computation. We report work in progress on exploring practical applications of quantum annealing in general, and this chip in particular. Some of this work is done in collaboration with Aspuru-Guzik's group at Harvard.   

Adiabatic Quantum Anomaly Detection and Machine Learning

We present methods of anomaly detection and machine learning using adiabatic quantum computing. The machine learning algorithm is a boosting approach which seeks to optimally combine somewhat accurate classification functions to create a unified classifier which is much more accurate than its components. This algorithm then becomes the first part of the larger anomaly detection algorithm. In the anomaly detection routine, we first use adiabatic quantum computing to train two classifiers which detect two sets, the overlap of which forms the anomaly class. We call this the learning phase. Then, in the testing phase, the two learned classification functions are combined to form the final Hamiltonian for an adiabatic quantum computation, the low energy states of which represent the anomalies in a binary vector space.   

Universal Blind Quantum Computation

Blind Quantum Computing (BQC) allows a client to have a server carry out a quantum computation for them such that the client's inputs, outputs and computation remain private. Recently we proposed a universal unconditionally secure BQC scheme, based on the conceptual framework of the measurement-based quantum computing model, where the client only needs to be able to prepare single qubits in separable states randomly chosen from a finite set and send them to the server, who has the balance of the required quantum computational resources. Here we present a refinement of the scheme which vastly expands the class of quantum circuits which can be directly implemented as a blind computation, by introducing a new class of resource states which we term {\em dotted-complete graph states} and expanding the set of single qubit states the client is required to prepare. These two modifications significantly simplify the overall protocol and remove the previously present restriction that only nearest-neighbor circuits could be implemented as blind computations directly. As an added benefit, the refined protocol admits a substantially more intuitive and simplified verification mechanism, allowing the correctness of a blind computation to be verified with arbitrarily small probability of error.   

Experimental demonstration of blind quantum computing

Quantum computers are among the most promising applications of quantum-enhanced technologies. Quantum effects such as superposition and entanglement enable computational speed-ups that are unattainable using classical computers. The challenges in realising quantum computers suggest that in the near future, only a few facilities worldwide will be capable of operating such devices. In order to exploit these computers, users would seemingly have to give up their privacy. It was recently shown that this is not the case and that, via the universal blind quantum computation protocol, quantum mechanics provides a way to guarantee that the user's data remain private. Here, we demonstrate the first experimental version of this protocol using polarisation-entangled photonic qubits. We demonstrate various blind one- and two-qubit gate operations as well as blind versions of the Deutsch's and Grover's algorithms. When the technology to build quantum computers becomes available, this will become an important privacy-preserving feature of quantum information processing.   

Classical Ising Models Realised on Optical Lattices

We describe a simple quantum algorithm acting on a register of qubits in $d$ spatial dimensions which computes statistical properties of $d+1$ dimensional classical Ising models. The algorithm works by measuring scattering matrix elements for quantum processes and Wick rotating to provide estimates for real partition functions of classical systems. This method can be implemented in a straightforward way in ensembles of qubits, e.g. three dimensional optical lattices with only nearest neighbor Ising like interactions. By measuring noise in the estimate useful information regarding location of critical points and scaling laws can be extracted for classical Ising models, possibly with inhomogeneity. Unlike the case of quantum simulation of quantum hamiltonians, this algorithm does not require Trotter expansion of the evolution operator and thus has the advantage of being amenable to fault tolerant gate design in a straightforward manner. Through this setting it is possible to study the quantum computational complexity of the estimation of a classical partition function for a 2D Ising model with non uniform couplings and magnetic fields. We provide examples for the $2$ dimensional case.   

Initialization and Readout of Spin Chains for Quantum Information Transport

Linear chains of spins acting as quantum wires are a promising approach to achieve scalable quantum information processors. Nuclear spins in apatite crystals closely emulate a one-dimensional spin chain, thus providing an ideal test-bed for the experimental study of quantum information transport by means of Nuclear Magnetic Resonance techniques. The natural dipolar interaction among the spins can be manipulated via the available collective NMR control to simulate the Hamiltonian capable of driving quantum transport. We present control protocols for initialization and readout of $^{19}$F spin chains in Fluorapatite, even in the absence of single-spin addressability. We experimentally prepare and read out desired initial states for transport tasks, such as the simulation of single-spin excitation transport and a two-spin encoded state for quantum information transfer. Our control schemes enable experimental characterization of quantum transport in spin chains and will allow further studies of protocols for perfect fidelity transfer.   

Dynamical decoupling and quantum error suppression in adiabatic quantum computation

Adiabatic quantum information processing, like other quantum computing paradigms, is susceptible to noise which can potentially spoil a computation. This talk will address two proposed methods to utilize stabilizer codes to combat such noise: dynamical decoupling and quantum error suppression. A combination of numerical and analytical techniques will illustrate the connections between these two approaches. The talk will conclude with a discussion of the practical advantages of dynamical decoupling over quantum error suppression.   

Complexity of the Quantum Adiabatic Algorithm

The Quantum Adiabatic Algorithm (QAA) has been proposed as a mechanism for efficiently solving optimization problems on a quantum computer. Here, we determine its efficiency by considering several constraint satisfaction (SAT) problems. We do this by studying the size dependence of their typical minimum energy gap using quantum Monte Carlo methods. We find that for most problems this gap decreases exponentially with the size of the problem, indicating that the QAA is not more efficient than existing classical search algorithms. However, for one specific problem, namely, MAX-2-XORSAT, there is evidence to suggest that the gap may be polynomial near the phase transition.   

Discrete-time quantum walks on the symmetric group (quantum card shuffling)

The next stage in uses of classical stochastic approaches, going beyond Markov chains (random walks on graphs), are walks on algebraic structures. The prime and classic example of such a problem is ``card shuffling,'' a walk on the permutation (symmetric) group. The richness of this non-Abelian group lends itself to modeling of complex phenomena, while it also quickly leads to rather complicated problems. The challenge of studying such quantum processes is no lesser, but the benefits can be expected to even outweigh the classical uses. We study a quantum analog of the classical ``top-to-random'' shuffle, where the top card is placed at random in the deck. We construct a ``coined'' DTQW on the permutation group: based on the action of a (unitary) ``coin'' operator in an additional (``coin'') space, (unitary) steps in the group space are taken, resulting in a (quantum) walk over group elements. We use general techniques for the eigenvalue problem of the combined coin and permutation operators, utilizing regularities in the block structure. We have reached preliminary solutions for low-dimensional cases. Currently we are integrating them into a more general solution, which will yield the first step in this deep and far-reaching, while challenging problem.   

Session T31: Focus Session: Topological Insulators: Synthesis and Characterization - Spin Transport and Superconductivity

Towards spin injection from silicon into topological insulators

Attempts to uncover evidence of spin-momentum coupling in a topological insulator (TI) using transport measurements are hampered by many challenges. Most importantly, injection of a spin polarized current from a ferromagnet that is in contact or close proximity to a topological insulator can easily give rise to anisotropic magnetoresistance signals or planar Hall effect from stray fields, which have the same symmetry and hence are indistinguishable from any signal coming from the spin-momentum-locked surface states. Here we propose a scheme to remove this difficulty by injecting spin-polarized electrons from undoped silicon into the TI surface states. In addition to providing a long-distance transport region to separate the ferromagnetic spin source from the TI by several hundred microns or even millimeters, this approach will also allow spin precession measurements (necessary for unambiguous identification of spin signals) whereas direct injection does not. Detection is provided by differential measurement from two ballistic current contacts on the topological insulator. We will describe our progress in fabrication and measurement of devices with exfoliated crystals of TI Bi$_2$Se$_3$, including the determination of the silicon-Bi$_2$Se$_3$ Schottky barrier height of 0.34 eV   

Spin-momentum helical locking induced spin-valve effects in topological insulator/ferromagnet heterostructures

Topological insulator is composed of an insulating bulk state and an odd number of massless spin-helical Dirac cone formed two dimensional surface state. Here we report a novel spin-valve effect in Bi$_{1.5}$Sb$_{0.5}$Te$_{1.8}$Se$_{1.2}$/CoFe heterostructures. This effect indicates the spin-momentum helical locking on the Bi$_{1.5}$Sb$_{0.5}$Te$_{1.8}$Se$_{1.2}$ topological surface state. It is also indicated that the characteristics of helical surface can be preserved at topological insulator/ferromagnet interface although the ferromagnetism can break the time reversal symmetry and therefore generate an energy gap at the topological Dirac cone.   

Spin Transport Experiments in Topological Insulator Bi$_{2}$Se$_{3}$ Thin Films

Topological insulators are an unusual phase of quantum matter with an insulating bulk gap and gapless spin-momentum locked Dirac surface states. Such a spin-helical surface state provides rich opportunities for potential applications in spintronics. We performed spin valve experiments on exfoliated Bi$_{2}$Se$_{3}$ thin films ($\sim $ 10 nm thick) with ferromagnetic electrodes using a DC driving current in an in-plane magnetic field. We observed the two- terminal resistances are asymmetric between the large positive ($>$ 0.5 T) and negative ($<$-0.5 T) in-plane magnetic fields. The high and low resistance states can be reversed by changing the direction of the driving DC current. Furthermore, the measured resistance asymmetry decreases as temperature increases. One interpretation of our observation is related to the spin-momentum helical locking of topological surface states producing a spin-polarized surface current. We also performed the non-local spin valve measurements, and observed an asymmetry in the measured signal between opposite large magnetic fields.   

Josephson supercurrent through a topological insulator surface state

The long-sought yet elusive Majorana fermion is predicted to arise from a combination of a superconductor and a topological insulator. An essential step in the hunt for this emergent particle is the unequivocal observation of supercurrent in a topological phase. Here, we present direct evidence for a Josephson supercurrent in superconductor (Nb) - topological insulator (Bi$_{2}$Te$_{3})$ - superconductor e-beam fabricated junctions by the observation of clear Shapiro steps under microwave irradiation, and a Fraunhofer-type dependence of the critical current on magnetic field. The dependence of the critical current on temperature and electrode spacing shows that the junctions are in the ballistic limit. Shubnikov-de Haas oscillations in magnetic fields up to 30 T reveal a topologically non-trivial two-dimensional surface state. We argue that the ballistic Josephson current is hosted by this surface state despite the fact that the normal state transport is dominated by diffusive bulk conductivity. The lateral Nb-Bi$_{2}$Te$_{3}$-Nb junctions hence provide prospects for the realization of devices supporting Majorana fermions.   

Hybrid Superconducting Junctions of Bi$_{2}$Se$_{3}$ Topological Insulator Nanoribbons

Topological insulators are exotic materials with bulk band gap and metallic edge states which are protected on their own boundary topologically. Here, we report on the fabrication and measurement results of the superconducting proximity junctions of topological insulator nanoribbons of Bi$_{2}$Se$_{3}$. Single-crystalline Bi$_{2}$Se$_{3}$ nanoribbons are synthesized using the vapor-liquid-solid method, while the superconducting Al electrodes are formed on top of the nanowire. When a magnetic field ($H)$ is applied along the axial direction, the magneto-resistance data exhibit quasi-periodic oscillations with an average periodicity of $H^{\ast } \quad \sim $ 0.4 T, which is consistent with the Aharonov-Bohm oscillations. In the superconducting state, the supercurrent branch with a critical current of $I_{c} \quad \sim $ 90 nA is clearly observed in the current-voltage curve as a result of the superconducting proximity effect in Bi$_{2}$Se$_{3}$ nanoribbon. Quantized voltage steps of the Bi$_{2}$Se$_{3}$ nanoribbon Josephson junction under the microwave irradiation satisfy the ac Josephson relation.   

Signature of Majorana Fermions in Josephson Junctions of Bi2Se3

At the surface of a three-dimensional topological insulator lie Dirac fermions. Placing a superconductor in proximity to these surface fermions has been theoretically shown to produce Majorana fermions, an as-yet unobserved elementary particle. We report on the fabrication and low-temperature transport of a topological insulator in proximity to two superconductors -- a device forming a Josephson Junction with a topological insulator (Bi2Se3) as a weak link. Several departures from conventional Josephson Junctions are observed and evaluated in the context of the presence of a one-dimensional wire of Majorana fermions induced in the device.   

Superconductivity in the topological semimetal YPtBi

Superconductivity was recently discovered in the half Heusler compound YPtBi. Electrical resistivity and Hall data provide compelling evidence that supports the idea that band structure calculations are correct and that YPtBi is indeed a semimetal with nontrivial topology. The low-temperature superconductivity emerges from a remarkable normal state with an extremely low carrier density, no crystalline inversion symmetry, and strong band inversion. I will discuss the normal state properties of YPtBi and details of its superconducting state, and compare them to the characteristics of other potential topological superconductors. This research was performed at the University of Maryland, College Park in collaboration with Paul Syers, Kevin Kirshenbaum, Andrew P. Hope, and Johnpierre Paglione.   

Superconductivity in Bi2Te3 type three dimensional topological compounds induced via pressure

We report experimental updates on pressure induced superconductivity in Bi$_{2}$Te$_{3}$ type topological compounds. The topological nature of the superconductivity observed will be discussed in conjunction with on site high pressure structure investigations {\&} first principles calculations. A phase diagram of superconductivity as function of pressure will be provided.   

Proximity-Induced High-Temperature Superconductivity in a Topological Insulator

New topological phases of matter have been proposed to exist at the surface of some materials with spin-orbit coupling called topological insulators. Among the different exotic features of topological insulators, the interface between a topological insulator and a superconductor is of great interest. It is predicted that combining these two materials would lead to the emergence of Majorana fermion excitations which enable several applications in spintronics and quantum computing. Towards this goal, we have investigated Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$(Bi-2212)- Bi$_{2}$Se$_{3}$ interface junctions made by a new mechanical-bonding technique. Current vs. voltage and differential conductance measurements have been performed in various temperatures ranging from room temperature to 5K. Several anomalies were observed in the Andreev spectra including a zero bias conductance peak appearing below the critical temperature of the superconductor Bi-2212 (85K), a reduced gap in Bi-2212 as well as the intrinsic gap of Bi-2212. These features suggest the induction of high-temperature superconductivity in the Bi$_{2}$Se$_{3}$ due to proximity to Bi-2212.   

Point-contact Andreev Reflection Spectroscopy on Bi$_2$Se$_3$ Single Crystal

Point-contact spectroscopy measurement is carried out on Bi$_2$Se$_3$ single crystals via approaching a superconducting niobium tip (T$_c$=9.5 K) to the crystal surface. The tip-sample junction conductance is studied as a function of DC bias voltage, temperature, and magnetic field. The resulting spectra show a conductance dip at zero bias, indicative of ballistic transport. A homebuilt positioning stage enables us to approach the superconducting tip in nanometer accuracy, to precisely control the inter-facial barrier strength. We find that our experimental results cannot be simply described by the standard Blonder, Tinkham and Klapwijk (BTK) model even when the inelastic scattering at the interface is considered. An improved model taking into account the spin-orbit coupling effect is needed to fit our data.   

Crystal growth and physical property of Bi-Sb-Te-Se topological insulator and CuxBi2Se3 topological superconductor materials

The discovery of 3D topological insulator and topological superconductor materials opens up a new research field in the condensed matter physics. In order to exploit the novel surface properties of these topological insulators, it is crucial to achieve a bulk-insulating state in these topological insulator crystals. Unfortunately, all available topological insulator crystals are not bulk-insulating. We have grown a number of Bi-Se, Bi-Te, Sb-Te-Se, Bi-Sb-Se, Bi-Sb-Te-Se and Bi-Sb-Te-Se-S topological insulator single crystals by using 5N and 6N pure elements. We have measured the physical properties on these single crystals. We have studied the effect of growth condition and impurity on the bulk electrical conductivity of these single crystals. We try to answer two questions if it is possible to grow the bulk-insulating topological insulator single crystals and which maximum resistivity of these topological insulator single crystals we can grow. We have also grown a number of CuxBi2Se3 topological superconductor single crystals.   

Crystal structure and superconducting properties in Cu$_{x}$Bi$_{2}$Se$_{3}$

The recent discovery of the anomalous superconductivity in Cu$_{x}$Bi$_{2}$Se$_{3}$ (0.10$<$x$<$0.25) has attracted much attention because of the relation between superconducting state and topological surface state. In order to understand the role of Cu doping in superconducting Bi$_{2}$Se$_{3}$, we study the doping dependence of the magnetic properties and the characteristics of crystal structures. We made high quality of Cu$_{x}$Bi$_{2}$Se$_{3}$ single crystals with several doping level of x by using melt growth technique. We confirmed the superconducting transition from Cu$_{x}$Bi$_{2}$Se$_{3}$ for several doping levels and determined the phase diagram of a function of x. The lattice constant increases with increasing Cu doping level, however it saturated around x=0.25 which corresponds to the saturation of $T_{c}$ as well. We analyzed the crystal structure in detail in explaining the occurrence of superconductivity. Details of the structural and magnetization study will be discussed in the conference.   

Electrical Transport Properties of Bi$_{2}$Te$_{3}$ Nanotubes and Nanowires

Electrical transport properties of promising topological insulator, Bi$_{2}$Te$_{3}$ nanowires and nanotubes are measured at different temperatures and magnetic field and the results are compared with the Bi$_{2}$Se$_{3}$ thin films. The nanotube and nanowire samples are synthesized by galvanostatic electrodepositon and solution phase methods, with diameters of 70nm (ex) and 50nm (in) for nanotubes and 80$\sim $100nm for nanowires, respectively. The contact leads (Pt) are fabricated by using Focusing Ion Beam (FIB). The magnetoresistance of Bi$_{2}$Te$_{3}$ nanotubes shows linear dependence as a function of magnetic field, with a notable peak around zero field. This is different from Bi$_{2}$Se$_{3}$ thin films which show quadratic behavior, with a significant dip near zero field. The results will be discussed based on the possible weak localization effect in the nanotubes in comparison with the weak anti-localization effect in the films.   

Session T32: Focus Session: Dielectric, Ferroelectric, and Piezoelectric Oxides - Manganites

Colossal magnetodielectric effect in DyMn2O5: Electromagnons or rare earth?

We report on the results of spectroscopic studies of the excitations responsible for the colossal magnetodielectric effect in DyMn2O5 [1]. On one hand, many RMn2O5 compounds have electromagnons capable of inducing large steps in the dielectric constant. On the other hand, rare earth ions can posses electric dipole moments and also can produce dielectric anomalies. Both types of excitations are expected in the experimentally difficult low energy range 0.1-1 meV. We use high frequency dielectric, Fourier transform and back-wave oscillator spectroscopies in combination with low temperature and magnetic field up to 9 T to clarify the origin of the dielectric anomaly in DyMn2O5. [1] N. Hur, S. Park, P. A. Sharma, S. Guha, and S-W. Cheong, Colossal Magnetodielectric Effects in DyMn2O5, PRL 93, 107207 (2004).   

Magnetism-Driven Ferroelectricity in GdMn$_{2}$O$_{5}$

REMn$_{2}$O$_{5}$(RE=rare-earth) is one of the well-studied multiferroics which exhibits the reversible switching of ferroelectric polarization under the application of external magnetic fields. It is known that the ferroelectricity in REMn2O5 originates from the symmetric exchange interaction between Mn ions. However, the role of the rare-earth elements has never been elucidated. In order to reveal the full magnetic structure and the contribution of rare-earth magnetism to the ferroelectricity, we have studied the detailed magnetic and structural properties of high-quality single-crystalline GdMn$_{2}$O$_{5}$ (space group, Pbam). We have performed the resonant x-ray scMn$_{2}$O$_{5}$attering experiment, and comprehensive measurements of physical properties of the system, including magnetic susceptibility, dielectric constant and ferroelectric polarization with the variation of temperature and magnetic fields.   

Raman and Infrared studies of the multiferroics TbMn2O5 and YMn2O5

Orthorhombic manganites of the $RMnO_{3}$ and $RMn_{2}O_{5}$ families develop an electric polarization induced, flipped and flopped by application of a magnetic field. The $Tb(Y)Mn_{2}O_{5}$ Anti-ferromagnetic order is incommensurate between $T_{N}=42K$ ($44K$) and $T_{C}=38K$ and becomes commensurate between $T_{C}=38K$ and $T=24K$ ($18K$); at this temperature ferroelectricicity appears and remains incommensurate below $24K$ ($18K$)[1,2]. We have studied the $TbMn_{2}O_{5}$ and $YMn_{2}O_{5}$ Raman active phonons as a function of temperature and compared their behavior to similar multiferroic compounds $Bi(Dy)Mn_{2}O_{5}$ phonons where the $A_{g}$ high frequencies modes soften between $T^{*}\sim 70K$ and $T_{N}$ and harden below $T_{N}\sim 42K$ [3]. The over-hardening of the phonon frequencies above anharmonicity at low temperatures confirm that the spin-lattice interaction plays an important role in the magnetoelectric properties. The $TbMn_{2}O_{5}$ infrared active phonon frequencies are also studied as a function of temperature and under applied magnetic field (up to 10 Tesla). As predicted theoretically the $TbMn_{2}O_{5}$ infrared-active phonon frequencies soften below $T_{N}$. Evolutions of the phonon frequencies under the applied magnetic field are reported and analyzed.   

Absence of ferroelectricity in hexagonal InMnO$_3$

So far, it was believed that hexagonal (h-) InMnO$_3$ exhibit the same type of multiferroic order as the other compounds from the h-RMnO$_3$ family (R = Sc, Y, Dy - Lu), including, in particular, a unit-cell-tripling improper ferroelectric order. Here we present experimental evidence for the \textit{absence} of ferroelectricity in hexagonal InMnO$_3$ based on three different techniques: x-ray diffraction (XRD), piezoresponse force microscopy (PFM) and optical second harmonic generation (SHG). XRD data are ambiguous because they can be described likewise by the non-ferroelectric $P\overline{3}c$ structure and by the ferroelectric $P6_3cm$ structure present in the other h-RMnO$_3$ compounds. However, PFM at room temperature and SHG measurements at low temperature uniquely reveal the absence of ferroelectric order in InMnO$_3$. We therefore propose that InMnO$_3$ exhibits antiferrodistortive, but non-ferroelectric order according to the $P\overline{3}c$ symmetry. Density functional calculations show that the relative energy between the $P\overline{3}c$ and $P6_3cm$ structures is determined by a competition between electrostatic and covalency effects, with an \textit{absence} of covalency favoring the ferroelectric structure.   

Long range order beyond vortices in h-REMnO$_{3}$

Fascinating vortices were discovered recently in ferroelectric domain patterns in hexagonal (h)-YMnO$_{3}$. One of the important ingredients for these vortex domain patterns is mutual interlocking of ferroelectric and structural antiphase domain walls. In contrast to expected vortex domain patterns, we have found intriguing stripe domain patterns in other h-REMnO$_{3}$ (RE=Ho, Er, Tm, Yb, Lu). These stripe domain patterns appear to indicate the presence of long-range-ordered state as the true ground state in h-REMnO$_{3}$. On the other hand, vortex domain patterns suggest the presence of a Kosterlitz-Thouless-like transition. We argue that this significant difference stems from very slow kinetics associated the ordering of six possible degrees of freedom.   

Electronic and Structural Properties Near the Ferroelectric Transition in Multiferroic Hexagonal RMnO$_{3}$

Combined local and long range structural measurements were conducted on RMnO$_{3}$ for temperatures extending significantly above the ferroelectric transition temperature, (T$_{FE})$. We find in hexagonal RMnO3 no large atomic (bond distance or thermal factors) or electronic structure changes on crossing T$_{FE}$. The born effective charge tensor is found to be highly anisotropic at the O sites indicating very strong hybridization of the charge. The tensor does not change significantly above T$_{FE}$ revealing no charge redistribution and suggests an unusual transition. Molecular dynamic simulations on large supercells are used to provide a general picture of the transition. This work is supported by DOE Grants DE-FG02-07ER46402 (NJIT) and DE-FG02-07ER46382 (Rutgers University).   

Role of the apical oxygen in RMnO3 (R = Ho and Lu) low temperature magneto-electric effect

Multiferroic materials are promising candidates for new innovative devices, particularly in the field of memory storage. The strong coupling between magnetic ordering and ferroelectricity characterizing these compounds allows the modulation of the electric polarization (magnetic moment) with an external magnetic (electric) field. Hexagonal RMnO$_{3}$ (Ho to Lu) compounds are type-I multiferroics in which ferroelectricity and magnetism have different sources giving a relative weak magneto-electric coupling with a large polarization. In this case ferroelectricity is induced at a relative high temperature (T$_{C }\sim $ 800K) following a structural transition, while magnetic ordering of Mn$^{3+}$ and R$^{3+}$ occurs at lower temperatures (T $<$ 100K). In order to determine which atoms play a major role in the giant low temperature magneto-electric effect, we study the evolutions of infrared active phonon frequencies in HoMnO$_{3}$ and LuMnO$_{3}$ under applied magnetic field below T$_{Ho }$= 5K. By comparing the renormalized force constants and the Born-effective charges, apical oxygen role in Ho$^{3+}$-Mn$^{3+}$ superexchange interaction is particularly underlined.   

Piezoelectric-response of charged 180$^{\circ}$ ferroelectric domain walls

We report ambient piezoresponse force microscopy (PFM) studies of the multiferroic hexagonal manganite HoMnO$_3$ performed on the cleaved (110) surface of a single crystal specimen. By changing the sample orientation with respect to the cantilever, we observed an unexpected out-of-plane PFM signal at domain walls which depends on domain wall orientation, in addition to the expected in-plane PFM signal in domains. Further studies confirmed that the domain wall PFM signal results from an out-of-plane displacement, which can be explained by a simple model of local elastic response with conservation of unit cell volume at head-on domain walls.   

A First Principle exploration of A site ordered Ho$_{0.5}$A$_{0.5}$MnO$_{3}$(A=Ge, Sn, Pb, As, Sb, Bi, Se, Te)

In this work a first principle attempt has been made to study the structure and properties of doping lone pair cations to ortho-HoMnO$_{3}$. Electronic structure calculations were carried out to study Ho$_{0.5}$A$_{0.5}$MnO$_{3}$ (A=Ge, Sn, Pb, As, Sb, Bi, Se, Te) under the Generalized Gradient Approximation of Density Functional Theory in an attempt to analyze the effect of lone pair cations towards electric polarization and to predict new multiferroics. Under the first principle calculations, Ho$_{0.5}$A$_{0.5}$MnO$_{3}$ (A=Ge, Sn, As, Sb, Bi, Se, Te) is found to be multiferroic. Doping 50{\%} of Se and Sn to HoMnO$_{3}$ is found to highly enhance the electric polarization compared to parent ortho-HoMnO$_{3}$. O2p- A valence p orbital hybridization is expected to be the cause of this polarization. Thus Ho$_{0.5}$Se$_{0.5}$MnO$_{3}$ and Ho$_{0.5}$Sn$_{0.5}$MnO$_{3}$ are expected to be good candidate multiferroics. A first principle attempt has thus been made to perform an extensive search for new multiferroics in which p-p hybridization is found to have a strong role in causing electric polarization predicting new multiferroics providing a pathway for experimentalists to synthesis new promising multiferroic compounds.   

Synthesis of Perovskite ScMnO$_{3}$ under High Temperature and Pressure

Perovskite type ScMnO$_{3}$ was synthesized under high temperature and pressure starting with hexagonal ScMnO$_{3}$. The detail of the structure is examined by synchrotron x-ray diffraction and IR spectroscopy at room temperature. A highly distorted perovskite phase which is similar to the structure of LaMnO$_{3}$ is identified by XRD Rietveld Refinement. Due to the small Sc ion radius, each Mn site has a distorted MnO$_{6}$ polyhedron. This work is supported by DOE Grant DE-FG02-07ER46402.   

Low Temperature Structural of ScMnO$_{3}$

We present the temperature dependent structural changes of hexagonal ScMnO$_{3}$ probed on multiple length scales. These measurements are compared by IR results. These results are used to assess the structural changes across the N\'{e}el temperature which may coincide and couple with the ferroelectric behavior. This work is supported by DOE Grants DE-FG02-07ER46402 (NJIT), by COMPRES, the Consortium for Materials Properties Research in Earth Sciences under NSF Cooperative Agreement EAR 10-43050 (X17B3) and EAR 01-35554 (U2A), and by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-98CH10886 (for use of the National Synchrotron Light Source at Brook Haven National Laboratory).   

Time-resolved imaging of magnetoelectric switching in MnWO$_4$

The interaction of magnetic and ferroelectric order is intrinsically strong in spin-spiral multiferroics. Here the complex magnetic long range order breaks inversion symmetry and induces a spontaneous electric polarization. The interaction allows to switch the magnetic order by an electric field and is thus of great interest for applications. Although such magnetoelectric switching is a major goal in multiferroics, hardly any work was devoted to the dynamic aspects of the actual switching process. Here we report time-resolved optical second harmonic generation measurements of the electric-field-induced reversal of the spin-spiral domains in multiferroic MnWO4. Ferroelectric and magnetic orders appear to remain rigidly coupled even during the non-equilibrium state of the transition. The switching is governed by domain wall motion on the millisecond time scale. Even though, locally domains can disappear within nanoseconds. The slow global response can be explained by an energy estimate: As the dipole energy in the electric field is much weaker than the magnetic anisotropy energy, the electric field is only a weak lever for manipulating the magnetic system. Therefore magnetoelectric switching in this compound is inherently slow.   

Displacement-type ferroelectric transition with magnetic Mn ions in perovskite Sr$_{1-x}$Ba$_{x}$MnO$_{3}$

Almost all the proper ferroelectrics with a perovskite structure discovered so far have no $d$-electrons in the off-center transition metal site, as exemplified by BaTiO$_{3}$ and Pb(Zr,Ti)O$_{3}$. This empirical $d^{0}$ rule is incompatible with the emergence of magnetism and has significantly restricted the variety of multiferroic materials. In this work, we have discovered a displacement-type ferroelectric transition originating from off-center Mn$^{4+}$ ions in antiferromagnetic Mott insulators Sr$_{1-x}$Ba$_{x}$MnO$_{3}$. As Ba concentration increases, the perovskite lattice shows the typical soft mode dynamics, and the ferroelectricity shows up for $x\!\ge\!0.45$. In addition to the large polarization and high transition temperature comparable to BaTiO$_{3}$, we demonstrate that the magnetic order suppresses the ferroelectric lattice dilation by $\sim$70\% and increases the soft-phonon energy by $\sim$50\%, indicating gigantic magnetoelectric effects [1]. This work was supported by the FIRST program on ``Quantum Science on Strong Correlation''. \\[4pt] [1] H. Sakai {\it et al}., Phys. Rev. Lett. {\bf 107}, 137601 (2011).   

Antiferromagnetic pinning of a phase-like mode below T$_{N}$ in NdMnO$_{3}$

We report on reflectivity and emission far infrared spectra of NdMnO$_{3 }$between$_{ }$4K and its dissociation temperature. Phonon bands at 300K are in agreement with orthorhombic Pbnm space group assignments. In addition, a broad strong band. reminiscent to a phase-mode in quasi-one dimension metals, is found at very low frequencies that it is understood originating in charge fluctuations in d-orbitals. There is no distinctive behaviors between 1073 K and 1173 K, where orthorhombic O and O' coexist. Beyond $\sim $700 K a mid-infrared polaron band turns into a Drude tail suggesting hopping conductivity double exchange due to air heating oxidation Mn$^{3+}\to $ Mn$^{4+ }$+1e$^{-}$. Below 300 K phonons are better defined and the low frequency giant dipole acquires strength. Few degrees above the antiferromagnetic transition it broadens as electrons loosing coherence. At T$_{N}\sim $76 K we find strong phonon magnetostriction while the band turns asymmetric locking-in to the underlying magnetic order. Preliminary measurements of hexagonal TmMnO$_{3}$, show that asymmetry split due to lower symmetry and the triangular magnetic lattice two exchange integrals J$_{1}$ and J$_{2}$ in the a-b plane. Similar to a soft mode those two bands and a lower frequency resonance undergo strong hardening down to 4 K.   

Low temperature Electrical and Magnetic studies of Nsutite

Nsutite is a naturally occurring Manganese Oxide of the composition Mn$^{4+}_{1-x}$Mn$^{2+}_{x}$O$_{2-2x}$(OH)$_{2x}$ where x = 0.06 -- 0.07. D.C. electrical transport measurements were carried out on samples from Nsuta, Ghana between 40 K and 400 K. Non-linear I-V curves were observed below 140 K even at very low currents. The resistivity vs. temperature data suggests electron transport is by the variable range hopping mechanism between 140 K and 400 K. Magnetic moment vs. temperature data were obtained between 5K and 300K at high field (10,000 Oe) and low field (1,000 Oe). Both high and low field data suggest paramagnetic behavior with a possible Neel temperature at about 15K, below which the materials exhibits antiferromagnetic behavior. The electrical and magnetic properties as well as high temperature thermal analysis (DSC) data will be discussed.   

Session T35: Focus Session: Plyler Award Symposium

Earle K. Plyler Prize for Molecular Spectroscopy and Dynamics Lecture: 2D IR Spectroscopy of Peptide Conformation

Descriptions of protein and peptide conformation are colored by the methods we use to study them. Protein x-ray and NMR structures often lead to impressions of rigid or well-defined conformations, even though these are dynamic molecules. The conformational fluctuations and disorder of proteins and peptides is more difficult to quantify. This presentation will describe an approach toward characterizing and quantifying structural heterogeneity and disorder in peptides using 2D IR spectroscopy. Using amide I vibrational spectroscopy, isotope labeling strategies, and computational modeling based on molecular dynamics simulations and Markov state models allows us to characterize distinct peptide conformers and conformational variation. The examples illustrated include the beta-hairpin tripzip2 and elastin-like peptides.   

Vibrational spectroscopy of interacting water molecules

I will discuss a new simulation model for water that includes three-body interactions explicitly, and describe our theoretical approach for calculating OH-stretch spectroscopic observables. I will present illustrative examples, involving pump-probe energy-transfer-induced anisotropy decay in liquid water, IR and Raman line shapes in ice Ih, phase-sensitive SFG spectra of the liquid/vapor interface, and energetics and IR spectra for the different conformations of the water hexamer.   

Two-dimensional Fourier transform electronic spectroscopy

Sensitive interference detection of the electric field of femtosecond four-wave mixing signals (stimulated photon echoes) at their point of origin in the sample can be used to record two-dimensional (2D) Fourier transform electronic spectra. In direct analogy to 2D nuclear magnetic resonance, 2D Fourier transform spectra have nearly homogeneous linewidths in each frequency dimension and sort the signal spectrum according to the initial excitation frequency. The initial excitation frequency information is stored in a robust population grating, so 2D spectra can be used to study both coherent and incoherent processes, and have revealed coherent aspects of energy transfer processes. Femtosecond 2D spectra also have the advantage of ``freezing out'' vibrational motions as inhomogeneities, raising interesting questions about what kinds of broadening can be rephased in 2D spectra recorded with stimulated photon echo pulse sequences. This talk will focus on coherent aspects of non-adiabatic electronic curve crossing and their manifestation in 2D electronic spectra.   

Session T37: Physics Education Research and Resources

Strength of Student Models of Force and Motion

With a three-year FIPSE grant, it has been possible to develop and implement activity-based algebra level introductory physics. The Force and Motion Conceptual Evaluation (FMCE) has been given as a pretest and a posttest to both the traditional lecture/lab classes and the activity-based classes. The responses are analyzed to determine the models that students use. The questions are separated into eight groups. Responses are divided into expert model, student model, and null model. Students are categorized as being in an expert state, a mixed state, or a student state. Previous work assumed a particular model if the answers to 70 percent (or more) of the questions in a group fit that model. To determine the strength of the models, the analysis is repeated assuming 85 percent and then 100 percent. The results are analyzed to determine if there is a significant difference from 70 percent to 85 percent to 100 percent. This will indicate the strength of the models in each group of questions.   

Project-Based Learning Courses: The Relationship Between Faculty-Intended Course Implementation and Students' Perceptions

Project-based learning (PjBL) has been shown to improve students' performance and satisfaction with their coursework, particularly in science and engineering courses. Specific aspects of PjBL that contribute to this improvement are student autonomy, course scaffolding, and instructor support. This study investigates two PjBL courses required for engineering majors at a small technical school, \textit{Introductory Mechanics Laboratory} and \textit{Introductory Engineering Design}. The three data sources used in this work are classroom observations (one laboratory and four design sessions) and semi-structured in-depth interviews with twelve students and six faculty. Grounded theory approach is used in a two-step fashion by (1) analyzing each data set individually and (2) performing full triangulation of all three data sets. In this talk, we demonstrate the relationship between faculty intentions and student perceptions regarding the three PjBL aspects -- student autonomy, course scaffolding, and instructor support -- within the context of these two courses. We further discuss implications for the course design and professional development of faculty.   

Combining Wikis and JiTT to enhance critical thinking abilities

I report the combine use of Just in Time Teaching (\textbf{JiTT}) and \textbf{W}ikispaces (\textbf{Wikis}) in introductory level, calculus based, physics classes. Over the years, JiTT had been effectively used in teaching physics and some uses on Wikis were also reported in the recent years.\footnote{H. Mohottala The Physics Teacher -- September 2011 -- Vol. 49, Issue 6} Wiki helps students, instructors and technology to interact with one another and JiTT boosts the self-confidence of students to tackle physics problems. Thus, the combine use of Wiki-JiTT is going to be a new experience for both instructors and students. In this experiment, I used Wikis as a platform for JiTT, and conventional JiTT was slightly altered to best fit the combination and to focus on enhancing critical thinking abilities in my students.   

Student Self-Efficacy in Introductory Project-Based Learning Courses

This study investigates first-year engineering students' self-efficacy in two introductory Project-Based Learning (PjBL) courses -- \textit{Physics} (\textit{Mechanics) Laboratory} and \textit{Engineering Design} -- taught at a small technical institution. Twelve students participated in semi-structured open-ended interviews about their experiences in both courses. Analysis was performed using grounded theory$.$ Results indicate that students had lower self-efficacy in \textit{Physics Lab} than in \textit{Engineering Design}. In \textit{Physics Lab}, students reported high levels of faculty-supported scaffolding related to final project deliverables, which in turn established perceptions of an outcome-based course emphasis. Conversely, in \textit{Engineering Design}, students observed high levels of scaffolding related to the intermediate project deliverables, highlighting process-centered aspects of the course. Our analyses indicate that this difference in student perceptions of course emphases -- resulting from the differences in scaffolding -- is a primary factor for the discrepancy in self-efficacy between \textit{Physics Lab }and \textit{Engineering Design}. Future work will examine how other variables (e.g., academic background, perception of community, gender) affect students' self-efficacy and perception of scaffolding in these PjBL courses.   

The IPAD as a Pedagogical Tool in an Algebra-Based Introductory Physics Class

We report our experience in using the IPAD as a pedagogical tool for enhancing physics learning in an introductory algebra-based physics laboratory course for primarily pre-med students. We used several applications including (1) video analysis for experiments in accelerated motion (2) virtual oscilloscope for studying wave motion and circuit response to low frequency driving voltages; (3) applications for visualization of electric fields and magnetic fields. We compare student responses to this platform versus more traditional experiments. Using student surveys and polls. We also evaluate the IPAD as a new and familiar interface versus traditional interfaces like the standard oscilloscope. We report on the advantages and disadvantages of using this mobile, popular platform in delivering experimental physics content and promoting student engagement.   

Physics: A student's guide through the great texts

Although memorizing formulae and learning how to perform calculations is crucial for acquiring a working knowledge of physical theories, the standard pedagogical method employed by many textbooks does not prepare the student to become a practicing scientist precisely because it tends to mask the actual scientific method: the science is presented as an accomplished fact; the prescribed questions revolve largely around technological applications of accepted laws. In this talk, I will describe a two-year general physics curriculum which I have developed and taught for the past decade to undergraduate students at Wisconsin Lutheran College. The curriculum is unique in that it provides students of the natural and mathematical sciences with a comprehensive introduction to physics based on the careful reading and analysis of selections from foundational texts in physics and astronomy. The curriculum is designed to encourage a critical and circumspect approach to the study of natural science, while at the same time developing a suitable foundation for advanced coursework in physics. Through the careful reading and analysis of foundational scientific texts, students learn skills which are essential when considering the practical and philosophical implications of scientific theories.   

A student's guide to searching the literature using online databases

A method is described to empower students to efficiently perform general and specific literature searches using online resources [Miller et al., Am. J. Phys. 77, 1112 (2009)]. The method was tested on multiple groups, including undergraduate and graduate students with varying backgrounds in scientific literature searches. Students involved in this study showed marked improvement in their awareness of how and where to find scientific information. Repeated exposure to literature searching methods appears worthwhile, starting early in the undergraduate career, and even in graduate school orientation.   

A jumping cylinder in an incline

The problem of a cylinder of mass m and radius r, with its center of mass out of the cylinder axis, rolling in an incline that makes an angle $\alpha $ respect to the horizontal is analyzed. The equation of motion is solved to obtain the site where the cylinder loses contact with the incline (jumps). Several simplifications are made: the analyzed system consists of an homogeneous disc with a one dimensional straight line of mass parallel to the disc axis at a distance d $<$ r of the center of the cylinder. To compare our results with experimental data, we use a Styrofoam cylinder of radius r = 10.0 $\pm $ 0.05 cm, high h = 5.55 $\pm $ 0.05 cm and a mass m$_{1}$ = 24.45 $\pm $ 0.05 g, to which a 9.50 $\pm $ 0.01 mm diameter and 5.10 $\pm $ 0.001 cm long brass road of mass m$_{2}$ = 30.75 $\pm $ 0.05 g was imbibed parallel to the disc axis at a distance of 5.40 $\pm $ 0.05 cm from it. Then the disc rolls on a 3.20 m long wooden ramp inclined at 30\r{ } and 45\r{ } respect to the horizontal. To determine the jumping site, the movements were recorded with a high-speed video camera (Casio EX ZR100) at 400 frames per second. The experimental results agree well with the theoretical predictions.   

Design and operation of an inexpensive far-field laser scanning microscope suitable for use in an undergraduate laboratory course

Scanning microscope applications span the science disciplines yet their costs limit their use at educational institutions. The basic concepts of scanning microscopy are simple. The microscope probe - whether it produces a photon, electron or ion beam - moves relative to the surface of the sample object. The beam interacts with the sample to produce a detected signal that depends on the desired property to be measured at the probe location on the sample. The microscope transforms the signal for output in a form desired by the user. Undergraduate students can easily construct a far-field laser scanning microscope that illustrates each of these principles from parts available at local electronics and hardware stores and use the microscope to explore properties of devices such as light dependent resistors and biological samples such as leaves. Students can record, analyze and interpret results using a computer and free software.   

Variational Calculations for Hydrogen in Introductory Solid State

Molecular hydrogen is very important in the introductory solid state physics course because it is used as one of the simplest molecular realistic models where bonding and anti-bonding takes place. This system is one of the first examples in which interactions among the ions and the electrons is incorporated realistically. To this end, we approach the system starting from the hydrogen atom. Here we introduce a numerical approach that reproduces the known analytic result for the ground state. The idea is to expand the hydrogenic wavefunction in terms of Gaussians (four of them) with variational parameters. As the parameters are varied the numerical approach stops when the energy is a minimum. The scheme is consistently extended through the ionized hydrogen molecule and the reproduction of its analytically known ground state energy result. We finally culminate with the hydrogen molecule using a variational wavefunction, a la Hartree, and proceed to repeat the process with a particular flavor of a Hartree-Fock wavefunction [1] and finally obtaining a hydrogen molecule total ground state energy of -31.10 eV with a bond length of 1.37 Bohr radius.\\[4pt] [1] ``Atomic and Electronic Structure of Solids,'' Efthimios Kaxiras (Cambridge UP, Cambridge UK, 2003).   

Session T40: Focus Session: Cytoskeleton and Biomechanics - Forced Dynamics

Dynamics of focals adhesions modulates active cellular response

The cytoskeleton of living cells connects to and senses the extracellular mechanical environment through protein clusters called focal adhesions. We study how the mechanics and dynamics of focal adhesions influence the distribution of mechanical stresses and deformations in a cell which is modeled as an active elastic gel. We carry out our investigations for two types of bond dynamics of focal contacts (a) slip bond dynamics where the bonds are weakened by a tensile mechanical force and (b) catch bond dynamics where they are initially strengthened upon application of a tensile mechanical force, and undergo failure at very large forces. We comment on the effect of different types of focal adhesions on the transmission and regulation of cell traction forces and on cellular mechanosensing.   

3D Neutrophil Tractions in Changing Microenvironments

Neutrophils are well-known as first responders to defend the body against life threatening bacterial diseases, infections and inflammation. The mechanical properties and the local topography of the surrounding microenvironment play a significant role in the regulating neutrophil behavior including cell adhesion, migration and generation of tractions. In navigating to the site of infection, neutrophils are exposed to changing microenvironments that differ in their composition, structure and mechanical properties. Our goal is to investigate neutrophil behavior, specifically migration and cellular tractions in a well-controlled 3D in vitro system. By utilizing an interchangeable 2D-3D sandwich gel structure system with tunable mechanical properties neutrophil migration and cell tractions can be computed as a function of gel stiffness and geometric dimensionality.   

Force transmission through intercellular fluid transfer

Cell force generation and transmission play a vital role in controlling cell-to-cell interactions and cell locomotion. Contraction of the cell's cytoskeletal network generates forces that can be transmitted directly to other cells by cell-cell adherens junctions or through a substrate by traction forces. Within monolayers, cytosolic fluid is transferred between cells through gap junctions. The coupling between intercellular fluid movement and contraction can give rise to a different type of cell-cell force transmission. Here we present preliminary results investigating the role of intercellular force transmission through fluid motion across gap junctions.   

Forcing it on: Cytoskeletal dynamics during lymphocyte activation

Formation of the immune synapse during lymphocyte activation involves cell spreading driven by large scale physical rearrangements of the actin cytoskeleton and the cell membrane. Several recent observations suggest that mechanical forces are important for efficient T cell activation. How forces arise from the dynamics of the cytoskeleton and the membrane during contact formation, and their effect on signaling activation is not well understood. We have imaged membrane topography, actin dynamics and the spatiotemporal localization of signaling clusters during the very early stages of spreading. Formation of signaling clusters was closely correlated with the movement and topography of the membrane in contact with the activating surface. Further, we observed membrane waves driven by actin polymerization originating at these signaling clusters. Actin-driven membrane protrusions likely play an important role in force generation at the immune synapse. In order to study cytoskeletal forces during T-cell activation, we studied cell spreading on elastic gels. We found that gel stiffness influences cell morphology, actin dynamics and receptor activation. Efforts to determine the quantitative relationships between cellular forces and signaling are underway. Our results suggest a role for cytoskeleton driven forces during signaling activation in lymphocytes.   

Aging phenomena in a network model of the cytoskeleton

Motivated by a series of experiments that study the response of the cytoskeleton in living cells to time dependent mechanical forces, we investigate, through Monte Carlo simulations, a three-dimensional network subjected to perturbations. After having prepared the system in a relaxed state, shear is applied and the relaxation processes are monitored. We measure two-time functions of various quantities such as the Euclidean distance between crosslinks and the energy of the system. We discuss possible implications of our results for relaxation processes taking place in the cytoskeleton.   

Mechanical interactions may explain synchronized growth of cytoskeletal actin networks in motile cells

Growing networks of actin fibers are able to organize into compact, stiff two-dimensional structures inside lamellipodia of crawling cells. We examine critically the hypothesis that the growing actin network is a critically self-organized system, in which long-range mechanical stresses arising from the interaction with the plasma membrane provide the selective pressure leading to organization. We show that a simple model based only on this principle leads to stochastic protrusion of lamellipodia (growth periods alternating with fast retractions) and several of the features observed in experiments: a growth velocity initially insensitive to the external force; the capability of the network to organize its orientation; a load-history-dependent growth velocity. Our model predicts that the spectrum of the time series of the height of a growing lamellipodium decays with the inverse of the frequency. This behavior is confirmed by optical tweezer measurements performed in vivo on neuronal growth cones. References L. Cardamone et al.: Cytoskeletal actin networks in motile cells are critically self-organized systems synchronized by mechanical interactions. PNAS, vol. 108, no. 34, pp. 13978-13983   

Investigations of biomechanical activity of macrophages during phagocytosis

Phagocytosis has traditionally been investigated in terms of the relevant biochemical signaling pathways that trigger the process and lead to the deformation of the cell as it engulfs a target. Physical changes in the cell include rearrangement and polymerization of actin in the phagocytic cup, large membrane deformations, increased membrane area via exocytosis, and closure of the phagocytic cup through membrane fusion. Hence, phagocytosis is a fine-tuned balance between biophysical cellular events and chemical signaling, which are responsible for driving these materials and mechanical changes. We present a series of assays designed to probe the physical/mechanical parameters that govern a cell during phagocytosis. Custom built micropipette manipulators are used to manipulate individual cells, facilitating high-resolution microscopy of individual phagocytic events. This work has been supported by NSF PoLS {\#}0848797.   

Collective cell migration during inflammatory response

Wound scratch healing assays of endothelial cell monolayers is a simple model to study collective cell migration as a function of biological signals. A signal of particular interest is the immune response, which after initial wounding in vivo causes the release of various inflammatory factors such as tumor necrosis alpha (TNF-$\alpha$). TNF-$\alpha$ is an innate inflammatory cytokine that can induce cell growth, cell necrosis, and change cell morphology. We studied the effects of TNF-$\alpha$ on collective cell migration using the wound healing assays and measured several migration metrics, such as rate of scratch closure, velocities of leading edge and bulk cells, closure index, and velocity correlation functions between migrating cells. We observed that TNF-$\alpha$ alters all migratory metrics as a function of the size of the scratch and TNF-$\alpha$ content. The changes observed in migration correlate with actin reorganization upon TNF-$\alpha$ exposure.   

Temperature dependence of optically induced cell deformations

The mechanical properties of any material change with temperature, hence this must be true for cellular material. In biology many functions are known to undergo modulations with temperature, like myosin motor activity, mechanical properties of actin filament solutions, CO2 uptake of cultured cells or sex determination of several species. As mechanical properties of living cells are considered to play an important role in many cell functions it is surprising that only little is known on how the rheology of single cells is affected by temperature. We report the systematic temperature dependence of single cell deformations in Optical Stretcher (OS) measurements. The temperature is changed on a scale of about 20 minutes up to hours and compared to defined temperature shocks in the range of milliseconds. Thereby, a strong temperature dependence of the mechanics of single suspended cells is revealed. We conclude that the observable differences arise rather from viscosity changes of the cytosol than from structural changes of the cytoskeleton. These findings have implications for the interpretation of many rheological measurements, especially for laser based approaches in biological studies.   

Biomechanical changes in endothelial cells result from an inflammatory response

During periods of infection and disease, the immune system induces the release of TNF-$\alpha $, an inflammatory cytokine, from a variety of cell types, such as macrophages. TNF-$\alpha $, while circulating in the vasculature, binds to the apical surface of endothelial cells and causes a wide range of biological and mechanical changes to the endothelium. While the biological changes have been widely studied, the biomechanical aspects have been largely unexplored. Here, we investigated the biomechanical changes of the endothelium as a function of TNF-$\alpha $ treatment. First, we studied the traction forces applied by the endothelium, an effect that is much less studied than others. Through the use of traction force microscopy, we found that TNF-$\alpha $ causes an increase in traction forces applied by the endothelial cells as compared to non-treated cells. Then, we investigated cell morphology, cell mechanics, migration, and cytoskeletal dynamics. We found that in addition to increasing applied traction forces, TNF-$\alpha $ causes an increase in cell area and aspect ratio on average, as well as a shift in the organization of F-actin filaments within the cell. Combining these findings together, our results show that an inflammatory response heavily impacts the morphology, cell mechanics, migration, cytoskeletal dynamics, and applied traction forces of endothelial cells.   

Healing of small circular model wounds

We develop a new method to produce numerous circular wounds in an epithelial tissue of MDCK cells in a non-traumatic fashion. The reproducibility of the wounds allows for a quantitative study of the dynamics of healing and for a better understanding of the key processes involved in those collective morphogenetic movements. First, we show different mechanisms of closing depending on the initial size of the wound. We then focus on the healing of the smallest wounds from an experimental and theoretical point of view. At the onset of closure, an actomyosin ring is formed around the wound and small protrusions appear and invade the free surface. Using inhibition and laser ablation experiments, we show the relative contribution of both processes to the dynamics of closing. Finally, we develop a theoretical model of the tissue as a whole, combined with the observed forces, in order to better understand the underlying mechanics of this process. We hope that this qualitative and quantitative description will prove useful in the future for the study of epithelial architecture, collective mechanisms in migrating tissues and, on a broader context, cellular invasion in cancerous tissues.   

Mechanical coupling of smooth muscle cells using local and global stimulations

Mechanical stresses can directly alter many cellular processes, including signal transduction, growth, differentiation, and survival. These stresses, generated primarily by myosin activity within the cytoskeleton, regulate both cell-substrate and cell-cell interactions. We report studies of mechanical cell-cell and cell-substrate interactions using patterned arrays of flexible poly(dimethylsiloxane) (PDMS) microposts combined with application of global stretch or local chemical stimulation. Bovine pulmonary artery smooth muscle cells are patterned onto micropost arrays to create multicellular structures to probe intercellular coupling. Global stimulation is applied by building the micropost arrays on a flexible membrane that can be stretched while allowing simultaneous observation of cell traction forces. Results for triangle wave stretches of single cells show increasing traction forces with increasing strain, and immediate weakening of traction forces as strain is decreased. ``Spritzing,'' a laminar flow technique, is used to expose a single cell within a construct to a drug treatment while cell traction forces are recorded via the microposts. Results will be described showing the response of cells to external stimulation both directly and through intercellular coupling.   

Session T41: Swimming, Motility and Locomotion

Undulatory swimming on a free surface

A wide variety of swimmers in nature use body undulations to generate a propulsive force, in part owing to the relative insensitivity of the principle of undulatory swimming to the value of the Reynolds number $Re=UL/\nu$, which measures the relative importance of viscous and inertial forces in the flow considered ($U$ and $L$ being the typical speed and length of the animal, and $\nu$ the kinematic viscosity of the surrounding fluid). Here we study a flexible filament forced to oscillate by imposing a harmonic motion to one of its extremities (using magnetic interactions) and propelling itself at the surface of a water tank. This experiment serves as a canonical model for studying the interactions between an elastic structure undergoing complex deformations and the surrounding fluid.   

Geometry, Curvature, and Locomotion

Many animals and robots locomote by undulating their bodies in traveling waves. Together with the generally inextensible nature of such systems, the large deformations involved in these motions introduce significant nonlinearities into their analysis. As a result, the equations of motion for these systems are often treated as black boxes -- the displacement resulting from a given input (e.g., wave amplitude) can be calculated, but the relationship between the inputs and the net displacement over a period of the wave is hidden inside the nonlinearities. Drawing on results from the geometric mechanics community, we have developed an analysis framework for high-deformation locomotion that looks inside this black box, based on three core principles: (1) Working in terms of body curvature provides a linear basis for describing nonlinear high-deformation shapes. (2) Lie bracket analysis (the exploitation of system nonlinearities through oscillatory inputs) captures the nonlinearity of the system interaction with the world. (3) Systematically optimizing the coordinate choice transforms the system nonlinearity into a form that can be geometrically analyzed over the space of body curvatures to characterize the system's ultimate locomotory capabilities.   

Optimizing turning for locomotion

Speed and efficiency are common and often adequate metrics to compare locomoting systems. These metrics, however, fail to account for a system's ability to turn, a key component in a system's ability to move a confined environment and an important factor in optimal motion planning. To explore turning strokes for a locomoting system, we develop a kinematic model to relate a system's shape configuration to its external velocity. We exploit this model to visualize the dynamics of the system and determine optimal strokes for multiple systems, including low Reynolds number swimmers and biological systems dominated by inertia. Understanding how shape configurations are related to external velocities enables a better understanding of biological and man made systems. Using these tools, we can justify biological system motion and determine optimal shape configurations for robots to maneuver through difficult environments.   

Effect of confinements: Bending in Paramecium

Paramecium is a unicellular eukaryote which by coordinated beating of cilia, generates metachronal waves which causes it to execute a helical trajectory. We investigate the swimming parameters of the organism in rectangular PDMS channels and try to quantify its behavior. Surprisingly a swimming Paramecium in certain width of channels executes a bend of its flexible body (and changes its direction of swimming) by generating forces using the cilia. Considering a simple model of beam constrained between two walls, we predict the bent shapes of the organism and the forces it exerts on the walls. Finally we try to explain how bending (by sensing) can occur in channels by conducting experiments in thin film of fluid and drawing analogy to swimming behavior observed in different cases.   

Enhanced swimming motion of nematode in a non-Newtonian fluid

Small organisms navigate their complex terrestrial substrates, which have the property of non-Newtonian complex fluids. Although a large body of literature exists on the locomotion of these organisms, the previous studies are mostly limited in simple Newtonian systems. Here we present experimental results on the locomotion of Caenorhabditis elegans (C. elegans), especially investigated in colloidal suspensions that exhibit the behavior of shear thinning fluid in the range of shear rate of undulating nematode. Interestingly, we observed that the swimming speed of nematodes was gradually increased with an increase of particle volume fraction in suspensions, and this enhanced motion of nematode is closely related to the shear thinning in the fluid viscosity.   

Hydrodynamic Optimality in the Bacterial Flagellum

Most bacteria swim through fluids by rotating helical flagella which can take one of 12 distinct polymorphic shapes, the most common of which is the normal form used during forward swimming runs. To shed light on the prevalence of the normal form in locomotion, we have gathered all available experimental measurements of the various polymorphic forms and computed their intrinsic hydrodynamic efficiencies. The normal helical form is found to be the most efficient of the 12 polymorphic forms by a significant margin--a conclusion valid for both the peritrichous and polar flagellar families, and robust to a change in the effective flagellum diameter or length. Hence, although energetic costs of locomotion are small for bacteria, fluid mechanical forces may have played a significant role in the evolution of the flagellum.   

Characterisation of metachronal waves on the surface of the spherical colonial alga \textit{Volvox carteri}

\textit{Volvox carteri} is a spherical colonial alga, consisting of thousands of biflagellate cells. The somatic cells embedded on the surface of the colony beat their flagella in a coordinated fashion, producing a net fluid motion. Using high-speed imaging and particle image velocimetry (PIV) we have been able to accurately analyse the time-dependent flow fields around such colonies. The somatic cells on the colony surface may beat their flagella in a perfectly synchronised fashion, or may exhibit metachronal waves travelling on the surface. We analyse the dependence of this synchronisation on fundamental parameters in the system such as colony radius, characterise the speed and wavelength of the observed metachronal waves, and investigate possible models to account for the exhibited behaviour.   

Collective dynamics of active suspensions in confined geometries

We discuss the collective dynamics of suspensions of self-propelled particles confined in confined geometries. First, we revisit the conventional description of the hydrodynamic couplings between swimmers living in thin films or in shallow channels. We show that these hydrodynamic interactions are chiefly set by the particle size and shape irrespective of the microscopic propulsion mechanism. Second, we use kinetic theory to study the phase behavior of dilute suspensions. Finally, we exploit these results to show that the hydrodynamic interactions destabilize isotropic suspensions of polar particles, thereby yielding spontaneous collective motion at large scales. In contrast, suspensions of apolar particles only display weakly cooperative motion at small scales. We also investigate the case of aligned suspensions. Their behavior is very similar to the bulk phase of dipolar swimmer. They display generic instabilities at all scales. Comparisons of our theoretical findings with experiments on artificial swimmers will be shown.   

Giant number fluctuations in self-propelled particles without alignment

Giant number fluctuations are a ubiquitous property of active systems. They were predicted using a generic continuum description of active nematics, and have been observed in simulations of Vicsek-type models and in experiments on vibrated granular layers and swimming bacteria. In all of these systems, there is an alignment interaction among the self-propelled units, either imposed as a rule, or arising from hydrodynamic or other medium-mediated couplings. Here we report numerical evidence of giant number fluctuations in a minimal model of self-propelled disks in two dimensions in the absence of any alignment mechanism. The direction of self-propulsion evolves via rotational diffusion and the particles interact solely via a finite range repulsive soft potential. It can be shown that in this system self propulsion is equivalent to a non Markovian noise whose correlation time is controlled by the amplitude of the orientational noise.   

Chemotactic Self-Organization of Bacteria in Three-Dimensions

Self-assembly with cellular building blocks represents an important yet relatively unexplored area of research. In this talk, we describe the self-assembly of motile cells using three-dimensional (3D) patterns of chemical (such as chemoattractants) that guide cellular and organization. These 3D chemical patterns are created when chemicals are released via diffusion from lithographically patterned self-assembled polyhedral containers. We show that a number of conceptually different strategies can be utilized for chemical patterns creation. In one such strategy, the overall shape of the container can be chosen to closely match the desired 3D spatial profile. As a part of a different strategy, we discuss how the chemical patterns can be engineered by specific placement of pores on the polyhedral containers. Combining these two strategies allows chemicals to be released in a variety of spatial patterns. To demonstrate applicability of our concept to in vitro organization of living cells in specific 3D geometries, we describe chemotactic self-organization of E. coli bacteria in a variety of well-defined shapes and space curves. We link the parameters that characterize the patterns of cells and the patterns of chemicals and describe how one can engineer the spatial shape of the multicellular constructs.   

Collective Dynamics of a Laboratory Insect Swarm

Self-organized collective animal behavior is ubiquitous throughout the entire biological size spectrum. But despite broad interest in the dynamics of animal aggregations, little empirical data exists, and modelers have been forced to make many assumptions. In an attempt to bridge this gap, we report results from a laboratory study of swarms of the non-biting midge {\it Chironomus riparius}. Using multicamera stereoimaging and particle tracking, we measure the three-dimensional trajectories and kinematics of each individual insect, and study their statistics and interactions.   

Dimensional transitions for coupled rotational/translational diffusion in powered nanorotors

Small colloidal particles in fluids are well-known to engage in rotational and translational Brownian motion. Over the past several years, experimentalists have developed a new class of colloidal particles which exhibit autonomous powered motion due to consumption of chemical fuels. Two such classes of nanomotor that have been developed are linear and rotary motors. Nanorotors engage in cyclical motions due to asymmetries in the distribution of force on the surface of the particles. We have analyzed the diffusion of powered rotary motors, considering how the addition of a powered component to their motion affects their diffusional properties.   

Swimming of bio-inspired micro robots in circular channels

In recent years, bio-inspired micro swimming robots have been attracting attention for use in biomedical tasks such as opening clogged arteries, carrying out minimally invasive surgical operations, and carrying out diagnostic tasks. There have been a number of experimental and modeling studies that address swimming characteristics of micro swimmers with helical tails attached to magnetic heads that rotate and move forward in rotating external magnetic fields. We carried out experimental studies with millimeter long helical swimmers in glass tubes placed in between Helmholtz coils, and demonstrated that swimming speed increases linearly with the frequency of the external field up to the step-out frequency. In order to study interaction of the swimmer with the circular boundary we used a computational fluid dynamics model. In simulations we compared swimming speeds of robots with respect to the frequency of the external magnetic field, wavelength and amplitude of the helical tail, and distance to the channel wall. According to simulation results, as the swimmer gets closer to the boundary swimming speed and efficiency improve. However step-out frequency decreases near the wall due to increased torque to rotate the swimmer.   

Bristle-Bots: a model system for locomotion and swarming

The term {\em swarming} describes the ability of a group of similarly sized organisms to move coherently in space and time. This behavior is ubiquitous among living systems: it occurs in sub-cellular systems, bacteria, insects, fish, birds, pedestrians and in general in nearly any group of individuals endowed with the ability to move and sense. Here we address the problem of the origin of collective behavior in systems of self-propelled agents whose only social capability is given by aligning contact interactions. Our model system consists of a collection of Bristle-Bots, simple automata made from a toothbrush and the vibrating device of a cellular phone. When Bristle-Bots are confined in a limited space, increasing their number drives a transition from a disordered and uncoordinated motion to an organized collective behavior. This can occur through the formation of a swirling cluster of robots or a collective dynamical arrest, according to the type of locomotion implemented in the single devices. It is possible to move between these two major regimes by adjusting a single construction parameter.   

Session T42: Focus Session: Evolutionary Systems Biology III - Evolutionary Games

Bacterial tower of Babel --How cheating and lying diversify bacterial communication

In microbial ``quorum sensing'' (QS) communication systems, microbes produce and respond to a signaling molecule, enabling a cooperative response at high cell densities. Many species of bacteria show fast, intraspecific, evolutionary divergence of their QS pathway specificity---signaling molecules activate cognate receptors in the same strain but fail to activate, and sometimes inhibit, those of other strains. Despite many molecular studies, it has remained unclear how a signaling molecule and receptor can coevolve, what maintains diversity, and what drives the evolution of cross-inhibition. Here I use mathematical analysis to show that when QS controls the production of extracellular enzymes ---``public goods''---diversification can readily evolve. Coevolution is positively selected by cycles of alternating ``cheating'' receptor mutations and ``cheating immunity'' signaling mutations. The maintenance of diversity and the evolution of cross-inhibition between strains are facilitated by facultative cheating between the competing strains. My results suggest a role for complex social strategies in the long-term evolution of QS systems. More generally, my model of QS divergence suggests a form of kin recognition where different kin types coexist in unstructured populations.   

Coupling between evolutionary and population dynamics in experimental microbial populations

It has been often been assumed that population dynamics and evolutionary dynamics occur at such different timescales that they are effectively de-coupled. This view has been challenged recently, due to observations of evolutionary changes occurring in short timescales. This has led to a growing interest in understanding eco-evolutionary dynamics of populations. In this context, recent theoretical models have predicted that coupling between population dynamics and evolutionary dynamics can have important effects for the evolution and stability of cooperation, and lead to extremely rich and varied dynamics. Here, we report our investigation of the eco-evolutionary dynamics of a cooperative social behavior, sucrose metabolism, in experimental yeast populations. We have devised an experimental strategy to visualize trajectories in the phase space formed by the population size (N) and the fraction of cooperator cells in the population (f). Our measurements confirm a strong coupling between evolutionary and population dynamics, and allowed us to characterize the bifurcation plots. We used this approach to investigate how sudden environmental changes affect the stability and recovery of populations, and therefore the stability of cooperation.   

Competition between species can drive public goods cooperation within a species

Costly cooperative strategies are vulnerable to exploitation by cheats. Microbial studies have suggested that cooperation can be maintained in nature by mechanisms such as reciprocity, spatial structure and multi-level selection. So far, however, almost all laboratory experiments aimed at understanding cooperation have relied on studying a single species in isolation. In contrast, species in the wild live within complex communities where they interact with other species. Little effort has focused on understanding the effect of interspecies competition on the evolution of cooperation within a species. We test this relationship by using sucrose metabolism of budding yeast as a model cooperative system. We find that when co-cultured with a bacterial competitor, yeast populations become more cooperative compared to isolated populations. We show that this increase in cooperation within yeast is mainly driven by resource competition imposed by the bacterial competitor. A similar increase in cooperation is observed in a pure yeast culture when essential nutrients in the media are limited experimentally.   

The emergence of cooperation from a single cooperative mutant

Population structure is one central condition which promotes the stability of cooperation: If cooperators more likely interact with other cooperators (positive assortment), they keep most of their benefit for themselves and are less exploited by non-cooperators. However, positive assortment can only act successfully if cooperation is already well established in the population such that cooperative individuals can successfully assort. But how can cooperation emerge when starting with a single cooperative mutant? Here we study this issue for a generic situation of microbial systems where microbes regularly form new colonies and show strong population growth. We show how and when the dynamical interplay between colony formation, population growth and evolution within colonies can provoke the emergence of cooperation. In particular, the probability for a single cooperative mutant to succeed is robustly large when colony-formation is fast or comparable to the time-scale of growth within colonies; growth supports cooperation.\\[4pt] [1]~A. Melbinger, J. Cremer, and E. Frey, Evolutionary game theory in growing populations, \emph{Phys. Rev. Lett.} {\bf 105}, 178101 (2010)\\[0pt] [2]~J. Cremer, A. Melbinger, and E. Frey, Evolutionary and population dynamics: a coupled approach, arXiv:1108.2604   

Coping with stress in a synthetic world

A major focus of synthetic biology is the engineering of gene circuits to perform user-defined functions. In addition to generating systems of practical applications, such efforts have led to the identification and evaluation of design strategies that enable robust control of dynamics in single cells and in cell populations. On the other hand, there is an increasing emphasis on using engineered systems programmed by simple circuits to explore fundamental biological questions of broad significance. In this talk, I will discuss our efforts along this line of research, whereby we have used engineered gene circuits to examine the evolutionary dynamics of two common bacterial survival strategies in stress response: programmed death and cell-cell communication.   

Bacterial cheating limits antibiotic resistance

The widespread use of antibiotics has led to the evolution of resistance in bacteria. 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 removing the antibiotic. The cooperative nature of this growth suggests that a cheater strain---which does not contribute to breaking down the antibiotic---may be able to take advantage of cells cooperatively inactivating the antibiotic. Here 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 observe stable coexistence between the two strains and find that a simple model successfully explains the behavior as a function of antibiotic concentration and cell density. We anticipate that our results will provide insight into the evolutionary origin of phenotypic diversity and cooperative behaviors.   

Bacterial Transformation and Competition Under Antibiotic Stress

Transformation, the process by which bacteria uptake DNA directly from their environment and incorporate it as their own genetic material, is a form of Horizontal Gene Transfer that occurs throughout nature as an important mechanism for spurring on bacterial evolution. We examine the capacity of bacteria to undergo transformation and will discuss work that has been done by the Austin group using Micro-Habitat Patches (MHPs) to examine the emergence of phenotypes due to horizontal gene transfer.   

Rapid Antibiotic Resistance Evolution of GASP Mutants

The GASP phenotype in bacteria is due to a mutation which enables the bacteria to grow under high stress conditions where other bacteria stop growing. We probe using our Death Galaxy microenvironment how rapidly the GASP mutant can evolve resistance to mutagenic antibiotics compared to wild-type bacteria, and explore the genomic landscape changes due to the evolution of resistance.   

Spatial vs. individual variability with inheritance in a stochastic Lotka-Volterra system

We investigate a stochastic spatial Lotka-Volterra predator-prey model with randomized interaction rates that are either affixed to the lattice sites and quenched, and / or specific to individuals in either population. In the latter situation, we include rate inheritance with mutations from the particles' progenitors. Thus we arrive at a simple model for competitive evolution with environmental variability and selection pressure. We employ Monte Carlo simulations in zero and two dimensions to study the time evolution of both species' densities and their interaction rate distributions. The predator and prey concentrations in the ensuing steady states depend crucially on the environmental variability, whereas the temporal evolution of the individualized rate distributions leads to largely neutral optimization. Contrary to, e.g., linear gene expression models, this system does not experience fixation at extreme values. An approximate description of the resulting data is achieved by means of an effective master equation approach for the interaction rate distribution.   

Session T44: Focus Session: Interparticle Interactions in Polymer Nanocomposites - Grafted Chains

Colloidal assembly on soft substrates

We studied -- by Monte Carlo computer simulations - ordering of hard sphere colloidal particles subject to gravity and soft interactions induced by polymer-coated substrates. The polymers are randomly anchored to a flat surface with an average density ranging from very dilute values to a situation where a dense polymer brush with the average height h forms. Studying a single colloid subject to such substrate and the gravity we observed a transition from a regime where it is confined to the hard surface at z=0, via a bimodal regime where it is equally likely to find it at the bottom or at the top, to the regime where it lies on top of the brush at z=h. In a system of many colloids the polymers induce an effective colloid-colloid interaction of entropic origin. We have performed Grand canonical Monte Carlo simulations and explored the structure formation as a function of the anchoring density and the effective gravity of the colloids. Colloids are initially attracted and grow into elongated assemblies with a well-defined lateral width. At low grafting densities such assemblies form percolated networks, while at high enough grafting densities finite clusters are observed. We discuss the relevance of our results to applications like particle sorting, reactions catalysis and passive diffusion.   

Molecular Dynamics Simulations on the Thermal and Mechanical Properties of Blend of Polymer and Polymer Grafted Nanoparticles

Grafting polymers onto the surface of NPs has become one of the most effective approaches to integrate NPs into polymer melts. It then becomes crucial to be able to understand how the presence of grafted chains affects the effective interactions between NPs as well as the mechanical properties of the resulting composites. Using molecular dynamics simulations we first measure the potential of mean force between grafted NPs from two-particle simulations. Simulations of systems containing many grafted NPs are then performed to determine the phase behavior and structure of grafted NPs in explicit polymer matrices. Finally, we cool the nanocomposites to temperatures below their glass transition and stress the systems to investigate how the presence of grafted NPs changes their mechanical properties.   

Self Assembly of Tethered Nanoparticle Telechelics

Simulations, theory, and experiement predict that aggregating nanoparticles functionalized with polymer tethers can self-assemble to form phases seen in block copolymer and surfactant systems, but with additional nanoparticle ordering and mesophase complexity. Here we consider a novel class of ``telechelic'' tethered nanoparticle building blocks, where two nanoparticles are connected together by a polymer tether. The architecture is similar to a triblock copolymer, but with additional geometric constraints imposed by the rigid particle end groups. Using Brownian dynamics simulations, we explore the phase diagrams of several examples of this class of nano-building-block, and present predictions of novel phases and their dependence on particle size, tether length, and thermodynamic parameters. We compare our results with recent simulations of di-tethered nanospheres [1, 2] and mono-tethered nanospheres [2, 3]. \begin{enumerate} \item Iacovella, C. R.; Glotzer, S. C.; \textit{Soft Matter} \textbf{2009}, 5, 4492-4498. \item Iacovella, C. R.; Keys, A.S..; Glotzer, S. C. \textit{PNAS}, in press. arXiv:1102.5589. \item Phillips, C. L.; Iacovella, C. R.; Glotzer, S. C.; \textit{Soft Matter}\textbf{ 2010}, 6, 1693-1703. \end{enumerate}   

Controlling the Phase Behavior of Gold Nanoparticles within Polymer Matrix by Varying Composition and Length of Ligands

Nanocomposites have been investigated for many years due to their facsinating features. In spite of the captivative properties, compatibility problem has been an obstacle for manufacturing the nanocomposites. To achieve the compatibility between NPs and polymer matrix, thiol-terminated polymeric ligands have been used for tuning the surface property of the NPs. However, in case of Au NPs, Au-thiol bond is unstable above 60 $^{\circ}$C. In our recent work, we designed thermally stable Au NPs by using thiol terminated photo crosslinkable block copolymer, PS-b-PSN3-SH. With the thermally stable Au NPs, we demonstrated that Au NPs are stable at high temperature and can serve as compatibilizers for PS/PMMA blends. Herein, we prepared Au NPs using photo crosslinkable polymeric ligands which have various ligand composition and lengths. As the ligands characteristics were changed, the phase behaviors of Au NPs in both homopolymer and block copolymer bulk sample were significantly different. For example, the NPs become more dispersed within the polymer matrix with longer polymer ligands, while they are aggregates when shorter ligands were used. In this work, morphologies of Au NPs within polymer matrix were systematically investigated using the cross-sectional transmission electron microscopy.   

Molecular Weight Distribution Effects on the Structure of Strongly Adsorbed Polymers by Monte Carlo Simulation

Monte Carlo simulations are used to investigate the adsorption of polymers from solution onto strongly attractive, perfectly smooth substrates. Using a coarse-grained united atom model for freely rotating polymer chains, three systems with different polydispersities are studied. The structure of the adsorbed layers, exemplified by density profiles, bond orientation order parameters, radii of gyration, and distribution of the adsorbed chain fractions, is shown to be highly dependent on the molecular weight distribution of the polymer phase. The results for the more monodisperse polymer systems are qualitatively similar to experimental and theoretical investigations, but devolve from very different chain conformations and statistics. For the first time ever, equilibrium polymer adsorption on highly attractive surface is studied, with all molecules in the adsorbed layers demonstrated to be indistinguishable from each other. The ergodicity of states explored by the polymer chains is in contrast to the kinetically constrained viewpoint of irreversible adsorption, and the observed behavior is explained in the context of the competition between polymers to make contact with the surface.   

Role of Stretchable Arms, Grafting Density and Parallel Reformable Bonds in the Self-Healing of Cross-Linked Star Nanogel Particles

We investigate the role of stretchable and reformable bonds in the self-healing of a network formed by star-like nanogel particles. The individual particles of the network are composed of a cross-linked gel core and a corona of grafted polymeric arms with sticky end groups. The sticky groups in the coronas of adjacent particles interact to form multiple labile bonds (up to N) that lead to the formation of the nanogel network. Interaction between soft colloids with polymeric arms is combined with the Bell model for rupture and formation of bonds to model the interaction of array of particles. While the stretch of the bonds is captured through the bond spring constant (k) and cutoff radius for bond breaking (rc), the equilibrium distance (req) at which the labile bonds reform is obtained from the corona thickness. We show that the presence of stretchable arms allows for rearrangements leading to either increase or decrease of the strength and ductility of the nanogel network depending on the grafting density. We also show that while the force required to rupture the nanogel network is proportional to the number of parallel bonds (N), the ductility is a more complex function of N.   

Poly(ethylene-oxide)/clay/silica nanocomposites: Morphology and thermomechanical properties

Poly(ethylene oxide) PEO/clay/silica nanocomposites were prepared via solution intercalation by exploiting phase separation based on the bridging of particles by polymer chains. The intercalated morphology of nanocomposites was confirmed by XRD. Vibrational modes of the ether oxygen of PEO in the hybrids are shifted due to the coordination of the ether oxygen with the sodium cations of clay and the H-bonding interactions of the ether oxygen with the surface silanols of hydrophilic fumed silica. Based on SEM, the overall density of nanoparticle aggregates in the interspherulitic region was observed to be higher compared to that inside spherulites. PEO/clay/silica hybrids show significant property improvements compared to PEO/clay hybrids and pure PEO. The system containing 10 wt.{\%} clay and 5 wt.{\%} silica has substantially higher modulus and much lower crystallinity compared to the 15 wt.{\%} clay system. The physics behind the reinforcement effect and the reduction of crystallinity as a function of fumed silica loading is discussed based on the morphological characterization of the hybrids. Lastly, PEO/clay/silica hybrids display good thermal stability and are much stiffer compared to pure PEO and PEO/clay nanocomposites.   

Copolymer mediated interactions in dense nanocomposites: role of chemical heterogeneity and sequence

Microscopic PRISM integral equation theory is applied to study the structure and dispersion of nanospheres in AB copolymer melts as a function of architecture and chemical heterogeneity of the interfacial attractions spanning the depletion, stabilization and bridging regimes. For a random copolymer (RCP) with coexisting weak and strong monomer-particle attractions, the nanoparticle potential-of-mean-force (PMF) at intermediate copolymer compositions varies non-monotonically between the two homopolymer limits. Non-adsorbing monomers are generically found to be crucial for achieving good filler dispersion in RCP melts. For 50/50 multiblock melts the role of block length, R, has been studied over a wide range (R=1,2,5,10,25,50). Filler miscibility dramatically increases when one of the monomers is weakly adsorbing (depletion). Dispersion is also improved for some block lengths when one of the monomers strongly adsorbs (bridging) due to the emergence of a long-ranged repulsive barrier in the PMF just beyond a local non-contact minimum, resulting in a positive second virial coefficient. Strikingly, better stability is predicted as the particle-to-monomer diameter ratio increases from 2 to 10, contrary to the behavior in homopolymer or RCP melts.   

Effect of bidispersity in grafted chain length on potential of mean force between polymer grafted nanoparticles in a homopolymer matrix

In polymer nanocomposites consisting of polymer grafted nanoparticles in a polymer matrix the molecular weight of the grafted polymers plays a key role in dictating the effective inter-particle interactions. Despite the importance of graft molecular weight on effective inter-particle interactions in monodisperse polymer grafted nanoparticles, and evidence of non-trivial polydispersity effects in systems containing polymers grafted on flat surfaces, not much work has been done to explore polydipsersity effects in polymer grafted nanoparticles. In this talk we will present self-consistent PRISM theory-Monte Carlo simulation studies showing how bidispersity in grafted chain lengths affects the grafted chain conformations and inter-particle interactions in a dense homopolymer polymer matrix. The value of the potential of mean force (PMF) between bidisperse grafted particles at contact is governed by the short grafts and values at large inter-particle distances are governed by the longer grafts. Our results suggest that by introducing bidispersity in grafted chains one can change the rules seen in monodisperse polymer grafted particles for wetting/dewetting of grafted polymers by matrix polymer.   

Concentration, Interaction and Temperature Dependent Chain Dynamics in Polybutadiene / Clay Nanocomposites Characterized by Solid State 1H Double Quantum NMR Spectroscopy

A concentration, interaction and temperature dependent multimode segmental chain dynamics of carboxyly terminated polybutadiene (CTPB) in CTPB/organo-clay (C18-clay) nanocomposite was investigated by solid state 1H double quantum (DQ) NMR spectroscopy. Here, the measurements were performed on a series of samples of CTPB physically attached to the surface of C18-clay. NMR results showed that the nanocomposite exhibit discrete dynamic component with stepwise increase in their motional freedom with decreasing clay content. A remarkable change of CTPB chain dynamics at organo-clay concentration of 40 wt{\%} was found, indicating a saturation effect of the polymer adsorbed on the clay surface. The transverse magnetization relaxation experiment help us quantitatively analysis the rigid, intermediate, and mobile components. Removal of either the end-group of CTPB or of the modifier on the clay changed the polymer-clay interaction profoundly, and thus changed polymer chain dynamics, especially for chains in proximity to the clay surface. The measurement confirmed our earlier hypothesis that the strong polymer-clay interaction was the key to the synergy effect in polymer/clay nanocomposites.   

Structural Transitions of Polymer Grafted Magnetic Nanoparticles

We decorate iron oxide nanoparticles with polymers to investigate the various interactions between particles and particle-polymer on the formation of different morphologies. We show that very low to intermediate grafting densities (2-20 chains/particle) can be achieved by controlling the concentration of free polymer chains in solution by grafting-to method. Nanostructural transitions of poly(styrene) grafted Fe3O4 nanoparticles are investigated upon varying the grafting densities and brush lengths. The roles of these parameters as well as dipolar force in the formation of various aggregates, such as star-like shape and chains, are discussed. This morphological transition is found to be sensitive to small grafting density change in very low to intermediate regime (0.01-0.04 chains/nm2). Interestingly, the matrix shows reverse effects on nanostructures with increment of brush lengths.   

Session T45: Polymeric Glasses

Formation of Polymer Glasses Under Stress and Its Influence on Physical Aging

Understanding and controlling the stability and physical aging of polymer glasses is important for many technological applications from gas separation membranes to optical coatings. We investigate the stability of polymer glasses when thermally quenched under different stress conditions. Ellipsometry is used to measure the physical aging rate of polystyrene films supported or transferred onto silicon wafers. We quantify the time-dependent decrease in film thickness that results from the increase in average film density during aging to obtain a physical aging rate. We have observed significant differences between films quenched in a free-standing versus supported state, even though all films were aged in a supported state. Films quenched in a free-standing state exhibit a strong thickness dependence to their physical aging rate at micron length scales, an order of magnitude or two larger than thicknesses where nanoconfinement effects on the glass transition and modulus are typically observed. In contrast, supported films do not display any film thickness dependence to their aging rate at this large length scale. All available evidence suggests that different stress conditions are the underlying cause of this effect. In order to investigate the role of stress during the vitrification of polymer glasses, we have constructed a unique jig to apply a known stress to free-standing films during the thermal quench.   

Deformation-induced molecular mobility allows polystyrene glasses to flow

Experiments on colloidal glasses show that local rearrangements occur more rapidly during deformation. For polymeric glasses, similar features are expected but cannot be directly imaged. Dye reorientation has been used to measure segmental mobility in polymer glasses during active deformation. In creep deformations, we see a hundred-fold enhancement of mobility occurring in polystyrene glasses lightly cross-linked with 2 and 4 weight percent of divinylbenzene. Qualitatively similar mobility enhancement has been previously reported for lightly cross-linked poly(methyl methacrylate). Data from all three systems superpose on a master plot of the mobility as a function of the local strain rate during creep. Additionally, in the flow regime we see a significant narrowing of the distribution of relaxation times for both the polystyrene and poly(methyl methacrylate) glasses, similar to what has been reported for colloidal systems. Because polystyrene lacks the prominent beta relaxation of poly(methyl methacrylate), we conclude that the changes in mobility during creep deformation are a result of changes in the alpha segmental relaxation time.   

Temperature Divergence of the Dynamics of a PVAc glass: Dielectric vs. Mechanical Behaviors

The dynamics of glass forming liquids as the glass transition is traversed has become of special interest because of the continuing question as to whether or not these dynamics diverge towards an ideal glass transition/Kauzmann temperature or if the apparent Vogel-Fulcher divergence is lost as one goes below the conventional T$_{g}$ but remains in equilibrium. Here we examine the response of a PVAc polymer glass-former using both dielectric and mechanical methods in the vicinity of T$_{g}$. Isothermal measurements were performed to study the aging behavior of PVAc and to assure that the equilibrium state was achieved and for temperatures to as much as 15 $^{o}$C below the T$_{g}$. Surprisingly, we found that the mechanical response took much longer to age into equilibrium than did the dielectric response. Also, although the dielectric and mechanical responses seem to probe the glassy dispersion, the temperature dependence of the time-temperature shift factors obtained from the two methods are different and the dielectric measurement response shows a turnover to Arrhenius behavior rather than a continuation of the VFT divergence at the lowest temperatures tested.   

Determination of effective correlation length in a glassy polymer using electrostatic force microscopy

Various fourth-order correlation functions have been used to study the size of dynamically correlated regions in colloidal glasses and simulated glass forming liquids or polymers. However, measuring these correlation functions in molecular glasses has been limited by the small length scales on which the dynamics occur. Electrostatic force microscopy techniques are employed here to probe dielectric noise in polyvinyl acetate. We analyze fourth-order statistical fluctuations in order to determine spatio-temporal correlation lengths and their temperature dependence near the sample's glass transition. The first harmonic response of an applied AC voltage between the conducting AFM tip and the conducting substrate beneath the thin film polymer sample is proportional to the local electric polarization. Noise in this signal is examined and many hours are recorded at various temperatures in order to improve statistical precision. We employ a variety of statistical analysis techniques ranging from power spectrum analysis to variance of autocorrelation functions in order to find deviations from Gaussian statistics. Super-sharp carbon nanotube EFM tips (nominal radius of 10 nm) are employed to probe smaller effective volumes and thus more easily detect these fluctuations.   

Stable Nanostructured Polymer Films Formed Via Matrix Assisted Pulsed Laser Evaporation

Via typical routes to the vitreous state, the ability to significantly alter the properties of amorphous solids is restricted due to the kinetic nature of the glass transition. In this talk, we show that matrix assisted pulsed laser evaporation (MAPLE) can be used to form ultra-stable and nanostructured glassy polymers with significantly reduced densities, enhanced glass transition temperatures, and superior kinetic stability at high temperatures. Relative to the standard poly(methyl methacrylate) glass formed on cooling at standard rates, glasses prepared by MAPLE can be 40 percent less dense and have 40 K higher glass transition temperatures. Furthermore, the kinetic stability in the glassy-state can be enhanced by 2-orders-of-magnitude. The unique combination of properties is a result of the glass morphology, i.e., the glassy films are formed by the assembly of nearly spherical-like polymer nanoglobules.   

A Scattering Model for Amorphous, Intrinsically Microporous Polymers

We discuss the development of a scattering model for glassy, porous polymers in which porosity is equivalent to free volume, deriving significant insight from molecular dynamics simulations. Polymers of intrinsic microporosity (PIMs) exhibit high gas permeability and a large concentration of pores smaller than 1 nm; their porosity arises from an unusual chain structure combining rigid segments with sites of contortion, rather than from any templating effect. Although for many porous materials, useful information such as pore sizes and specific surface areas can be extracted from scattering patterns, a successful scattering model for PIMs must account for several unusual features. Simulated structures that reproduce characteristic scattering features are used to test model assumptions, with the ultimate goal of increasing the utility of scattering for studying microporous polymeric membrane processing and physical aging.   

Non-Equilibrium Water-Glassy Polymer Dynamics

For many applications (e.g., medical implants, packaging), an accurate assessment and fundamental understanding of the dynamics of water-glassy polymer interactions is of great interest. In this study, sorption and diffusion of pure water in several glassy polymers films, such as poly(styrene) (PS), poly(methyl methacrylate) (PMMA), poly(lactide) (PLA), were measured over a wide range of vapor activities and temperatures using several experimental techniques, including quartz spring microbalance (QSM), quartz crystal microbalance (QCM), and time-resolved Fourier transform infrared-attenuated total reflectance (FTIR-ATR) spectroscopy. Non-Fickian behavior (diffusion-relaxation phenomena) was observed by all three techniques, while FTIR-ATR spectroscopy also provides information about the distribution of the states of water and water transport mechanisms on a molecular-level. Specifically, the states of water are significantly different in PS compared to PMMA and PLA. Additionally, a purely predictive non-equilibrium lattice fluid (NELF) model was applied to predict the sorption isotherms of water in these glassy polymers.   

Self-consistent Mixing Rule for the Viscoleasticity of Heterogeneous Systems

Heterogeneous systems --like glasses mixtures - can exhibit huge local fluctuations of their viscoelastic modulus. The average viscoelastic modulus is often approximated either as the average modulus, or as the inverse of the average of the inverse of the modulus. Here we test a self-consistent method based on the Olroyd Palierne model for blend viscoelasticity [1]. We test this method on polymer miscible blends, with a very different glass transition temperature. We first deduce from Differential Scanning Calorimetric measurements the distribution of glass transition and thus of local viscoelastic modulus. From that we predict quantitatively the viscoelastic modulus of the polymer blends. It appears thus that the self-consistent averaging for disordered systems is extremely efficient, describing quantitatively systems where the modulus varies locally by at least 3 decades. [1] F. Lequeux, A. Ajdari,``\textit{Averaging rheological quantities in descriptions of soft glassy materials}`` Phys. Rev E 63 R030502 (2001)   

Understanding failure behavior of polymer glasses: a molecular viewpoint

In surveying the vast literature we note that a unified simple picture appears to be lacking to account for all the known facts on failure behavior of polymer glasses. In this work, we first apply the fresh insight we have gained from studying nonlinear extensional rheology of entangled melt to show why a melt-stretched polystyrene turns ductile. We further show that the ductile polycarbonate can also turn brittle upon pre-melt-stretching. Finally, blending oligomeric PC into an originally ductile PC also causes the mixture to become brittle. All these old and new phenomena point to the fact that the strength of the load bearing chain network dictates at a given temperature whether the polymer glass would undergo ductile failure through shear yielding or brittle fracture via crazing. This presentation will provide a description of how the entanglement structure can be altered by melt deformation or the choice of different chemical specificity (that influences the packing length) to affect the strength of polymer glasses. It is this network strength relative to the yield strength associated with the inter-segmental van der Waals interactions that determines how strain localization (shear yielding -- necking vs. crazing) takes place.   

Heterogeneous Dynamics During Creep of Rod Containing Polymer Nanocomposites

Polymer glasses exhibit regions of locally higher or lower mobility leading to heterogeneous dynamics. While heterogeneous dynamics have been examined in some detail in pure polymers, less is known about polymer nanocomposites (PNCs). We have previously studied PNCs, providing descriptions of how particles alter the network of entanglements, measuring local mechanical heterogeneity, demonstrating strain response under uniaxial deformation, and examining crazing and failure under multiaxial deformation. In the present work, we examine dynamic heterogeneity in rod-containing PNCs by performing creep deformation simulations and monitoring several measures of mobility. We are able to directly probe how dynamic heterogeneity evolves during deformation, and explore the origins of molecular mobility in polymer glasses. Examination of the segmental motion of a PNC undergoing creep reveals that the glassy heterogeneity of these systems decreases significantly following the onset of flow. It is found that the more heterogeneous distribution of relaxation times characteristic of PNCs in the bulk remains unaltered regardless of deformation state. It is found that the mobility and heterogeneity of PNCs are less susceptible to change upon deformation than those for the pure polymer.   

Molecular dynamics simulations of highly cross-linked polymer networks: prediction of thermal and mechanical properties

We use all-atom molecular dynamics (MD) simulations to predict the mechanical and thermal properties of thermosetting polymers. Atomistic simulation is a promising tool which can provide detailed structure-property relationships of densely cross-linked polymer networks. In this work we study the thermo-mechanical properties of thermosetting polymers based on amine curing agents and epoxy resins and have focused on the DGEBA/DETDA epoxy system. At first we describe the modeling approach to construction of realistic all-atom models of densely cross-linked polymer matrices. Subsequently, a series of atomistic simulations was carried out to examine the simulation cell size effect as well as the role of cross-linking density and chain length of the resin strands on thermo-mechanical properties at different temperatures. Two different methods were used to deform the polymer networks. Both static and dynamic approaches to calculating the mechanical properties were considered and the thermo-mechanical properties obtained from our simulations were found in reasonable agreement with experimental values.   

Heterogeneity: A Solution to the Mysteries of the Glass transition?

For most phase transitions, dynamic slowdown is accompanied by static structure change. However, in supercooled liquids there is a pronounced dynamic slowdown, i.e. diffusion coefficient, relaxation time and viscosity change 14 orders of magnitude within a small temperature range, without any static structure change. Over the past several decades, extensive research has been performed to understand this dramatic dynamical slowing, i.e., why the glass transition occurs? What exactly is the glass transition? And how molecules move near the glass transition? In the present work, the idea that the large decrease in mobility in supercooled liquids during cooling from above T$_{g}$ occurs due to the increasing length scale of heterogeneous sub-regions, or the Cooperative Rearranging Regions (CRR) proposed by Adam and Gibbs, is evaluated by analyzing both experiment and computer simulation results. Although the existence of microscopic heterogeneous regions is confirmed, the values of the fitting parameters obtained from both VFT and power law fits of the temperature dependent heterogeneity data suggest that the heterogeneity, itself, might not play in the key role in the T$_{g}$ and/or tightly connect with the CRRs.   

The effect of polar interactions on the dynamics in vitreous liquids

It is known that in small molecule and polymeric systems the long-range process like diffusion and chain relaxation decouple from the local structural relaxation temperature dependence as system approaches its T$_{g}$. Recently, it was shown by Sokolov and Scweizer (\textit{Phys. Rev. Lett. }\textbf{2009}, 102, 248301) that these decoupling phenomena seem to have similar underlying mechanism irrespective whether system is a polymeric or a molecular liquid. The degree of decoupling for both polymers and small molecule systems show very similar trend with respect to the fragility of the material. More fragile systems show higher degree of decoupling. However, such behavior was shown only on the example of dynamics in weakly interacting van der Waals systems. On the example of three polymers and one room temperature ionic liquid (RTIL) it is demonstrated that the presence of polar interactions leads to rather steep temperature dependence of large length scale dynamic processes, like chain relaxation and self-diffusion. As a result, the degree of decoupling between large length scale and local dynamic processes in such polar materials is significantly lower than in weakly interacting liquids with comparable fragilities. The microscopic mechanism behind an unusual dynamic behavior seen in polar polymers and RTILs remains unclear. Nevertheless, knowledge of such structure-property relationship can significantly aid in the development of novel materials. Authors are thankful to NSF and (U.S.) DOE, Office of Basic Energy Sciences for the financial support.   

The Twinkling Fractal Theory of the Glass Transition: Applications to Soft Matter

The Twinkling Fractal Theory (TFT) of the glass transition has recently been demonstrated experimentally [J.F. Stanzione et al., J. Non Cryst. Sol., (2011, 357,311]. The hard to-soft matter transition is characterized by the presence of solid fractal clusters with liquid-like pools that are dynamically interchanging via their anharmonic intermolecular potentials with Boltzmann energy populations with a characteristic temperature dependent vibrational density of states g($\omega ) \quad \sim \quad \omega ^{df}$ . The twinkling fractal frequencies $\omega $ cover a range of 10$^{12}$ Hz to 10$^{-10}$Hz and the fractal solid clusters of size R have a lifetime $\tau \quad \sim $ R$^{Df/df}$, where the fractal dimension D$_{f}$ $\approx $ 2.4 and the fracton dimension d$_{f}$ = 4/3. Here we explore its application to a number of soft matter issues. These include (a) Confinement effects on T$_{g}$ reduction in thin films of thickness h, where by virtue of large cluster exclusion, $\Delta $T$_{g} \quad \sim $ 1/h$^{Df/df}$; (b) T$_{g}$ gradients near bulk surfaces, where the smaller clusters on the surface have a faster relaxation time; (c) Effect of twinkling surfaces on cell growth, where at T $\approx $ T$_{g}$ + 20 C, there exists a twinkling fractal range that leads to bell-shaped enhancement of cell growth and chemical up-regulation via the twinkling surfaces ``communicating `` with the cells through their vibrations; and (d) adhesion above and below T$_{g}$ where topological fluctuations associated with g($\omega )$ promotes the development of nano-nails at the interface.   

Nano-indentation of Polycarbonate and Diamine Blends

Nanoindentation of complex surfaces is of great interest from academic and industrial point of view. There are unique properties such as indentation effects resulting in strain softening and strain hardening. There is a differentiation in structure with the depth exhibited with variation of Tg. Hertzian and non-linear deformation models including usage of FEM offer opportunity in analyzing nano-indentation. In polycarbonate, the effective elastic modulus and the hardness decreases as the applied load is increased. As the hold time was increased, the effective elastic modulus and the hardness also decreased. The contact stress increases as the contact strain rate is increased. Presence of diamine(MTBD) in polycarbonate results in making the surface and bulk brittle and acts as an anti-plasticizer by increasing it modulus and reducing yield stress (hardness) and strain to break. Data on modulus and hardness of polycarbonate and blends of diamine as function of depth (strain) and strain rate are presented and compared with those of composites with silica.   

Session T46: Invited Session: Keithley Award Session: Photoacoustic and Photothermal Measurement Science

Joseph F. Keithley Award For Advances in Measurement Science Lecture: Thermophotonic and Photoacoustic Radar Imaging Methods for Biomedical and Dental Imaging

In the first part of this presentation I will introduce thermophotonic radar imaging principles and techniques using chirped or binary-phase-coded modulation, methods which can break through the maximum detection depth/depth resolution limitations of conventional photothermal waves. Using matched-filter principles, a methodology enabling parabolic diffusion-wave energy fields to exhibit energy localization akin to propagating hyperbolic wave-fields has been developed. It allows for deconvolution of individual responses of superposed axially discrete sources, opening a new field: depth-resolved thermal coherence tomography. Several examples from dental enamel caries diagnostic imaging to metal subsurface defect thermographic imaging will be discussed. The second part will introduce the field of photoacoustic radar (or sonar) biomedical imaging. I will report the development of a novel biomedical imaging system that utilizes a continuous-wave laser source with a custom intensity modulation pattern, ultrasonic phased array for signal detection and processing coupled with a beamforming algorithm for reconstruction of photoacoustic correlation images. Utilization of specific chirped modulation waveforms (``waveform engineering'') achieves dramatic signal-to-noise-ratio increase and improved axial resolution over pulsed laser photoacoustics. The talk will conclude with aspects of instrumental sensitivity of the PA Radar to optical contrast using cancerous breast tissue-mimicking phantoms, super paramagnetic iron oxide nanoparticles as contrast enhancement agents and in-vivo tissue samples.   

Photoacoustics and Photothermal instrumentation in the study of thermal properties of liquids and semisolids

The fundamentals of the measurements of the thermal properties of solids and semisolids using photoacoustics and photothermal techniques are presented. It is shown that photoacoustics is a high stability technique which allows the monitoring of complex process in which the physical properties of the liquid can evolve. Additionally, it is shown that the methodology known as thermal wave cavity can be used successfully in high accuracy measurements for a wide variety of materials. In particular the case of magnetic fluids in which the viscosity can be varied, using an external magnetic fluid, is presented. It is also shown that the thermal wave cavity permits the study of magnetic fluids in which high aspect ratio particles are introduced in the fluid matrix. The effect of the orientation of non-magnetic particles inside the magnetic fluid generated by external magnetic field is also investigated. The possible applications and consequences in the development of windows of controlled thermal conductivity are discussed.   

Photoacoustic and Photothermal Effects in Periodic Structures and Acoustic Resonators

Laser excited photoacoustic and photothermal waves can be generated in one-dimensional structures whose acoustic or thermal properties vary sinusoidally in space. The wave equations describing the pressure or the temperature in such structures can be shown to reduce to inhomogeneous Mathieu equations. Solutions of the Mathieu equation are obtained based on both the method of variation of parameters and expansion of the pressure or temperature in a summation over eigenfunctions. The solutions for the photoacoustic effect show the space equivalent of subharmonic generation where resonances occur at one half of the period of the structure. The positions of the band gaps and the dispersion relations for any modulation depth of the acoustic properties of the structure can be found directly from the Mathieu characteristic exponent. Since the photoacoustic effect is governed by an inhomogeneous differential equation, excitation within forbidden gaps is possible. For excitation within a finite region of the structure, the Mathieu equation equivalent of Hankel functions are defined. From these functions the properties of the photoacoustic waves excited within or outside of the band gaps are found. For thermal waves, the character of the waves and the dispersion relation can be found as well, however no band gaps result from the periodicity of the thermal properties of the structure. The generation of sound by continuous, unmodulated irradiation of an absorbing gas in a resonant cavity is discussed. A longitudinal resonance of the cavity is predicted to be excited since any pressure increase from optical absorption is accompanied by a density increase, the latter resulting in additional energy deposition by the laser beam. Thus, on each return of the pressure pulse to the window of the resonator where laser beam enters the acoustic signal is amplified. Calculations show that for a strongly absorbing gas, the acoustic modes of the resonator become mode locked.   

Linear and Nonlinear Laser-Based Guided Acoustic Waves Propagating at Surfaces (2D) and Edges (1D)

In recent years photoacoustics opened the door to many new applications of 2D linear surface acoustic waves (SAWs), e.g., nondestructive evaluation (NDE) of surface-breaking cracks. Real partially-closed cracks of micrometer size have been analyzed. More recently also pulsed laser excitation of solitary elastic surface pulses and their detection with a continuouswave probe laser has been achieved, by generating dispersion with a thin film coating that introduces a length scale. In addition, such laser-based pump-probe experiments allow the excitation of short nonlinear SAW pulses developing steep shock fronts that fracture brittle materials such as silica or silicon. With this method it is possible to measure the fracture strength of materials and compare the critical failure stress with ab initio calculations of the ideal strength of the corresponding perfect single crystal. The excitation and detection of 1D edge or wedge waves propagating along a wedge formed by two planar surfaces that meet at the apex of the wedge or wedge tip has been performed by laser irradiation. The characteristic features of the non-dispersive linear wedge waves such as their small phase velocity below the Rayleigh velocity, the very high degree of localization of the displacement field at the wedge tip, and their existence for certain geometries in anisotropic media such as silicon could be verified by photoacoustic experiments. Despite the strong nonlinearity of certain edge-localized modes, as expected from theoretical considerations, 1D solitary waves and nonlinear wedge waves with steep pulse profiles could not be detected up to now. The latest progress will be discussed.   

Understanding climate: the role of photoacoustic spectroscopy at NIST

Sophisticated climate models predict that soot aerosols have a significant impact on Earth's energy budget; however, the uncertainty of these predictions is large, in part, because soot in the atmosphere and in the laboratory is poorly characterized. In the atmosphere, soot's optical and physical properties change as it combines with water vapor and sulfuric acid. We will describe a novel photoacoustic spectrometer system that measures the optical absorption cross section of various soots as they age in diverse environments. We also measure the albedo (optical scattering) of aerosols ranging from black-carbon-like to brown-carbon-like using simultaneous photoacoustic spectroscopy and cavity ring-down spectroscopy. Lastly, we developed a photoacoustic spectrometer system that measures the concentration of carbon dioxide in atmospheric air with sub-ppm uncertainty. We will report results of field tests of this spectrometer.   

Session T47: Focus Session: Heterogeneous Colloids I

Janus and Multiblock Colloids

This talk surveys emerging areas opened up by the directional interactions presented by the specially-designed spheres known as Janus. The ``diblock'' motif, mutually attractive on one domain and repulsive on another, makes this a prototypical system for elucidating, on a mechanistic level, how concepts of chemical reaction kinetics explain the development of stable and highly ordered nonequilibrium structures. With the ``triblock'' motif, spheres that attract one another on two polar regions but repel at the middle band, we go beyond this to demonstrate the self-assembly of a useful low-density lattice of spheres, the colloidal Kagome lattice, and visualize its aqueous assembly dynamics on the single-particle level. A newer area of opportunity is ``dynamic self-assembly,'' in which energy fed into the system as a control variable generates big surprises. The generalization of these design rules will be discussed.   

Synchronized Dancing of Magnetic Janus Particles

With Janus particle coated with magnetic material on one side, we demonstrate here first a complicated dance of single particle under external field. Then we show various quasi-one dimensional and two dimensional assembly from synchronized motion of a collection of these microspheres. With combination of experiment and simulation, we show how they are phase-locked in motion and self-organize into unexpected structures. By exploring a range of parameters, we also demonstrate fine control of the phase behavior of such dynamic self-assembled materials. We provide an vivid example here how synchronization in both time and space could lead to a new class of responsive materials.   

Hierarchical assemblies and cluster growth regimes of bipolar Janus nanoparticles: effect of particle characteristics

Numerous current and potential applications have motivated fundamental understanding of self assembly of colloidal Janus particles (JP). Experimental studies on nano and micron sized JPs have demonstrated a plethora of simple and complex structures. However, computational approaches to date have lacked the sophistication required to capture the rich free energy landscape of suspension of JPs especially for nanoscale particles and hence have been unable to elucidate the underlying principles that govern their complex self assembly. In this study, molecular dynamic simulation of a restricted primitive model, which also includes long range columbic interaction, has been performed in order to elucidate the underlying physics in the self assembly of bipolar JP at different surface charge density (0.2$\sim $1.3 e/nm2) , salt concentration(0$\sim $3 mM) and particle sizes. Our results clearly indicate formation of two distinct sub structures in very low JP concentration, namely: strings and rings. As the concentration of JP increases these sub structures joins and/or hierarchically assemble into larger clusters. Furthermore, the interconnection between the ionic cloud around a single JP and sequential cluster growth in JPS as a function of surface charge density, particle size and steric hindrance of surface ions has been elucidated.   

Stability of helical Janus clusters

Recent experimental and computational work has elucidated the importance of kinetic pathways in the formation of helical structures by hydrophobic-charged Janus particles.\footnote{Q. Chen, J.K. Whitmer, \emph{et al.}, Science \textbf{331}, 199 (2011).} Motivated by these findings, we perform free-energy calculations to investigate the equilibrium structure and relative stability of helical aggregates as a function of cluster size and Janus balance. These results simultaneously aid in the interpretation of experimental observations and in the design of building blocks for specific structures.   

Hierarchical Self-assembly of Triblock Janus Spheres

We show how monodisperse triblock Janus spheres in aqueous suspension, whose poles are attractive and middle band repulsive, self-assemble into hierarchical supracolloidal structures, on two sequential levels. Based upon the delicate dependence of interactions on ionic strength, we first activate attraction between larger patches, obtaining finite-sized 3D clusters. These clusters, now concrete objects themselves, are triggered later to be linked through topologically determined orientations. A family of unprecedented, complex structures is produced, with order over multiple length scales.   

Janus particles at fluid-fluid interfaces: the third face of Janus particles

Janus spheres are asymmetric particles with polar and apolar hemispheres. In this work, we study the interactions and assembly of Janus spheres -- bubbles and solid particles -- at fluid-fluid interfaces. Both the Janus bubbles and the Janus particles have strikingly different interfacial behaviour compared to their homogeneous counterparts. Janus spheres at a fluid-fluid interface interact with each other via long-ranged attractions. We show that the attractive interactions between interface-trapped Janus spheres are induced by the presence of diffuse boundary between the two hemispheres. Three phase contact line anchored around the rugged Janus boundary deforms that the fluid interface leading to attractive interactions between the spheres. The orientation and fluid deformation caused by Janus spheres are directly observed using a gel trapping method. We also show that the surface chemistry of Janus spheres plays a critical role in determining their interfacial behaviour. Potential implications of the observed long-range attractions will be discussed.   

Self Assembly of Hard, Space-Filling Polytopes

The thermodynamic behavior of systems of hard particles in the limit of infinite pressure is known to yield the densest possible packing [1,2]. Hard polytopes that tile or fill space in two or three spatial dimensions are guaranteed to obtain packing fractions of unity in the infinite pressure limit. Away from this limit, however, other structures may be possible [3]. We present the results of a simulation study of the thermodynamic self-assembly of hard, space-filling particles from disordered initial conditions. We show that for many polytopes, the infinite pressure structure readily assembles at intermediate pressures and packing fractions significantly less than one; in others, assembly of the infinite pressure structure is foiled by mesophases, jamming and phase separation. Common features of these latter systems are identified and strategies for enhancing assembly of the infinite pressure structure at intermediate pressures through building block modification are discussed.\\[4pt] [1] P. F. Damasceno, M. Engel, S.C. Glotzer arXiv:1109.1323v1 [cond-mat.soft]\\[0pt] [2] A. Haji-Akbari, M. Engel, S.C. Glotzer arXiv:1106.4765v2 [cond-mat.soft]\\[0pt] [3] U. Agarwal, F.A. Escobedo, {\em Nature Materials} {\bf 10}, 230--235 (2011)   

Self Assembly of Colloids

We are exploring the self assembly of colloidal matter using building blocks with complex shapes and functionalities. Our toolbox includes particles with tunable cavities and protrusions, particles with flexible ball-and-socket joints, colloidal cubes and particles with magnetic patches. Using these building blocks and a variety of interactions, including chemical, steric, magnetic and lock-and-key shape recognition, we aim to develop new assembly schemes to build structures with a reconfigurable structural arrangement.   

Surface Roughness directed Self-Assembly of Patchy Particles into Colloidal Micelles

Self-assembly of colloidal particles into larger structures bears potential for creating materials with unprecedented properties, such as full photonic band gaps in the visible spectrum. Colloidal particles with site-specific directional interactions, so called ``patchy particles,'' are promising candidates for bottom-up assembly routes towards such complex structures with rationally designed properties. Here we present an experimental realization of patchy colloidal particles based on material independent surface roughness specific depletion interactions. Smooth patches on rough colloids are shown to be exclusively attractive due to their different overlap volumes. We discuss in detail the case of colloids with one patch that serves as a model for molecular surfactants both with respect to their geometry and their interactions. These one-patch particles assemble into clusters that resemble surfactant micelles. We term these clusters ``colloidal micelles.'' Similarities as well as differences between the colloidal model system and molecular surfactants are discussed and quantified by employing computational and theoretical models.   

Entropic selection of patchy particle assemblies

We explore the statistical physics of triblock patchy colloids with degenerate valency, i.e., particles with excessively large attractive areas on two opposite sides, via analytic theory, which has the advantage of revealing fundamental laws of self-assembly more easily compared to the usual ``trial-and-error'' approach taken in experiments and simulations. From calculations of the free energy of multiple possible ground states, we conclude that the rotational entropy of individual particles favors certain bond angles, whereas vibrational entropy favors open rather than close-packed structures. Our analytic calculation is readily generalizable to other types of patchy particles and provides guidelines for new designs. We conclude that whereas the seemingly unfavorable degenerate valency of patchy colloids can lead to multiple energetic ground states and difficulties in selecting a unique ordered state, it also opens doors to surprising ordering phenomena. This shares pleasing commonalities with the ``order-from-disorder'' effect in frustrated magnets.   

Assembling Colloidal Clusters from Spherical Codes

Anisotropic building blocks assembled from colloidal particles are attractive building blocks for self-assembled materials because their complex interactions can be exploited to drive self-assembly. In this work we consider the thermodynamically driven self-assembly of terminal clusters of particles. We predict that clusters related to spherical codes, a mathematical sequence of points, can be synthesized via self-assembly. These anisotropic clusters, which derive from packing solutions of spheres around a sphere, can be tuned to different anisotropies via the ratio of sphere diameters and temperature. Structural and dynamical analysis of these tiny systems reveal rich and sometimes surprising properties.   

Session T48: Focus Session: Advanced Optical Probes of Soft Matter - Microrheology, Microbiography

Colloidal Diffusion and Hydrodynamic Interactions near Boundaries

Holographic optical tweezers allow trapping of colloidal spheres in fluid in three dimensions. In-line digital holographic microscopy yields time-resolved information on the three dimensional distribution of material in a sample. Analysis of in-line holographic images of diffusing colloidal spheres provides their three dimensional positions with nanometer resolution. We studied diffusion of colloidal spheres in three dimensions as a function of distance from boundary by analyzing particle trajectories generated by blinking optical tweezers and digital holographic microscopy. From the trajectories we calculated the particle-particle and particle-wall hydrodynamic interactions as a function of distance from the boundary. The results will help in understanding interactions between micron-sized colloidal particles near a boundary.   

Non-contact microrheology at the air-water interface

Mechanical properties of biological interfaces, such as cell membranes, have the potential to be measured with optical tweezers. We report on an approach to measure air-water interfacial properties through microrheology of particles near, but not contacting, the surface. An inverted optical tweezer traps beads of micron size or greater in the bulk, and can then translate them perpendicular to the interface. Through the measurement of thermally driven fluctuations, the mobility of the particle is found to vary as a function of submerged depth and the boundary conditions at the interface. Near a rigid wall, the mobility is confirmed to decrease in a way consistent with Fax\`{e}n's law. Very close to the free air-water interface, the mobility changes with the opposite sign, increasing by about 30{\%} at the surface, consistent with recent calculations by Shlomovitz and Levine. In addition, the presence of a Langmuir monolayer at the interface is found to significantly change the mobility of the particle close to the interface. With an accurate theory, it should be possible to infer the shear modulus of a monolayer from the fluctuations of the particle beneath the interface. Since particles are not embedded in the monolayer, this technique avoids impacting the system of study.   

Competing effects of inertia in passive microrheology

Single-point passive microrheology is generalized to account for both bead and medium inertia, and to incorporate a nonlinear optical trap or elastic trap. We first show that inertial motion of the bead couples with the elasticity of the viscoelastic material, resulting in a resonant oscillation of the mean-square displacement (MSD) of the bead well beyond the time scales of bead inertia. However, this prediction is rather different from both the original result of GSER and what is typically observed for viscoelastic materials. We next show that medium inertia tends to attenuate the oscillations because it dissipates bead energy by radiation of transverse sound waves through the Basset force. Thus, bead inertia competes with medium inertia for the MSD's oscillation. We find that it is sufficient to damp bead oscillations via Basset forces when the bead density is $>4/7$ of the fluid density, independent of most other details in the system. We also show that the non-conservative forces that exist in an optical trap [Roichman et al., PRL, \textbf{101}, 128301 (2008)] also result in circulation in a viscoelastic medium. However, the rates are not sufficiently rapid to excite elastic modes.   

High bandwidth linear viscoelastic properties of complex fluids from the measurement of their free surface fluctuations

We present a new optical method to measure the linear viscoelastic properties of materials, ranging from complex fluids to soft solids, within a large frequency range (about 0.1--10$^{4}$ Hz). The surface fluctuation specular reflection technique is based on the measurement of the thermal fluctuations of the free surfaces of materials at which a laser beam is specularly reflected. The propagation of the thermal surface waves depends on the surface tension, density, and complex viscoelastic modulus of the material. For known surface tension and density, we show that the frequency dependent elastic and loss moduli can be deduced from the fluctuation spectrum. Using a viscoelastic solid (a cross-linked PDMS), which linear viscoelastic properties are known in a large frequency range from rheometric measurements and the time--temperature superposition principle, we show that there is a good agreement between the rheological characterization provided by rheometric and fluctuation measurements. We also present measurements conducted with complex fluids that are supramolecular polymer solutions. The agreement with other low frequency and high frequency rheological measurements is again very good, and we discuss the sensitivity of the technique to surface viscoelasticity.   

Holographic microrefractometer

In-line holographic microscopy of micrometer-scale colloidal spheres yields heterodyne scattering patterns that may be interpreted with Lorenz-Mie theory to obtain precise time-resolved information on the refractive index of the suspending medium. We demonstrate this method's efficacy with measurements on calibrated refractive index standards, and apply it to measurements of varying Sucrose concentration in a microfluidic channel. Using commercial colloidal spheres as probe particles and a standard video camera for detection yields volumetric refractive index measurements with a resolution approaching $10^{-3}$~RIU for each probe particle in each holographic snapshot. The combination of spatial resolution, temporal resolution, multi-point \emph{in situ} access and technical simplicity favor this approach for cost-effective lab-on-a-chip applications.   

Studying colloidal particles on an emulsion droplet with digital holographic microscopy

Interactions between colloidal particles at a curved liquid-liquid interface remain poorly understood. We study how the interactions between micron-sized polymethyl methacrylate (PMMA) particles bound to the surface of $\sim$5 $\mu$m decane droplets dispersed in an aqueous continuous phase influence the particle dynamics. We track the 3D position of up to 6 particles moving on a droplet by imaging particle-laden droplets with digital holographic microscopy and fitting the recorded holograms with Lorenz-Mie scattering calculations. We demonstrate particle tracking with $\sim$10 nm precision in all directions at up to millisecond frame rates, which allows the study of rapid particle motions. In addition, we use negative dielectrophoresis to keep the droplets far away from the walls of our sample holders during imaging. Our measurements probe the interparticle interactions and allow us to determine particle contact angles \textit{in situ}.   

Brownian motion goes ballistic

It is the randomness that is considered the hallmark of Brownian motion, but already in Einstein's seminal 1905 paper on Brownian motion it is implied that this randomness must break down at short time scales when the inertia of the particle kicks in. As a result, the particle's trajectories should lose its randomness and become smooth. The characteristic time scale for this transition is given by the ratio of the particle's mass to its viscous drag coefficient. For a 1 $\mu $m glass particle in water and at room temperature, this timescale is on the order of 100 ns. Early calculations, however, neglected the inertia of the liquid surrounding the particle which induces a transition from random diffusive to non-diffusive Brownian motion already at much larger timescales. In this first non-diffusive regime, particles of the same size but with different densities still move at almost the same rate as a result of hydrodynamic correlations. To observe Brownian motion that is dominated by the inertia of the particle, i.e. ballistic motion, one has to observe the particle at significantly shorter time scales on the order of nanoseconds. Due to the lack of sufficiently fast and precise detectors, such experiments were so far not possible on individual particles. I will describe how we were able to observe the transition from hydrodynamically dominated Brownian motion to ballistic Brownian motion in a liquid. I will compare our data with current theories for Brownian motion on fast timescales that take into account the inertia of both the liquid and the particle. The newly gained ability to measure the fast Brownian motion of an individual particle paves the way for detailed studies of confined Brownian motion and Brownian motion in heterogeneous media. \\[4pt] [1] Einstein, A. \"{U}ber die von der molekularkinetischen Theorie der W\"{a}rme geforderte Bewegung von in ruhenden Fl\"{u}ssigkeiten suspendierten Teilchen. Ann. Phys. 322, 549--560 (1905). \\[0pt] [2] Lukic, B., S. Jeney, C. Tischer, A. J. Kulik, L. Forro, and E.-L. Florin, 2005, Direct observation of nondiffusive motion of a Brownian particle, Physical Review Letters 95, 160601 (2005). \\[0pt] [3] Huang, R., Lukic, B., Jeney, S., and E.-L. Florin, Direct observation of ballistic Brownian motion on a single particle, arXiv:1003.1980v1 (2010). \\[0pt] [4] Huang, R., I. Chavez, K.M. Taute, B. Lukic, S. Jeney, M.G. Raizen, and E.-L. Florin, 2011, Direct observation of the full transition from ballistic to diffusive Brownian motion in a liquid, Nature Physics 7, 576--580 (2011).   

Imaging dynamics and transitions in colloidal clusters

We use digital holographic microscopy to measure the relative motions of particles in colloidal clusters containing micron-sized spherical particles interacting through short-range attractions. These clusters explore many configurations as they approach their equilibrium states. Furthermore, clusters formed with weak interactions continue to transition between equal-energy configurations. We solve the challenge of tracking closely-packed, thermally-driven colloidal spheres in three dimensions by fitting the holograms using an exact solution for the scattering from multiple spheres. The method allows us to track each sphere with 10 nm precision in all three dimensions with millisecond time resolution.   

Holography of Cells fitted to DDA scattering solutions

Understanding the dynamics of cells is important to many areas of biophysics. Digital Holography offers a way to observe these dynamics at high speed, in 3D, in relatively native conditions. I will present work studying single cell dynamics through in-line digital holography. To quantify the motion of subcellular components, we fit our holograms to models of scattering based on the Discrete Dipole Approximation. In particular, we apply the technique to determine the the fluctuations of the cell membrane. The technique allows us to interrogate the cells over a broad range of time scales, from 10$^{-3}$ s up to the time scale for cell division.   

Holographic deconvolution microscopy for high resolution particle tracking

Rayleigh-Sommerfeld back-propagation can be used to generate a volumetric reconstruction of the light field responsible for the recorded intensity in an in-line hologram. Deconvolving the three dimensional light intensity with an optimal kernel derived from the Rayleigh-Sommerfeld propagator itself emphasizes the objects responsible for the scattering pattern while suppressing undesired artifacts. Bright features in the deconvolved volume may be identified with such objects as colloidal spheres and nanorods. Tracking their thermally-driven Brownian motion through multiple holographic video images provides estimates of the tracking resolution, which approaches 1 nm in all three dimensions.   

Measuring Nanoparticle Dynamics with Real-Time, 3D Tracking

Nanoparticles in liquids are an important platform for nanofabrication and nanomanufacturing processes. Few \textit{in situ }methods are available for measuring the time-resolved dynamics of individual nanoparticles at nanoscale spatial resolution. Drawing on recent advances in real-time single-particle feedback control, we have developed an apparatus that enables us to measure the 3D motion and dynamics of individual fluorescent nanoparticles in liquid environments. Real-time feedback control methods enable us to monitor the dynamics of individual nanoparticles by locking them in focus in an optical microscope, which enhances both the temporal and spatial resolution of our instrument. We applied the technique to study diffusion dynamics of polystyrene nanoparticles adsorbed at liquid-liquid interfaces. This tool can also be applied to study nanoparticle binding, self-assembly processes, and single-molecule biophysics.   

Nano-domains of high viscosity and stiffness mapped in the cell membrane by thermal noise imaging

The cell membrane is thought to contain spatial domains, created by cholesterol-lipid clusters and by interactions with the membrane cytoskeleton. The influence of these domains on membrane protein mobility and cell signaling has clearly been demonstrate. Yet, due to their small size and transient nature, the cholesterol stabilized domains cannot be visualized directly. We show here that thermal noise imaging (TNI) which tracks the diffusion of a colloid labeled membrane protein with microsecond and nanometer precision, can visualize cholesterol stabilized domains, also know as lipid raft, in intact cells. Using TNI to confine a single membrane protein to diffuse for seconds in an area of 300nm x 300nm provides sufficient data for high resolutions maps of the local diffusion, local attraction potentials and membrane stiffness. Using a GPI-anchored GFP molecule to probe the membrane of PtK2 cells we detect domains of increased membrane stiffness, which also show increase viscosity and are the preferred location for the GPI-anchored protein. These domains are further stabilized by addition of ganglioside cross linking toxins and disappear after removal of the cholesterol.   

Fluorescence correlation spectroscopy enumerate the number of nanoparticles in optical confinement

In the presence of an optical trap, both the concentration and diffusion dynamics of the nanoparticles near the center of the laser focus are affected. This phenomenon could affect the interpretation of the result from fluorescence correlation spectroscopy (FCS) where highly focused laser is often used. A recent Monte Carlo simulation study shows, for non-interacting particles under trapping energy up to 2 KT, the zero-time autocorrelation function G(0) can be used to enumerate the mean number of particles N in the trap. It is not clear, however, how particle interactions or higher trapping will affect this prediction. To address these issues, we conducted FCS experiments to examine G(0) as a function of trapping energy and particle interaction strength. We discovered that G(0) = 1/N is true up to 6 kT as long as the particle interactions are negligible. As the particle interaction is increased, the validity of the above relation quickly breaks down. We interpret our experimental finding based on the consideration of Poisson statistics.   

Session T49: Focus Session: Organic Electronics and Photonics: Structure - Property Correlations

Correlating the efficiency and nanomorphology of polymer blend solar cells utilizing resonant soft x-ray scattering

Enhanced scattering contrast afforded by resonant soft x-ray scattering (R-SoXS) is used to probe the nanomorphology of all-polymer solar cells based on blends of the donor poly(3-hexylthiophene) (P3HT) with the acceptor either poly((9,9-dioctylfluorene)-2,7-diyl-alt-[4,7-bis(3-hexylthien-5-yl)-2,1,3- benzothiadiazole]- 2',2"-diyl) (F8TBT) or poly([N,N'- bis(2-octyldodecyl)-11 naphthalene-1,4,5,8- bis(dicarboximide)- 2,6-diyl]- alt-5,5'- (2,2'-12 bithiophene)) (P(NDI2OD-T2)). A bimodal distribution of domain sizes is observed for P3HT:P(NDI2OD-T2) blends with small domains of $\sim $ 5 - 10 nm that evolve with annealing and larger domains of $\sim $ 100 nm insensitive to annealing. P3HT:F8TBT blends in contrast show a broader distribution but with the majority structured on 10 nm length scale. For both blends an evolution in device performance is observed, correlated with a coarsening and purification of domains on the 5 - 10 nm length scale. Grazing-Incidence Wide Angle X-ray Scattering (GI-WAXS) reveals 25 - 40 nm thick P(NDI2OD-T2) crystallites embedded in the larger domains observed by R-SoXS. A higher degree of P3HT crystallinity is observed in blends with P(NDI2OD-T2) compared to F8TBT. The propensity of the polymers to crystallize in P3HT:P(NDI2OD-T2) blends is also observed to hinder the morphological development on the sub-10 nm length scale. More broadly, this work also highlights the complementarity of R-SoXS and GI-WAXS.   

Hierarchical Nanomorphologies Promote Exciton Dissociation in Polymer: Fullerene Bulk Heterojunction Solar Cells

In the last fifteen years, research efforts have led to organic photovoltaic (OPV) devices with power conversion efficiencies (PCEs) up to $\sim $8{\%}, but these values are still insufficient for the devices to become widely marketable. To further improve solar cell performance a thorough understanding of the complex structure-property relationships in the OPV devices is required. In this work, we demonstrated that the OPV active layer of PTB7:fullerene bulk heterojunction (BHJ) solar cells, which set a historic record of PCE (7.4{\%}), involves hierarchical nanomorphologies ranging from several nanometers of crystallites to tens of nanometers of nanocrystallite aggregates in PTB7-rich and fullerene-rich domains, themselves hundreds of nanometers in size. These hierarchical nanomorphologies with optimum crystallinity and intermixing of PTB7 with fullerenes are coupled to significantly enhanced exciton dissociation, which consequently contribute to photocurrent, leading to the superior performance of PTB7:fullerene BHJ solar cells. New insights of performance-related structures afforded by the current study should aid in the rational design of even higher performance polymeric solar cells.   

Unexpected Morphological Traits of Bulk Heterojunction Organic Solar Cells with Exceptional Power Conversion Efficiencies

The synthesis of new polymers for polymer/fullerene bulk heterojunction solar cells has boosted the power conversion efficiency (PCE) of these devices to levels now exceeding 5{\%}. Even with these advancements in efficiency, relatively little is known of the morphological characteristics of the active layer including domain size and purity, material crystallization and orientation, and miscibility of the bulk heterojunction components. Herein, we employ a suite of soft and hard x-ray scattering and microscopy techniques to probe defining traits of the morphology for the high-performing polymers, poly[4,8-(3-butylnonyl)benzo[1,2-b:4,5-b']dithiophene-\textit{alt}-2-(2-butyloctyl)-5,6-difluoro-2H-benzo[d][1,2,3]triazole] (BnDT-FTAZ) and thieno[3,4-b]thiophene-\textit{alt}-benzodithiophene (PTB7) blended with phenyl-C61-butyric acid methyl ester (PC$_{61}$BM) and PC$_{71}$BM, respectively. PCEs of 7.4{\%} for BnDT-FTAZ and 5.3{\%} for PTB7 based solar cells are achieved when processing methods result in smaller, more mixed polymer/fullerene phases where non-zero miscibility is measured for each system. Furthermore, the polymers do not strongly crystallize in the active layer and average domain sizes larger than 50 nm are noted for both systems.   

Correlating Free-Carrier production in P3HT with Solid-State Microstructure using Time-Resolved Microwave Conductivity

The nature of the primary photoexcitation in conjugated polymers has been a subject of interest for a number of years, and two models have emerged: neutral excitons and free charge carriers. While excitons are recognized as the dominant of the two species, there are a small fraction of carriers that appear directly upon photoexcitation that have been detected experimentally either spectroscopically or through conductivity measurements. The fraction of near-instantaneous free charge carriers produced depends both on the chemical structure of the polymer and on the time-scale on which the study is performed. For example, poly(3-hexylthiophene) (P3HT) thin films have been reported to have free carrier yields as high as 15\%, when measured on a fast time scale, but as low as 3\% when measured on a slow time scale. It is unclear why these numbers are so different, and from where these carriers originate. This presentation will report studies using flash photolysis, time-resolved microwave conductivity (fp-TRMC) to probe carriers produced in a number of thin films of P3HT of differing molecular weights. By correlating the free carrier yield with the solid-state microstructure of the polymer, and the corresponding electronic absorption spectra, we will propose a model that explains the origins of these carriers.   

Controlling Active Layer Morphology in Polymer/Fullerene Solar Cells

The active layer in most polymer solar cells is based on the bulk heterojunction (BHJ) design. BHJs are prepared by arresting the phase separation of a polymer/fullerene blend to produce a nanoscale, interpenetrating network. Such non-equilibrium structures are very difficult to control and reproduce, posing a significant challenge for fundamental structure-property investigations. We demonstrate a new approach to control the active layer morphology with a simple two-step process: First, a thin film of poly(3-hexylthiophene) (P3HT) is cross-linked into stable nanostructures or microstructures with electron-beam lithography [1]. Second, a soluble fullerene is spun-cast on top of the patterned polymer to complete the heterojunction. Significantly, irradiated P3HT films retain good optoelectronic properties and bilayer P3HT/fullerene heterojunctions yield power-conversion efficiencies near 0.5{\%}. We have performed preliminary studies with model nanostructured devices and we find that efficiency increases with interfacial area [2]. These model devices are very valuable for fundamental studies because the interfacial area is accurately measured with small-angle X-ray scattering, and the active layer can be ``deconstructed'' for imaging with atomic force microscopy. \\[4pt] [1] S. Holdcroft, Adv. Mater. 2001, 13, 1753-1765.\\[0pt] [2] He et al., Adv Funct. Mater. 2011, 21, 139-146.   

The Miscibility of PCBM in Low Band-Gap Conjugated Polymers in Organic Photovoltaics

Understanding the morphology of the photoactive layer in organic photovoltaics (OPVs) is essential to optimizing conjugated polymer-based solar cells to meet the targeted efficiency of 10{\%}. The miscibility and interdiffusion of components are among the key elements that impact the development of morphology and structure in OPV active layers. This study uses neutron reflectivity to correlate the structure of low band gap polymers to their miscibility with PCBM. Several low band gap polymers that exhibit power conversion efficiencies exceeding 7{\%}, including PBnDT-DTffBT were examined. The intermixing of low band-gap polymer and PCBM bilayers was monitored by neutron reflectivity before and after thermal annealing, providing quantification of the miscibility and interdiffusion of PCBM within the low band gap polymer layer. These results indicate that the miscibility of PCBM ranges from 3{\%} to 26{\%} with the low band-gap polymers studied. The correlation between low band gap polymer structure and miscibility of PCBM will also be discussed.   

Self-assembly Columnar Structure in Active Layer of Bulk Heterojunction Solar Cell

Bulk Heterojunction (BHJ) polymer solar cells are an area of intense interest due to their flexibility and relatively low cost. However, due to the disordered inner structure in active layer, the power conversion efficiency of BHJ solar cell is relatively low. Our research provides the method to produce ordered self-assembly columnar structure within active layer of bulk heterojunction (BHJ) solar cell by introducing polystyrene (PS) into the active layer. The blend thin film of polystyrene, poly (3-hexylthiophene-2,5-diyl) (P3HT) and [6,6]-phenyl C$_{61}$ butyric acid methyl ester (PCBM) at different ratio are spin coated on substrate and annealed in vacuum oven for certain time. Atomic force microscopy (AFM) images show uniform phase segregation on the surface of polymer blend thin film and highly ordered columnar structure is then proven by etching the film with ion sputtering. TEM cross-section technology is also used to investigate the column structure. Neutron reflectometry was taken to establish the confinement of PCBM at the interface of PS and P3HT. The different morphological structures formed via phase segregation will be correlated with the performance of the PEV cells to be fabricated at the BNL-CFN.   

Dissipative Particle Dynamics Studies of Rod-Coil Polymer Nanocomposites

Organic solar cell efficiency depends strongly on the morphology within the active layer consisting of donor (e.g. conjugated polymer) and acceptor (e.g. fullerene derivative) materials. Higher device efficiency can be obtained if the donor-acceptor morphology has high interfacial area, small domains, and continuous pathways. One way to control donor-acceptor morphology is via copolymerization of the conjugated ``rod'' polymer and an acceptor ``coil'' block. Past theory and experimental studies have characterized the phase behavior of pure rod-coil block copolymers. In this talk we will present dissipative particle dynamics simulation studies of composites of symmetric rod-coil block copolymers and nanoscale additives of varying selectivity (rod-, coil- and non-selective). With increasing volume fraction of non- and rod- selective nanoadditives we see a shift in the liquid crystalline and microphase transitions to lower temperatures, and new morphologies (e.g. helical twists in rod block domain and zig-zag lamellae) not seen in pure symmetric rod-coil polymers. These shifts in phase transition are explained by where the nanoadditives reside, which in turn is dictated by where the system can maximize enthalpic gain and minimize loss of nanoadditive translational entropy.   

Model Hamiltonian for predicting the bandgap of conjugated systems

We calculate the bandgaps for conjugated systems using the adapted Su-Schrieffer-Heeger Hamiltonian and find good agreement with 130 independent experimental points. The 2D version of the model correctly demonstrates the decrease in bandgap from the addition of vinylene bridges to both poly(\emph{p}-phenylene) and polythiophene indicating that planarization is not a significant effect. Expanding the model to 3D shows that interchain interactions systematically reduces the bandgap. In fused rings sharing dissimilar bonds, such as in isothianaphthene, the bond length dimerization along the carbon backbone decreases leading to a decrease in the bandgap. In contrast, when fusing two of the same rings along equivalent bonds, for example thienoacene, the bandgap change is less than 10\% at best when normalized by the number of carbon atoms in the conjugation path. From porphyrin and pyrrole-benzothiadiazole we learn that tautomerization significantly affects the bandgap, as the $\varepsilon$ value for NH had to be used for both NH and N, indicating that H is being shared by both. In modeling donor-acceptor co-polymers we accurately calculate the reduction in the bandgaps when compared to their parent homopolymers.   

The Effect of Side-Chain Length on the Solid-State Structure and Optical Properties of F8BT: A DFT Study

Using the long-range corrected hybrid density functional theory (DFT/B97D) approach, we have performed bulk solid state calculations to investigate the influence of side-chain length on the molecular packing and optical properties of poly (9,9-di-n-octylfluorene-alt-benzothiadiazole) or F8BT. Two different packing structures, the lamellar and nearly hexagonal, were obtained corresponding to longer and shorter side-chains respectively. This behavior can be attributed to the micro-phase separations between the flexible side-chains and the rigid backbones and is in agreement with previous investigations for other hairy-rod polymers. In addition, as a result of the efficient inter-chain interactions for the lamellar structure, the dihedral angle between the F8 and BT units is reduced providing a more planar configuration for the backbone which leads to the decreased band gap (by 0.2-0.3 eV) in comparison to the hexagonal phase and the gas phase with no side-chain. Time-dependent DFT (TDDFT/B3LYP) was also used to study the excited states of the monomer of F8BT optimized in solid-state structures with different side-chain lengths. It is found that the absorption spectrum is red shifted for the polymers with lamellar structure relative to the polymers in hexagonal and gas phases.   

Polymer blend photovoltaics with conjugated block copolymers as surfactants

Conjugated polymer blend photovoltaics are a class of devices where the active layer is composed of a polymer acceptor and a polymer donor. These devices suffer from macrophase separation in the active layer, where it is challenging to kinetically trap domains with characteristic sizes below micron length scales. Thus, for mixtures of poly(3-hexylthiophene) (P3HT) and poly((9,9-dioctylfluorene)-2,7-diyl-alt-[4,7-bis(thiophen-5-yl)-2,1,3-benzothiadiazole]-2',2''-diyl) (PFOTBT), we have synthesized a conjugated block copolymer to act as an A/B surfactant and stabilize a microstructure. The performance of devices where the active layer is composed of P3HT, PFOTBT, and P3HT-PFOTBT block copolymer blends is found to depend on the composition of the mixture and processing conditions. In addition, we have utilized energy-filtered transmission electron microscopy to characterize the morphology of the blends and correlated the microstructure with device performance.   

Self-assembly and characterization of two-component films of semiconducting nanoparticles

Polymer-based semiconducting materials are promising candidates for large-scale, low-cost photovoltaic devices. To date, the efficiency of these devices has been low in part because of the challenge of optimizing molecular packing while also obtaining a bicontinuous structure with a length scale of approximately 10nm. Here we demonstrate an alternative approach to solving this problem by packing nanoparticles of electron- and hole-transporting semiconductors into a two-component film. We first make nanoparticles of semiconducting materials (P3HT, PCBM, CdSe, etc) suspended in liquid. Then a binary suspension of nanoparticles is dried onto a non-volatile liquid surface to form a solid, two-component film with uniform thickness. The absorbance, photoluminescence, structure, and charge mobility of the films are measured. For a range of stoichiometries, we obtain bicontinuous structures and significant luminescence quenching, indicating charge transfer. This study shows that two-component nanoparticulate films may be an effective route toward bulk heterojunctions with controlled morphology. We acknowledge support from the US Department of Energy, Office of Basic Energy Sciences, through grant DE-SC0001087.   

Session T50: Focus Session: Phase Behavior and Structure in Copolymers

Self-assembly of semiflexible-flexible block copolymers

We apply self-consistent Brownian dynamics simulations to study the self-assembly behavior of semiflexible-flexible block copolymers. A Maier-Saupe interaction model was applied for the orientational interactions between the semiflexible polymers, while the enthalpic interactions between semiflexible and flexible polymers were modeled through a standard Flory-Huggins approach. To develop a physical understanding of the phases and their regimes of occurrence as a function of varying persistence length of the semiflexible block, we computed the $2D$ phase diagram for our model. We quantify the progression of the self-assembly morphologies in transitioning from coil-coil block copolymers on the one hand to rod-coil block copolymers on the other hand. The results obtained are in qualitative agreement with the existing experimental and numerical results.   

Effect of chain shape on the self-assembly of bioinspired block copolymers

Polymer chain shape has been shown to affect both polymer properties and block copolymer self-assembly. Polypeptoids, a class of sequence-specific bioinspired polymer, have a chain shape that can be tuned by the introduction of monomers with bulky, chiral side chains, allowing one to change the polymer conformation while preserving the chemical nature of the side chains. Here, it is shown that introducing chiral, aromatic monomers into the polypeptoid chain increases the glass transition by 20 C for a chiral, helical polypeptoid compared to its achiral, non-structured analog. Incorporation of these polypeptoids into block copolymers with poly(methyl acrylate) enables a systematic study of the effect of chain shape while maintaining similar enthalpic interactions. For two otherwise analogous block copolymers, conformational asymmetry is shown to affect both the morphological domain spacing and the order-disorder transition temperature. Future work will focus on interfacial segregation experiments to determine the effect of conformational asymmetry on the Flory-Huggins parameter.   

Processing-Dependent Self-Assembly of Protein-Polymer Diblock Copolymers

Self-assembly of globular protein-polymer diblock copolymers is a novel method for nanopatterning protein-based materials which maintains a high fraction of protein activity as well as the folded protein structure. By subjecting these copolymers to different processing conditions, long range ordering and the fraction of active protein can be controlled. Here, self-assembly of model mCherry-b-poly(N-isopropyl acrylamide) (PNIPAM) block copolymers is induced by water evaporation from dilute aqueous solutions of conjugate material, and followed by solvent annealing of the resulting nanostructures. Different pathways towards self-assembly are accessed by orthogonally manipulating the solvent quality for each block of the copolymer using temperature and pH. Small-angle scattering and transmission electron microscopy show nanostructure depends heavily on PNIPAM coil fraction and solvent annealing condition, with solution self-assembly reflected in the solid state structure under certain conditions. Protein structure is unaffected by the processing pathway, while protein activity levels in the nanodomains depend strongly on processing conditions and can retain up to 80\% of the initial activity.   

Helical Ordering in Chiral Block Copolymers

Introducing molecular chirality into the segments of block copolymers can influence the nature of the resultant morphology. Such an effect was found for poly(styrene-$b$-L-lactide) (PS-$b$-PLLA) diblock copolymers where hexagonally packed PLLA helical microdomains (H* phase) form in a PS matrix. However, molecular ordering of PLLA within the helical microdomains and the transfer of chirality from the segmental level to the mesoscale is still not well understood. We developed a field theoretic model to describe the interactions between segments of chiral blocks, which have the tendency to form a ``cholesteric'' texture. Based on the model, we calculated the bulk morphologies of chiral AB diblock copolymers using self-consistent field theory (SCFT). Experiments show that the H* phase only forms when microphase separation between PS and PLLA block happens first and crystallization of PLLA block is suppressed or happens within confined microdomain. Hence, crystalline ordering is not necessary for H* phase formation. The SCFT offers the chance to explore the range of thermodynamic stability of helical structures in the phase diagram of chiral block copolymer melts, by tuning parameters not only like the block segregation strength and composition, but also new parameters such as the ratio between preferred helical pitch to the radius of gyration and the Frank elastic constant for inter-segment distortions.   

Phase Behavior of Binary Blends of AB+AC Block Copolymers with compatible B and C blocks

Recently the experimental studies of phase behavior of binary blends of PS-b-P2VP and PS-b-PHS demonstrated an interesting effect: blends of symmetric PS-b-P2VP and shorter symmetric (PS-b-PHS) formed cylindrical HEX and spherical BCC phases, while each pure component formed lamellas. The miscibility of P2VP and PHS is caused by the hydrogen bonding between P2VP and PHS,which can be described as a negative Flory ?-parameter between P2VP and PHS. We developed a theory of the microphase segregation of AB+AC blends of diblock copolymers based on strong stretching theory. The main result of our theory is that in the copolymer brush-like layer formed by longer B chain and shorter C chains, the attraction between B and shorter C chains causes relative stretching of short C chains and compression of longer B chains. The latter manifests in an excessive bending force towards the grafting surface (BC$|$AA interface). Such bending force causes a transition from a symmetric lamella phase to a HEX cylinder or BCC spherical phases with the BC phase being a ``matrix'' component. In a blend of asymmetric BCC sphere forming copolymers (where B and C segments are the minor components), such bending force may unfold BCC spherical phase to a HEX cylinder phase, or even highly uneven lamella phases.   

Universality in block copolymers: a corresponding states hypothesis

Phase behavior and fluctuations of very long block copolymers are well described by self-consistent field theory, and by the random-phase (RPA) approximation for concentration fluctuations. The SCF / RPA predicts behavior that depends on only a few dimensionless parameters. More sophisticated coarse-grained theories instead suggest an extended form of this principle of corresponding states, in which the behavior is predicted to depend on one additional parameter, the independent degree of polymerization $\bar{N}$. We are testing this prediction by comparing extensive computer simulations of several different coarse-grained simulation models of AB diblock copolymer melts. We utilize a novel simulation methodology based on graphical processing unit (GPU) accelerated hybrid molecular dynamics / Monte Carlo replica exchange simulations on a cluster of many GPUs. We present data for off-lattice models with soft- and hard-core non-bonded interactions, and a lattice model, comparing simulations of different models that are designed to have matched values of $\bar{N}$. The results provide extremely strong evidence for the corresponding states hypothesis, which is found to remain accurate even for chains that are much too short to be accurately described by SCFT or the RPA   

Manipulating triblock copolymer morphology using tapered block interfaces

Tapered block copolymers offer the opportunity to manipulate copolymer segregation strengths independently of the molecular weight and chemical constituents. This independent control allows the design of materials with designer interactions and improved mechanical properties, while retaining the desired self-assembled nanostructures. The tapered interfaces between blocks have been shown to significantly decrease the effective interaction parameters between blocks, leading to lower order-to-disorder transition temperatures relative to corresponding non-tapered block copolymers. In this work, we synthesized a series of tapered triblock copolymers using a combination of anionic polymerization, atom transfer radical polymerization, and click chemistry. Comparing the morphologies of our tapered and non-tapered triblock copolymers suggests that the phase behavior of the tapered materials can differ from the non-tapered triblock materials due to the manipulated interfacial profile.   

Manipulating the morphological behavior of ABA triblock copolymers with block polydispersity

As an extension of our ongoing efforts to understand the effects of middle B segment polydispersity on the melt-phase behavior of ABA triblock copolymers, we describe the morphological consequences of block polydispersity in the context of poly(lactide-b-1,4-butadiene-b-lactide) (LBL) triblock copolymers. The complete melt-phase behavior of 52 well-defined LBL triblock copolymers was evaluated using a combination of synchrotron small-angle X-ray scattering (SAXS) and transmission electron microscopy (TEM). Through careful comparisons with monodisperse copolymer control samples, we show that block polydispersity causes large shifts in the composition-dependent phase windows in a manner consistent with previous reports. However, these polydisperse LBL triblocks do not exhibit the substantial domain dilation observed in more weakly segregated SBS triblock copolymers. Based on these observations, we discuss the possibility of using block polydispersity as a new means of tailoring the morphological behavior of microphase separated ABA triblock copolymers.   

Phase Behavior of Linear ABC Tri Block-Random Copolymers with a Semicrystalline Endblock

The solid-state structure of semicrystalline block copolymers is set either by block incompatibility or by crystallization of one or more blocks. A variety of solid-state morphologies may be observed depending on the block interaction strength, ranging from spherulitic to confined crystallization within preexisting microphase-separated domains. We aim to explore crystallization from both homogeneous and microphase-separated melts and to characterize the resulting solid-state structure of linear ABC ``block-random'' copolymers that incorporate a semicrystalline polyethylene endblock. Linear triblock copolymers, poly[butadiene-$b$-isoprene-$b$-(isoprene-$r$-styrene)], are synthesized via anionic polymerization. Two hydrogenation schemes are then applied, either complete saturation of all double bonds or a selective saturation of only diene units. Both schemes yield semicrystalline polyethylene endblocks but dissimilar interblock segregation strengths. In both derivatives of a 30-14-14 kg/mol triblock-random copolymer, small-angle x-ray scattering reveals the formation of a well-ordered three-domain lamellar melt from which crystallization of the polyethylene endblock proceeds. Crystal orientation within the lamellae has been determined by wide-angle x-ray scattering after lamellar orientation in a channel die. We are currently varying relative block and overall molecular weights, and the block sequence to further explore these materials.   

Discovering Complex Ordered Phases of Block Copolymers

Block copolymers with their rich phase behavior and ordering transitions have become a paradigm for the study of structured soft materials. Understanding the structures and phase transitions in block copolymers has been one of the most active research areas in polymer science in the past two decades. One of the achievements is the self-consistent field theory (SCFT), which provides a powerful framework for the study of ordered phase of block copolymers. I will present a generic strategy to discover complex ordered phases of block copolymers within the SCFT framework. Specifically, a combination of real-space and reciprocal-space techniques is used to explore possible ordered phases in multiblock copolymer melts. These candidate phases can then be used to construct phase diagrams. Application of this strategy to linear and star ABC triblock copolymers has led to the discovery of a rich array of ordered phases.   

Thermodynamic Behavior of Poly(1,4-isoprene-b-DL-lactide) Diblock Copolymers

The phase behavior of a series of poly(1,4-isoprene-$b$-DL-lactide) (IL) diblock copolymers near the order-disorder transition temperature ($T_{ODT}$) was investigated using a combination of dynamic mechanical spectroscopy (DMS), small angle x-ray scattering (SAXS) and differential scanning calorimetry (DSC). IL copolymers of relatively low molecular weight ($\sim$ 2.5 -- 6 kg/mol) formed ordered phases with experimentally accessible $T_{ODT}$s due to the large segment-segment interaction parameter (\textit{$\chi _{IL}$}). The order-disorder transitions were accompanied by distinct signatures in the DSC traces, where the magnitude of the latent heat of the ODT ($\Delta H_{ODT}$) depends strongly on the ordered phase morphology. Symmetric compounds exhibited almost no hysteresis in the onset temperature for ordering and disordering, indicative of an absence of a nucleation barrier, while asymmetric IL diblocks displayed considerable hysteresis. These finding will be discussed in the context of composition fluctuation effects in the disordered melt near $T_{ODT}$.   

Direct Comparisons among Fast Off-Lattice Monte Carlo Simulations, Integral Equation Theories, and Gaussian Fluctuation Theory for Disordered Symmetric Diblock Copolymers

Based on the same model system of symmetric diblock copolymers as discrete Gaussian chains with soft, finite-range repulsions as commonly used in dissipative-particle dynamics simulations, we directly compare, without any parameter-fitting, the thermodynamic and structural properties of the disordered phase obtained from fast off-lattice Monte Carlo (FOMC) simulations$^1$, reference interaction site model (RISM) and polymer reference interaction site model (PRISM) theories, and Gaussian fluctuation theory. The disordered phase ranges from homopolymer melts (i.e., where the Flory-Huggins parameter $\chi=0$) all the way to the order-disorder transition point determined in FOMC simulations, and the compared quantities include the internal energy, entropy, Helmholtz free energy, excess pressure, constant-volume heat capacity, chain/block dimensions, and various structure factors and correlation functions in the system. Our comparisons unambiguously and quantitatively reveal the consequences of various theoretical approximations and the validity of these theories in describing the fluctuations/correlations in disordered diblock copolymers. [1] \textit{Q. Wang and Y. Yin}, \textbf{J. Chem. Phys., 130}, 104903 (2009).   

The power spectrum of thermal composition fluctuations in a lamellar mesophase

We derive an analytic expression for the power spectrum of Gaussian thermal composition fluctuations in an ordered lamellar mesophase. We compare this expression to the power spectrum measured in stochastic simulations of a two-dimensional diblock copolymer melt based on the Leibler-Brazovskii Hamiltonian. The analytic expression fits the simulation data with zero adjustable fitting parameters over a relatively wide range of model parameters. This expression will facilitate line-edge roughness (LER) modeling in block copolymer directed self-assembly applications, and it can serve as a model component in a scattering-based LER metrology framework.   

Session T52: Non-equilibrium Systems, Especially using Fluctuation Theorems and Fluctuation-Dissipation Relations

Transient and steady state behavior of full counting statistics in thermal transport

We study the statistics of heat transferred in a given time interval $t_M$, through a finite harmonic system, which is connected with two heat baths, maintained at two different temperatures. We calculate the cumulant generating function (CGF) for heat transfer using non-equilibrium Green's function method. The CGF can be concisely expressed in terms of Green's functions of the system and the self-energy of the lead with shifted arguments, $\Sigma^A(\tau, \tau') = \Sigma_L\bigl(\tau +\hbar x(\tau), \tau' + \hbar x(\tau')\bigr) - \Sigma_L(\tau, \tau')$, where $\Sigma_L(\tau,\tau')$ is the contour-ordered self-energy of the left lead. The expression of CGF is valid in both transient and steady state regimes. We present a transient result of the first four cumulants of a graphene junction. It is found that measurement causes the energy to flow into the leads. In the steady state we show that the CGF obey {\it``steady state fluctuation theorem''}. We also study the CGF for the joint probability distribution of left and right lead heat flux $P(Q_L,Q_R)$, which is important to calculate the correlations between $Q_L$ and $Q_R$, and also the total entropy that flows into the leads. We also discuss the CGF for the total entropy production for two lead system without the center part.   

Langevin dynamics beyond the weak coupling limit

Many popular results of non-equilibrium statistical mechanics hold only in leading order in a small parameter $\lambda$ which controls the strength of the system-environment coupling. In this approximation the equations for the first two moments $\langle v\rangle$ and $\langle v^2\rangle$ of the Brownian particle's velocity are closed and describe exponential relaxation to thermal equilibrium. To higher orders in $\lambda$ these equations are not closed but coupled to higher moments $\langle v^n\rangle$. This may result in much richer dynamics (both transient and stationary) and non-trivial ergodic properties. Generalized fluctuation-dissipation relations are derived microscopically and shown to ensure convergence to thermal equilibrium to any order in $\lambda$. One exception is the regime of superlinear diffusion, characterized by zero integral friction (vanishing integral of the memory kernel), when the generalized Langevin equation may have non-ergodic solutions that do not relax to equilibrium values. Also, for specific memory kernels the equation may have non-dissipative (non-stationary) solutions even if the integral friction is finite and diffusion is normal.   

Jarzynski equality for spin glasses and its application

We study an application of Jarzynski equality to spin glasses with gauge symmetry. It is shown that the exponentiated free-energy difference appearing in the Jarzynski equality reduces to a simple analytic function written explicitly in terms of the initial and final temperatures if the temperature satisfies a certain condition related to gauge symmetry. This result can be used to derive a lower bound on the performed work during the nonequilibrium process by changing the external magnetic field as well as a pseudo work done during changing temperature. The latter case serves as useful information to implement the population annealing developed in numerical use of the Jarzynski equality to equilibrate the many-body system. We also prove several exact identities that relate equilibrium and nonequilibrium quantities. These identities show possibility of the population annealing to evaluate equilibrium quantities from nonequilibrium computations, which may be useful for avoiding the problem of slow relaxation in spin glasses.   

Thermodynamic reversibility in feedback processes

The information acquired during a thermodynamic process with feedback can be converted into useful work. However, the second law of feedback restricts the amount of useful work that can be obtained from this information. In this presentation, I will discuss optimal thermodynamic processes with feedback, where all the information is converted into work. Utilizing the detailed fluctuation theorem for feedback, I will demonstrate that such processes are feedback-reversible: they are indistinguishable from their time-reversal, thereby extending the notion of thermodynamic reversibility to feedback processes.   

Entropy production in non-equilibrium steady states

We discuss entropy production in non-equilibrium steady states by focusing on paths obtained by sampling at regular (small) intervals, instead of sampling on each change of the system's state. This allows us to directly study entropy production in systems with microscopic irreversibility. The two sampling methods are equivalent otherwise, and the fluctuation theorem also holds for the different paths. We focus on a fully irreversible three-state loop, as a canonical model of microscopic irreversibility, finding its entropy distribution, rate of entropy production, and large deviation function in closed analytical form, and showing that the observed kink in the large deviation function arises solely from microscopic irreversibility [1].\\[4pt] [1] D. ben-Avraham, S. Dorosz, and M. Pleimling, Phys. Rev. E 84, 011115 (2011)   

Information, entropy, and heat far from equilibrium

For equilibrium states, the Shannon entropy, $H =- \int d\Gamma \,p(\Gamma) \ln p(\Gamma) $, coincides with the thermodynamic entropy. It has lately been recognized that for systems in nonequilibrium steady states a thermodynamic description based on $H$ becomes feasible, as well. In the present work we derive various generalizations of the second law for nonequilibrium processes with additional information supplied from an external or an internal memory. We will show that the irreversible entropy production is bounded from below by the information transferred from the memory to the system.   

Effective temperature determines density distribution in a slowly varying external potential beyond linear response

We consider a sheared colloidal suspension under the influence of an external potential that varies slowly in space in the plane perpendicular to the flow and acts on one selected (tagged) particle of the suspension. Using a Chapman-Enskog type expansion we derive a steady state equation for the tagged particle density distribution. We show that for potentials varying along one direction only, the tagged particle distribution is the same as the equilibrium distribution with the temperature equal to the effective temperature obtained from the violation of the Einstein relation between the self-diffusion and tagged particle mobility coefficients. We thus prove the usefulness of this effective temperature for the description of the tagged particle behavior beyond the realm of linear response. We illustrate our theoretical predictions with Brownian dynamics computer simulations.   

Dynamic phase transitions in large work production of linear diffusion systems

We present the theoretical study on non-equilibrium (NEQ) fluctuations for diffusion dynamics in high dimensions driven by a linear drift force. We find the time-dependent probability distribution function exactly as well as the NEQ work production distribution P(W) in terms of solutions of nonlinear differential equations. In two dimensions, we find analytically a sequence of dynamic phase transitions in the exponential tail shape of P(W). Their implications and orgins are discussed.   

Driven Langevin dynamics: heat, work and pseudo-work

Common algorithms for simulating Langevin dynamics are neither microscopically reversible, nor do they preserve the equilibrium distribution. Instead, even with a time-independent Hamiltonian, finite time step Langevin integrators model a driven, nonequilibrium dynamics that breaks time-reversal symmetry. Herein, we demonstrate that these problems can be resolved with a Langevin integrator that splits the dynamics into separate deterministic and stochastic substeps. This allows the total energy change of a driven system to be divided into heat, work, and pseudo-work -- the work induced by the finite time step. The extent of time-symmetry breaking due to the finite time step can be measured and true equilibrium properties recovered. This interpretation of discrete time step Langevin dynamics as a driven process provides new insights into the practical use of stochastic integrators for molecular simulation.   

Statistical interpretation of heat and work and the adiabatic theorem in irreversible processes

By generalizing the traditional concept [1] of heat and work to include their irreversible components allows us to express them in statistical terms so that dW is the \textit{isentropic} energy change; this generalizes the equilibrium adiabatic theorem. Then dQ is then nothing but the energy change solely due to the change in the microstate probability. Accordingly dQ=TdS [2] so that \textit{all powerful aspects of the equilibrium formulation are preserved}, a quite remarkable but unexpected result. The traditional formulation of the first law of thermodynamics, which uses the fields (temperature, pressure, etc.) of the medium can be \textit{equivalently} written as dE=dQ-dW using the fields of the system. This makes the two descriptions using the fields of the medium or the system equivalent and settles the long existing dispute in the literature regarding the proper choice of the fields. Moreover, the use of system fields (including affinities) allows us to analyze non-equilibrium processes such as free expansion between non-equilibrium states, which cannot be analyzed in the traditional approach. \\[4pt] [1] P.D. Gujrati, arXiv:1105.5549.\\[0pt] [2] P.D. Gujrati, Phys. Rev. E \textbf{81}, 051130 (2010).   

Application of the generalized fluctuation-dissipation theorem on a sheared suspension

We explore the validity of the generalized fluctuation-dissipation theorem for steady-state systems (proposed by Prost, Joanny and Parrondo, PRL 103, 090601 2009) in an experimental system: a suspension of non-colloidal spheres under slow periodic strain. The system is out-of-equilibrium and typically undergoes a phase transition from an active fluctuating to an absorbing state as the strain amplitude is decreased. It is a good candidate for applying the proposed theory since it has Markovian dynamics and fluctuating steady states. The control parameters are the applied strain amplitude and its volume fraction and fluctuations of proper observables such as the individual particle locations can be readily measured. Perturbations of the control parameter of strain can lead in new steady states after a transient response, which in turn can be correlated with the fluctuating observable, thus providing a way of verifying the validity of the proposed version of the generalized fluctuation-dissipation theorem.   

Entropy rate of non-equilibrium growing networks

In order to quantify the complexity of networks, new entropy measures have recently been introduced. Most of these entropy measures pertain to static networks or to dynamical processes defined on static complex networks. In this talk, we will discuss the entropy rate of growing network models, which quantifies how many labeled networks are typically generated by those growing network models. We will present an analytical evaluation of the difference between the entropy rate of growing tree network models and the entropy of tree networks that have the same asymptotic degree distribution. We will outline our finding that growing networks with linear preferential attachment generated by dynamical models are exponentially less in number than the static networks with the same degree distribution for a large variety of relevant growing network models. We will also discuss the entropy rate for growing network models that show structural phase transitions, including models with non-linear preferential attachment. We will conclude by presenting numerical simulations showing that the entropy rates above and below the structural phase transitions follow a different scaling with the network size.   

Persistency and Uncertainty Across the Academic Career

Recent shifts in the business structure of universities and a bottleneck in the supply of tenure track positions are two issues that threaten to change the longstanding patronage system in academia and affect the overall potential of science. We analyze the longitudinal publication rate $n_{i}(t)$ on the 1-year scale for 300 physicists $i=1...300$. For most careers analyzed, we observe cumulative production acceleration $N_{i}(t) \approx A_{i} t^{\alpha_{i}}$ with $\alpha_{i} >1$, reflecting the benefits of learning and collaboration spillovers which constitute a cumulative advantage. We find that the variance in production scales with collaboration radius size $S_{i}$ as $\sigma^{2}_{i} \sim S_{i}^{\psi}$ with $0.4 < \psi < 0.8$. We develop a preferential growth model to gain insight into the relation between career persistency and career uncertainty. This model shows that emphasis on nonstop production, a consequence of short-term contract systems, results in a significant number of ``sudden death'' careers that terminate due to unavoidable negative production shocks. Hence, short-term contracts may increase the strength of ``rich-get-richer'' mechanisms in competitive professions and hinder the upward mobility of young scientists.   

A Random Walk Picture of Basketball

We analyze NBA basketball play-by-play data and found that scoring is well described by a weakly-biased, anti-persistent, continuous-time random walk. The time between successive scoring events follows an exponential distribution, with little memory between events. We account for a wide variety of statistical properties of scoring, such as the distribution of the score difference between opponents and the fraction of game time that one team is in the lead.   

Session T53: Focus Session: Wave Propagation in Strongly Scattering Media

Fluctuations in Intensity in disordered media as a New Sub-wavelength Microscopy Tool

The intensity-intensity correlations of waves that propagate coherently through a disordered system are discussed, in the mesoscopic scale. Since many of the properties of those correlations are independent of the transport regime (ballistic, diffusive or localized) they can be discussed using the macroscopic approach of random matrix theory [1]. In that framework we have considered the problem of multiple sources emitting simultaneously in a disoredered medium, and we will show that the correlations and even the intensity fluctuations at a fixed point outside the turbid system can provide useful information about both the relative position of the sources and their coherence. Moreover, the information obtained is relevant at subwavelength lengths, opening the possibility of new applications to fluorescence studies, communications and image processing in turbid environments, complementary to traditional techniques. \\[4pt] [1] G. Cwilich, L. Froufe, J.J. Saenz, Phys Rev E74, 045603 (R) (2006)   

Photon localization in a nematic liquid crystal

The nematic liquid crystal MBBA, due to director fluctuations, is a highly scattering material with low absorption. We previously\footnote{ J. P. McClymer and H.M. Shehadeh, Photon Localization in a Nematic Liquid Crystal, Phys. Rev. A~79, 031802(R)~(2009)} reported that the transmission coefficient for laser light at 633 nm decays exponentially with a decay length of approximately 0.8 mm while the absorption length is over 30 times larger which we interpret as evidence for photon localization. The data does not fit a model of diffusion or diffusion with absorption. We have extended this work by measuring the decay coefficient for incoherent light from 475 to 825 nm. We find that the absorption remains low over this range, with absorption lengths ranging from 8 mm at the blue end of the spectrum to 12 mm in the near IR. The transmission coefficient in the nematic phase shows an exponential decrease with decay constants an order of magnitude smaller than the absorption length, 0.4 mm, in the blue end while increasing to 3 mm in the near IR. The data indicates that photon localization is observed throughout the visible region into the near IR.   

Light Transport in Disordered Media with PT-symmetry

The localization properties of randomly layered optical media with ${\cal PT}$-symmetric refraction index are studied both theoretically and numerically using the transfer-matrix method. The transmission coefficient decays exponentially as a function of the system size, with a rate $\xi_{\gamma}(W)^{-1}=\xi_0(W)^{-1}+\xi_{\gamma}(0)^{-1}$, where $\xi_0(W)$ is the localization length of the equivalent passive disordered system and $\xi_{\gamma}(0)$ is the attenuation/amplification length of the corresponding perfect system with combined gain/loss refraction index profile. While transmission processes are reciprocal to left and right incident waves, one-sided reflection is found.   

New perspectives on waves in random media: Speckle, modes, transmission eigenchannels, and focusing

The understanding of electron localization and conductance fluctuations has been advanced by utilizing notions of speckle, modes, and transmission eigenchannels. These concepts cannot be probed directly for electronic systems but can be explored for classical waves utilizing spectra of field transmission coefficients between arrays of points on the incident and output surfaces of ensembles of random samples. This is illustrated in microwave measurements of transmission through random waveguides in the Anderson localization transition. These experiments supply the link between the statistics of intensity and conductance and show that transmitted wave can be decomposed simultaneously into the underlying quasi-normal modes and transmission eigenchannels of the sample. The power of each of these approaches and the richness of the links between them will be illustrated by examples that reveal new aspects of wave propagation. The delayed onset of transmission following pulse excitation is shown to be the result of destructive interference between highly correlated speckle patterns of neighboring modes, while the falling decay rate at later times reflects the incoherent decay of increasingly prominent long-lived modes. We determine the individual eigenvalues \textit{$\tau $}$_{n}$ of the transmission matrix and achieve nearly complete transmission in opaque diffusive samples. We demonstrate that when reflection at the sample interface is taken into account, the spacing between average values of ln\textit{$\tau $}$_{n}$ is equal to the inverse of the bare conductance, in accord with predictions by Dorokhov [1]. We find that the distribution of total transmission relative to the conductance is determined by the effective number of transmission eigenvalues, $N_{eff} =\left( {\sum\nolimits_{n=1}^N {\tau _n } } \right)^2/\sum\nolimits_{n=1}^N {\tau _n^2 } $, which provides the link between the statistics of intensity and conductance. For diffusive waves, $N_{eff}$ is the inverse of the degree of intensity correlation. The contrast between the peak and background of maximally focused radiation in the transmitted wave, achieved when the incident is phase conjugated relative to the selected focal point, is equal to $(1+N_{eff})$. \\[4pt] [1] O. N. Dorokhov, Solid State Commun. \textbf{51}, 381 (1984).   

Experimental Observation of Brachistochrone Wave Dynamics in PT Symmetric Structures

Mutually coupled modes of a pair of active LRC circuits, one with amplification and another with an equivalent amount of attenuation, provide an experimental realization of a wide class of systems where gain and loss mechanisms break the Hermiticity while preserving parity-time (PT) symmetry. For a value $ \gamma_{ PT} $ of the gain and loss strength parameter the eigenfrequencies undergo a spontaneous phase transition from real to complex values, while the normal modes coalesce, acquiring a definite chirality. A dramatic manifestation of PT symmetry is observed in the brachistochrone wave dynamics. Experimental findings support the theoretical prediction of arbitrarily small energy transfer times between the LRC elements of the circuit. We envision that realization of such design strategies can have applications in telecommunications and metamaterial structures.   

Experimental studies of PT-scattering in arrays of active $LRC$ elements

One of the fundamental tasks in antenna theory is getting an antenna to radiate by removing mismatch losses between the loaded antenna and the transmission line that delivers the power. We will present experimental data suggesting that ${\cal PT}$-symmetric antenna structures, where active elements associated with the real part of impedance ($\pm R$) are involved, can lead to a broadband, reflectionless behavior. The suggested {\it optimal matching} strategy can potentially be superior to the existing one which uses active $LC$ elements in order to balance the reactance. Along these lines, we also envision antenna arrangements with unidirectional ultrafast communication capabilities, where the signal will transfer faster (or slower) between the active elements of the ${\cal PT}$-structure depending on the entrance point of the incident wave.   

Measurement of the Probability Distribution of Optical Transmittance on the Crossover to Anderson localization

We report measurements of spectra of the field transmission matrix $t$ for microwave radiation propagating through waveguide filled with randomly positioned dielectric scattering spheres in the Anderson localization transition. Diagonalizing the matrix product \textit{tt}$^{\dag }$ gives the transmission eigenvalues \textit{$\tau $}$_{n}$, which yields the optical transmittance, $T=\sum\nolimits_{a,b=1}^N {\left| {t_{ba} } \right|^2} =\sum\nolimits_{n=1}^N {\tau _n } $. The ensemble average of the transmittance is equal to the dimensionless conductance, $g=$. We show the probability distribution of transmittance $P(T)$ changes from Gaussian to log-normal as the value of $g$ decreases. The distribution $P(T)$ is analyzed in terms of the underlying transmission eigenvalues \textit{$\tau $}$_{n}$. For random samples with $g\sim $3.9, we found $P(T)$ follows a Gaussian distribution. For $g\sim $0.37, we observe a highly asymmetric distribution for --ln$T. $The sharp drop for high values of $T$ is attributed to the restriction that \textit{$\tau $}$_{n}<$1 and the repulsion between transmission eigenvalues even for localized samples. For $g\sim $0.04, the distribution of transmittance is nearly log-normal. The variance of -ln$T$, \textit{$\sigma $}$^{2}$, scales linearly with $<$-ln$T>$ as predicted by single parameter scaling even for weakly localized waves.   

Mode Statistics in Random Media

The nature of transport through a material is determined by the spectrum of modes or energy levels. We have analyzed the frequency variation of the transmitted microwave field speckle pattern for quasi one-dimensional random samples to obtain the central frequencies, linewidths and speckle patterns of the modes for an ensemble of samples at lengths of two and three times the localization length. The number of modes can be determined unambiguously from the spectrum of the goodness of fit. From these results we obtain the statistics of mode spacings and widths. The distribution of spacings between adjacent modes is close to the Wigner surmise predicted for diffusive waves exhibiting strong level repulsion. However, deviations from the Wigner surmise can be seen in the distribution of spacings beyond nearest modes. A weakening in the rigidity of the modal spectrum is observed as the sample length increases because of reduced level repulsion for more strongly localized waves. In contrast to residual diffusive behavior for level spacing statistics, the distribution of level widths are log-normal as predicted for localized waves.   

A Random Matrix Approach for Understanding Wave Statistics from Wireless Communications to Quantum Dots

Complexity of a wave propagation environment is advantageous from the perspective of wave chaos theory because, in the semiclassical limit, the corresponding ray trajectories of the wave propagation have chaotic dynamical behavior, and a statistical description is most appropriate. Random matrix theory (RMT) successfully describes universal properties of the system. We combine RMT with our random coupling model that includes non-universal effects, such as the radiation impedance of the ports and the effect of short ray trajectories in the system, and we establish a first-principles model for wave statistical properties such as the fading amplitude in wireless communications, the scattering matrix, the impedance matrix, and the thermopower of quantum dots. We also report experimental tests on two ray-chaotic microwave cavities with different degrees of loss. In the high loss regime the results demonstrate that our RMT model agrees with traditional fading models (Rayleigh fading and Rice fading) and provides a more general understanding of the models and a detailed physical basis for their parameters. Moreover, in the low loss regime the RMT approach describes the data better.   

Quantifying Volume Changing Perturbations to a Wave Chaotic System

The Loschmidt Echo and Fidelity decay are used to measure perturbations on a quantum wave chaotic system. We extended these concepts to classical waves to detect perturbations. [1]. In this work, we show that volume changing perturbations to a classical wave chaotic cavity can be quantified with a sub-wavelength sensitivity. This is demonstrated both numerically and experimentally. A wave chaotic quasi-1D star graph model [2], was initially used to show the results. The quantification of electrical-volume changing perturbations to a one cubic meter aluminum box will be demonstrated experimentally; the experimental results are also supported by a finite difference time domain simulation of the box. Finally, the approach to quantify these perturbations will be shown to apply to a generic wave chaotic system by using a time domain version of our Random Coupling Model.   

Nonlinear Time-Reversal in a Wave Chaotic System

Time reversal mirrors are particularly simple to implement in wave chaotic systems and form the basis for a new class of sensors [1-3]. These sensors work by applying the quantum mechanical concepts of Loschmidt echo and fidelity decay to classical waves. The sensors make explicit use of time-reversal invariance and spatial reciprocity in a wave chaotic system to remotely measure the presence of small perturbations to the system. The underlying ray chaos increases the sensitivity to small perturbations throughout the volume explored by the waves. We extend our time-reversal mirror to include a discrete element with a nonlinear dynamical response. The initially injected pulse interacts with the nonlinear element, generating new frequency components originating at the element. By selectively filtering for and applying the time-reversal mirror to the new frequency components, we focus a pulse only onto the element, without knowledge of its location. Furthermore, we demonstrate transmission of arbitrary patterns of pulses to the element, creating a targeted communication channel to the exclusion of 'eavesdroppers' at other locations in the system. [1] Appl. Phys. Lett. 95, 114103 (2009) [2] J. Appl. Phys. 108, 1 (2010) [3] Acta Physica Polonica A 112, 569 (2007)   

Low-Diffracting Modes in Surface Plasmon Metamaterials

Plasmonic structures, with periodic arrays of thin PMMA ridges on metal substrates have been shown experimentally to overcome the diffraction limit. Here we present a theoretical description of this phenomenon. We use mode matching technique to analyze the dynamics of the electromagnetic waves in the periodic systems, taking into account the extended 3D-geometry and the finite thickness of the PMMA ridges. Specifically, we focus on the behavior of plasmonic mode and its non-trivial coupling to the free space waves and to the other guided modes of the system. The eigen states of the periodic system dominated by the surface waves are identified and their dispersion is analyzed via generalization of mode-matching formalism and Bloch-periodic approach. An analytical approximation, adequately describing the behavior of the system is derived and is used to explain the suppression of diffraction in the system.   

Nonsymmorphic Phononic Metamaterials: shaping waves over multiple length scales

The vector nature of the phonon makes rational design of phononic metamaterials challenging, despite potential in unique wave propagation behavior, such as negative refraction and hyper-lensing. While most designs to date focus on the ``meta-atom'' (building block) design, their ``spatial arrangement'' (non-locality) is equally instrumental in dispersion engineering. Here, we present a generalized design framework (DF) for PMM design, utilizing both ``global'' and ``local'' symmetry concepts. We demonstrate, utilizing specific properties of nonsymmorphic plane groups, PMMs possessing i) a low-frequency in-plane complete spectral gap (ICSG) of 102{\%} (CSG of 88{\%}), ii) a set of polychromatic ICSGs totaling over 100{\%} in normalized gap size. Within the same DF, we further integrate broken symmetry states (BSS) (edge states, waveguides, etc) with designed polarization, (de)localization and group velocities. In particular, we demonstrate how these BSS may be utilized to elucidate signatures of complex polarization fields through phonon-structure interactions, leading to interesting applications in elastic-wave imaging, as well as information retrieval by probing polarization states of scattering bodies over multiple scales.   

Session T54: Superconductivity: Mostly Spectroscopy and Pairing

Probing the Photoresponse of Superconducting Materials and Devices by Laser Scanning Microscopy

We present the results of photoresponse experiments on superconducting rf/microwave devices, including Niobium and Cuprate resonators and metamaterials, by means of laser scanning microscopy. The spatially inhomogeneous photoresponse of these devices reveals the distribution of rf/microwave currents. Moreover, it will be discussed that the dependence of the phase of the photoresponse to the exciting microwave frequency may be used to bifurcate the kinetic and resistive parts of the photoresponse mechanism, which, in turn, could be used to probe the evolution of the local order parameter at different temperatures. Furthermore, we will examine the possibility of imaging the anisotropy of superconducting properties, as in the anisotropic Meissner effect, by investigating the photoresponse of a working superconducting resonator to visible light. While most of the aforementioned devices consist of thin films and cast into resonant structures, we will further discuss the techniques through which these measurements can be extended to bulk materials as well as non-resonant structures. These results are particularly useful for identifying the sources of quench and hot spots in a variety of superconducting devices including superconducting RF cavities.   

Far infrared study of magnetic field induced normal states of La$_{1.94}$Sr$_{0.06}$CuO$_{4}$

We report on the ab-plane optical properties of the magnetic field induced normal state of La$_{1.94}$Sr$_{0.06}$CuO$_4$ ($T_c=5.5 K$), the first such study. We apply strong magnetic fields (4 T and 16 T) along the c-axis . We find that at 4 T fields, which are strong enough to destroy superconductivity, the normal state at 1.4 K is very similar to the normal state at 20 K in zero field. However at higher fields we observed a gap-like depression in the optical conductivity at low frequency along with parallel growth of a broad absorption peak centered at higher frequency. The spectral weight loss in the depression at low frequency is recovered by the spectral weight in the broad peak. We attribute the magnetic field induced gap-like depression and the broad peak to a competing charge order to superconducting order or charge localization in ab-plane of the system.   

Electron energy loss spectroscopy study of superconducting Nb and its native oxides

Niobium has attracted increasing attention in recent years due to its usage in superconducting RF-cavities in next generation particle accelerators. In particular, the possible role of oxidation or the presence of oxygen vacancies on the superconducting properties of niobium metals used in superconducting RF cavities has been the focus on many recent studies. Here, we present a series of electron energy-loss spectroscopy (EELS) studies on niobium (Nb) and its oxides (NbO, NbO$_{2}$, Nb$_{2}$O$_{5})$ to develop a reliable method for quantifying the oxidation state in mixed niobium oxide thin films. Our approach utilizes a combination of transmission electron microscopy and EELS experiments with density functional theory calculations to distinguish between metallic niobium and the different niobium oxides. Based on these observed changes in the core-loss edges, we propose a linear relationship that correlates the peak positions in the Nb M- and O K-edges with the Nb valence state. The methods developed in this paper will then be applied to ultrathin niobium oxide films to examine the effects of low-temperature baking on the films' oxidation states. In addition to oxides, Niobium hydrides are considered as one of the main reasons for Q-decrease under high field. The different phases of Nb hydride can be identified directly using electron diffraction and EELS, which allows for the local hydrogen concentration to be examined at room temperature as well as 95 K.   

Strong-Field Pulsed THz Study of Superconductivity Breakdown in NbN

We report the ultra-fast breakdown of the superconducting state in a NbN thin film (${T}_C\approx\mathrm{14K}$) when exposed to an intense single-cycle THz pulse. The THz pulse's transform-limited spectral content was kept below the NbN pair-breaking energy threshold near 2$\Delta/hc=$ 35 cm$^{-1}$ (i.e., $<$1 THz). Thus, the initial electronic response was dominated by the inductive behavior of the pair condensate. At low THz E-field strength, the NbN film transmitted less for the superconducting state than for the normal state, as expected. As a function of increasing THz E-field strength, the film transmittance remained constant until a threshold range was reached, after which the transmittance changed over to its normal state value. Through this threshold range we also observed a significant non-linear response in the form of THz upconversion to frequencies approaching 3 times the optical gap, corresponding to time scales well below 1 picosecond.   

Spatial Complexity Due to Bulk Electronic Liquid Crystals in Superconducting Dy-Bi2212

Surface probes such as scanning tunneling microscopy (STM) have detected complex electronic patterns at the nanoscale in many high temperature superconductors. In cuprates, the pattern formation is associated with the pseudogap phase, a precursor to the high temperature superconducting state. Rotational symmetry breaking of the host crystal (i.e. from C4 to C2) in the form of electronic nematicity has recently been proposed as a unifying theme of the pseudogap phase [Lawler Nature 2010]. However, the fundamental physics governing the nanoscale pattern formation has not yet been identified. Here we use universal cluster properties extracted from STM studies of cuprate superconductors to identify the funda- mental physics controlling the complex pattern formation. We find that due to a delicate balance between disorder, interactions, and material anisotropy, the rotational symmetry breaking is fractal in nature, and that the electronic liquid crystal extends throughout the bulk of the material.   

Search for order parameter domains in single crystal flakes of chiral $p$-wave superconductor Sr$_2$RuO$_4$ using micrometer size Josephson junctions

Even though the odd-parity, spin-triplet superconductivity in Sr$_2$RuO$_4$ is supported by many experimental studies, the existence of order parameter domains and domain walls remains to be an open question. In addition, how these domains can be controlled experimentally is not understood. We fabricate small Al-Sr$_2$RuO$_4$ Josephson junctions using flakes of singlecrystalline Sr$_2$RuO$_4$ prepared by mechanical exfoliation, using Ti as an interlayer for adhesion purpose. The 3 $\mu$m wide junctions defined by photolithography on a natural $ac$ plane was found to show Josephson coupling. Experiments on the effect of domain walls on Josephson coupling and the control of domain walls are being explored. The work is supported by DOE under Grant No. DE-FG02-04ER46159 and Penn State nanofabrication lab.   

T-linear resistivity and hot Fermi surface from spin-density wave quantum critical fluctuations

The linear dependence in temperature $T$ of the resistivity observed in the normal phase of unconventional superconductors is often attributed to quantum critical behavior. We use the two-particle self-consistent (TPSC) approach to the Hubbard model to study this problem. The quantum critical point is associated with a spin-density wave (SDW) phase transition at zero-temperature on the 2D square lattice at finite doping. Our approach satisfies the Mermin-Wagner theorem, the Pauli principle and conservation laws, and is valid from weak to intermediate coupling. We take into account vertex corrections. For the model with nearest neighbors only and also with $t'$ and $t''$, we compute, as a function of $T$, contributions to the conductivity coming from different directions in the Brillouin zone. Our results show that the low temperature resistivity is linear because the whole Fermi surface is hot down to the lowest temperatures studied. This occurs because the SDW correlation length and the thermal de Broglie wavelength both scale as $1/T$.   

Controlled Intergrowth of 248 and 247 Phases of Y-Ba-Cu-O in Epitaxial Films and Heterostructures

Recent studies have shown that superconductivity in the Y-Ba-Cu-O (YBCO) family of cuprates can also be rooted in the quasi-1D Cu-O chains [1], even when the $\rm{CuO_2}$ planes are not conducting [2]. The critical temperature ($T_c$) depends on the phase of YBCO present, such as $\rm{Y_2Ba_4Cu_8O_{16}}$ (248) and $\rm{Y_2Ba_4Cu_7O_{15}}$ (247). Recent studies have also shown that heterostructuring YBCO with other oxides such as $\rm{La_{2/3}Ca_{1/3}MnO_3}$ (LCMO) can strongly influence the former's $T_c$ [3]. This talk reports on a reexamination of these issues, by probing and controlling the intergrowth of the various YBCO phases in thin films and heterostructures. The samples were grown epitaxially by pulsed laser-ablated deposition, and characterized by electrical transport, XRD and high-resolution TEM with in-situ EELS. We observed the presence of 248 and 247 phases in YBCO/LCMO heterostructures. We also observed conversion between different phases of YBCO depending on the thermodynamics of the growth and annealing conditions. The implication of our results on the $T_c$ variation in YBCO/LCMO heterostructure is discussed. \\[4pt] [1] J. Ngai \emph{et al.}, PRL. 98, 177003 (2007).\\[0pt] [2] E. Berg \emph{et al.}, PRB. 76, 214505 (2007).\\[0pt] [3] Z. Sefrioui \emph{et al.}, PRB. 67, 21451 (2003)   

Quantitative measurements of the magnetic field profile in superconductors

Measurement of the magnetic field profile $B(z)$, $z$ being the distance from the sample surface, in the Meissner state of superconductors is one of the longest standing problems of experimental superconductivity. Importance of $B(z)$ follows, in particular, from the fact, that it provides a direct way to determine the key intrinsic parameters, such as the London penetration depth at zero temperature $\lambda_L(0)$ and the Pippard coherence length $\xi_0$. None of these parameters is known with justified uncertainty for $any$ superconductor. $B(z)$ can be measured using Low-Energy Muon Spin Rotation spectroscopy (LE-$\mu$SR) and Polarized Neutron Reflectometry (PNR). To verify abilities of these techniques for quantitative measurements of $B(z)$ in unconventional superconductors and to examine the nonlocal electrodynamics effect predicted by Pippard in 1953, we performed an extensive series of cross LE-$\mu$SR and PNR measurements of $B(z)$ with two extreme type-I superconductors, In and Sn. Results obtained at the initial stage of this project were reported last year. Now the project is completed. Results unambiguously validate the nonlocal effect. Conditions which have to be met to use LE-$\mu$SR and/or PNR for measurements of $\lambda_L(0)$ and $\xi_0$ will be discussed.   

The critical magnetic field in the intermediate state of a Pippard superconductor

One of the fundamental problems of unconventional superconductivity is the magnetic structure of vortices. In order to contribute to the solution of this problem and to address number of unsolved questions of the intermediate state (IS) we undertook an experimental and theoretical study of IS in an extreme type-I superconductor focusing on the critical field of the IS-N (normal) transition. Results shed new light on the structure and evolution of the magnetic flux density in normal domains and may lead to new insights in the structure of vortices in type-II materials. A 2.5 $\mu$m thick indium film with mean free path 11 $\mu$m was placed in the superconducting vector (3D) magnet. Magneto-optical images were taken simultaneously with measurements of the sample resistance using a small low frequency AC current. The equilibrium domain structure of the IS state was investigated as a function of independently controlled in- and out-of-plane magnetic fields and/or DC transport current applied to the sample. The observed critical field varied in a range from 100\% down to 40\% of the thermodynamic critical field. A theoretical model based on the classical Landau laminar structure quantitatively accounts for the experimental results for both ordered and disordered domain patterns.   

Evidence for s+d wave pairing in copper oxides superconductors from an analysis of NMR and NQR data

Knight shift and spin-lattice relaxation rate data of high temperature copper oxide superconductors are analyzed within a two-band model for superconductivity with coupled s+d wave superconducting gaps. The two-gap approach leads to substantial modifications of the coherence factors, which reflects itself in the Knight shift and the relaxation rate 1/T$_{1}$T. From the analysis it is concluded that the data are consistent with 40{\%} s-wave and 60{\%} d-wave gap admixtures in agreement with earlier penetration depth data.   

Pseudogap studied by optical conductivity spectra of Zn-substituted YBa$_{2}$Cu$_{3}$O$_{y}$

The pseudogap and the superconducting gap cause a similar suppression of the low energy optical conductivity, but the behaviors of the spectral weight transfers are different, which enables us to distinguish these two gaps. In the \textit{c}-axis spectra of YBa$_{2}$Cu$_{3}$O$_{y}$, however, it is difficult to discuss these spectral weight transfers because of the additional structures due to a transverse Josephson plasma mode [1]. To overcome this problem, we substituted Zn for Cu, which is known to suppress those supplementary structures [2]. In this study, we performed temperature dependent reflectivity measurements in Zn-substituted YBa$_{2}$Cu$_{3}$O$_{y} $ system. We have revealed the continuous transfer of the low energy spectral weight to the higher energy region even below Tc, which suggests the coexistence of the pseudogap and the superconducting gap. [1]C. Bernhard et al. Phys. Rev. B, 61 (2000) 618. [2]R. Hauff et al., Phys. Rev. Lett., 77 (1996) 4620.   

Evidence of gate-tunable topological excitations in two-dimensional electron system

We report experimental observation of a new mechanism of charge transport in two-dimensional electron systems (2DES) in the presence of strong Coulomb interaction and disorder. We show that at low enough temperature the conductivity tends to zero at a non-zero carrier density, which represents the point of essential singularity in a Berezinskii-Kosterlitz-Thouless (BKT)-like transition. Our experiments with many 2DESs in GaAs/AlGaAs heterostructures suggest the charge transport at low carrier densities to be due to the melting of an underlying ordered ground state through proliferation of topological defects. Independent measurement of low-frequency conductivity noise supports this scenario. \\[4pt] [1] R. Koushik\textit{ et al}., Phys. Rev. B \textbf{83}, 085302 (2011) \\[0pt] [2] M. Baenninger\textit{ et al}., Phys. Rev. Lett. \textbf{100}, 016805 (2008).