Session A1: Competing Order in High-Tc Superconductors

Quantum melting of the hole crystal in the spin ladder of Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$

The ``spin ladder'' is a reduced-dimensional analogue of the t-J model that has been shown theortically to exhibit close competition between d-wave superconductivity and a ``hole crystal" (HC) phase in which the carriers form a static lattice. An example of a real doped spin ladder is the cuprate Sr$_{14-x}$Ca$_{x}$Cu$_{24}$O$_{41}$, which exhibits superconductivity at $x=13.6$ (under pressure) and a commensurate HC at $x=0$. In this talk I will present a resonant soft x-ray scattering (RSXS) study of the effects of discommensuration on this HC, i.e. how it evolves with the hole density. As $x$ is varied the HC forms only with the commensurate wave vectors $L=1/5$ and $L=1/3$; for incommensurate values it ``melts.'' A simple scaling between $L$ and temperature is observed, $\tau_{1/3} / \tau_{1/5} = 5/3$, indicating an inverse relationship between the interaction strength and the HC period. Our results suggest that the HC consists of hole pairs crystallized through an interplay between lattice commensuration and a poorly screened Coulomb interaction. I will discuss the relationship between the HC and the static ``stripe" phase that has been observed in the closely related system La$_{2-x}$Ba$_x$CuO$_4$.   

An intrinsic Cu-O-Cu bond-centered electronic glass with disperse 4$a_0$-wide unidirectional domains in strongly underdoped Ca$_{1.88}$Na$_{0.12}$CuO$_2$Cl$_2$ and Bi$_2$Sr$_2$Dy$_{0.2}$Ca$_{0.8}$Cu$_2$O$_y$

Hole doping into the CuO$_2$ charge transfer insulator alters the electronic correlations, leading to the high-$T_{\rm c}$ superconductivity (HTS). The correlation alterations are accompanied by spectral weight transfers from the high energy states of the insulator to low energies. Recently, it has been proposed~[1,2] that these effects might be observable as an asymmetry of electron tunneling currents with bias voltage across the chemical potential. Atomic-scale TA-phenomena would then be of crucial importance to understand the fundamental electronic structure of the CuO$_2$ plane from whence the HTS emerges.\par In this talk, we will report the first application of atomic resolution TA-imaging by STM, detecting virtually identical phenomena in two different lightly hole-doped cuprates: Ca$_{1.88}$Na$_{0.12}$CuO$_2$Cl$_2$ and Bi$_2$Sr$_2$Dy$_{0.2}$Ca$_{0.8}$Cu$_2$O$_y$. We find intense spatial variation primarily on planer oxygen sites. Their spatial arrangements appear to be a Cu-O-Cu bond-centered electronic glass, breaking translational symmetry of lattice and 90$^{\circ}$-rotational symmetry. 4$a_0$-wide unidirectional domains ($a_0$: Cu-O-Cu length) are embedded throughout this matrix and running along the both Cu-O bonds without preferred orientation. Relationship to the electronic cluster glass, the bond-centered stripe, and the high-$T_{\rm c}$ superconductivity will be discussed.\par \par This work is done in collaboration with C. Taylor, A. Schmidt, C. Lupien, T. Hanaguri, M. Azuma, M. Takano, K. Fujita, H. Eisaki, H. Takagi, S. Uchida, and J. C. Davis. \par \par [1] P. W. Anderson, N. P. Ong, cond-mat/0405518 \& {\it J. Phys. Chem. Solid} {\bf 67}, 1 (2006).\par [2] M. Randeria, R. Sensarma, N. Trivedi, F. -C. Zhang, {\it Phys. Rev. Lett.} {\bf 95}, 137001 (2005).   

Nature of the electronic gap in stripe-ordered cuprates

The {\it ab}-plane optical properties of single crystals of the high-temperature superconductor La$_{2-x}$Ba$_x$CuO$_4$, with chemical dopings of $x=0.095$ (slightly underdoped) and $0.125$ ($1/8$ doping) and critical temperatures ($T_c$'s) of 32 and $\simeq 2.4$~K, respectively, have been measured over a wide frequency and temperature range. The optical conductivity has been determined from a Kramers-Kronig analysis. In the slightly underdoped material, the reflectance increases monotonically over the far-infrared frequency range, with an abrupt increase in the reflectance below $T_c$ below about 200~cm$^{-1}$ (about 25~meV) signaling the formation of a superconducting energy gap; the suppression of the conductivity for $T\ll T_c$ occurs below this energy. This is close to the estimate of the gap maximum $2\Delta_0$ determined from angle resolved photoemission spectroscopy. In contrast, the 1/8 doping shows a dramatically different behavior.\footnote{C.C.~Homes {\it et al.}, Phys. Rev. Lett. {\bf 96}, 257002 (2006).} The reflectance increases monotonically with decreasing temperature. Below $\simeq 60$~K, corresponding to the onset of charge-stripe order, the far-infrared reflectance continues to increase; however, the reflectance over much of the infrared is suppressed. The conductivity, Drude-like above the ordering temperature, shows a rapid loss of spectral weight below about 40~meV for $T < 60$~K. This behavior is quite different from that typically associated with the pseudogap in the normal state of the cuprates. Instead, the gapping of the normal-state single-particle excitations looks surprisingly similar to that observed in superconducting La$_{2-x}$Sr$_{x}$CuO$_4$, including the presence of a residual Drude peak with reduced weight.   

Neutron scattering evidence for spin and charge inhomogeneity in cuprate superconductors

Neutron diffraction studies have provided clear evidence for charge and spin stripe order in La$_{2-x}$Ba$_{x}$CuO$_{4}$ and La$_{1.6-x}$Nd$_{0.4}$Sr$_{x}$CuO$_{4}$ for a range of $x$, with a maximum ordering temperature at $x$ = 1/8. The ordering of stripes competes with superconducting order. Recent measurements of the magnetic excitation spectrum in La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ show that: 1) the energy scale corresponds to antiferromagnetic superexchange, 2) the qualitative features do not change when static stripe order disappears [1], and 3) the spectrum is very similar to that found in other cuprate superconductors. New measurements on optimally-doped Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ [2] are consistent with the concept of a universal spectrum. Results on over-doped La$_{2-x}$Sr$_{x}$CuO$_{4}$ show that the magnetic spectral weight disappears as the superconductivity goes away [3]. These results suggest that slowly-fluctuating charge inhomogeneity is common to the cuprates and underlies the high-temperature superconductivity. \begin{enumerate} \item Guangyong Xu, J.M. Tranquada, T.G. Perring, G.D. Gu, M. Fujita, and K. Yamada, (unpublished). \item Guangyong Xu, J.M. Tranquada, B. Fauqu\'{e}, G.D. Gu, M. H\"{u}cker, T.G. Perring, L.-P. Regnault, and J.S. Wen, (unpublished). \item S. Wakimoto, K. Yamada, J.M. Tranquada, C.D. Frost, R.J. Birgeneau, and H. Zhang, cond-mat/0609155. \end{enumerate}   

Duality and the vibrational modes of a Cooper-pair Wigner crystal

When quantum fluctuations in the phase of the superconducting order parameter destroy the off-diagonal long range order, duality arguments predict the formation of a Cooper pair Wigner crystal. This effect is thought to be responsible for the static checkerboard patterns observed recently in various underdoped cuprate superconductors by means of scanning tunneling spectroscopy. I will sketch the calculation of the vibrational modes of this pair crystal using a continuum version of the standard vortex-boson duality. Such calculations yield bounds on the sound velocity of the phonon modes which are in agreement with the numbers extracted from the thermal conductivity measurements but indicate that vibrations are robustly three dimensional in nature. Generalization of the inherently two-dimensional vortex-boson duality to three dimensions is outlined and an intriguing connection to the theory of bosonic strings is pointed out.   

Session A2: Future of Fossil Fuels

Energizing our Future: How Disinformation and Ignorance are Misdirecting Our Efforts

Most of the energy-source choices that are being considered or implemented for future use by governments and by a wide variety of would-be manufacturers are driven by assumptions that are often uninformed and sometimes intentionally \textit{misinformed}. These dangerous assumptions relate to ``drivers'' that range from the causes (and proposed fixes) of \textit{Global Warming} to the myth of \textit{``Peak Oil''} to the dubious viability of \textit{Hydrogen} as a vehicle fuel to the uncertain feasibility of replacing most of our conventional fossil energy supplies with fuels such as \textit{Ethanol} derived from \textit{Renewable Resources}. Regrettably, many of these misinformed assumptions and misplaced beliefs are being used as the basis for major decisions involving huge investments in technologies that simply cannot do the job, a potential catastrophe. There is no place for what we will call ``Faith-Based Science'' in major business decisions of this kind. This talk will examine some of the key beliefs that are driving our current energy decision-making process and will expose the uncomfortable facts that dictate that \textit{fossil fuels}, like it or not, should and will remain our primary energy source for many years to come, at least until solar energy becomes economically viable. For example, it will be shown that biomass-based fuels can, at best, be only a minor contributor to meeting the world's future energy needs; that the use of nuclear power, whether or not we consider it environmentally attractive; will be severely limited by a shortfall in nuclear fuel supplies; and that hydrogen as a transportation fuel will at best be a niche player and perhaps not a player at all. As we re-activate, improve and implement the many ``clean'' fossil-fuel technologies that were developed 25 years ago, we must also focus intensely on developing the energy technologies that really can replace fossil fuels in the years following 2050 or so when their availability will really be in decline. It will be argued that the optimum choices then will clearly be a combination of the various forms of solar energy and, of course, wind energy.   

Clean Fossil Energy Conversion Processes

Absolute and per-capita energy consumption is bound to increase globally, leading to a projected increase in energy requirements of 50{\%} by 2020. The primary source for providing a majority of the energy will continue to be fossil fuels. However, an array of enabling technologies needs to be proven for the realization of a zero emission power, fuel or chemical plants in the near future. Opportunities to develop new processes, driven by the regulatory requirements for the reduction or elimination of gaseous and particulate pollutant abound. This presentation describes the chemistry, reaction mechanisms, reactor design, system engineering, economics, and regulations that surround the utilization of clean coal energy. The presentation will cover the salient features of the fundamental and process aspects of the clean coal technologies in practice as well as in development. These technologies include those for the cleaning of SO$_{2}$, H$_{2}$S, NO$_{x}$, and heavy metals, and separation of CO$_{2}$ from the flue gas or the syngas. Further, new combustion and gasification processes based on the chemical looping concepts will be illustrated in the context of the looping particle design, process heat integration, energy conversion efficiency, and economics.   

The future of fossil fuels

With today's energy technology, the world faces a stark choice between economic growth and a healthy environment. The accumulation of CO$_{2}$ in the atmosphere must stop, while energy services to a growing world population striving for a high standard of living must improve. New technologies must eliminate CO$_{2}$ emissions. Only carbon capture and storage can maintain access to fossil carbon reserves that by themselves could satisfy energy demand for centuries. Technologies for CO$_{2}$ capture at power plants and other large sources already exist. A new generation of efficient, clean power plants could capture its CO$_{2}$ and deliver it for underground injection or mineral sequestration. However, the remaining CO$_{2}$ emissions from distributed sources are too large to be ignored. Either hydrogen or electricity need to substitute for carbonaceous energy carriers, or CO$_{2}$ emissions must be balanced out by capturing an equivalent amount of carbon from the environment. Biomass growth offers one such option; direct capture of CO$_{2}$ from the air provides another. Carbon capture and storage technologies can close the anthropogenic carbon cycle and, thus, provide one possible avenue to a world that is not limited by energy constraints.   

Assessing the promise of natural gas hydrates as an unconventional source of energy

Gas hydrates are a naturally occurring ``ice-like'' combination of natural gas and water that have the potential to provide an immense resource of natural gas from the world's oceans and polar regions. The amount of natural gas contained in the world's gas hydrate accumulations is enormous, but these estimates are speculative and range over three orders-of-magnitude from about 2,800 to 8,000,000 trillion cubic meters of gas. By comparison, conventional natural gas accumulations (reserves and technically recoverable undiscovered resources) for the world are estimated at approximately 440 trillion cubic meters as reported in the ``U.S. Geological Survey 2000 World Petroleum Assessment.'' Despite the enormous range in reported gas hydrate volumetric estimates, even the lowest reported estimates seem to indicate that gas hydrates are a much greater resource of natural gas than conventional accumulations. However, it is important to note that none of these assessments has predicted how much gas could actually be produced from the world's gas hydrate accumulations. Proposed methods of gas recovery from hydrates generally deal with dissociating or ``melting'' in-situ gas hydrates by heating the reservoir beyond the temperature of hydrate formation, or decreasing the reservoir pressure below hydrate equilibrium. Computer models have been developed to evaluate natural gas production from hydrates by both heating and depressurization. Depressurization is considered to be the most economically promising method for the production of natural gas from gas hydrates. Estimates vary on when gas hydrate production will play a significant role in the total world energy mix; however, it is possible that hydrates will be able to provide a sustainable supply of gas for the world's future energy needs.   

The Physics of Heavy Oils: Implications for Recovery and Geophysical Monitoring

Our capacity to find and produce conventional light petroleum oils are unable to keep pace with the growth in the growing global demand for energy. With the breakpoint between petroleum production and consumption imminent, a good deal of recent efforts have focused on developing the `heavy' hydrocarbon reserves. Such resources include the extensive heavy oil deposits of Venezuela, the bitumen resources of Canada, and even the solid kerogens (oil shale) of the United States. Capital investments, in particular, have been large in Canada's oil sands due in part to the extensive nature of the resource and already in excess of 30{\%} of Canada's production comes from heavier hydrocarbon deposits. The larger input costs associated with such projects, however, requires that the production be monitored more fully; and this necessitates that both the oils and the porous media which hold them be understood. Geophysical `time-lapse' monitoring seeks to better constrain the areal distribution and movements of fluids in the subsurface by examining the changes in a geophysical response such as seismic reflectivity, micro-gravity variations, or electrical conductivity that arise during production. For example, a changed geophysical seismic character directly depends on relies on variations in the longitudinal and transverse wave speeds and attenuation and mass densities of the materials in the earth. These are controlled by a number of extrinsic conditions such as temperature, fluid pressure, confining stress, and fluid phase and saturation state. Understanding the geophysical signature over a given reservoir requires that the behavior of the porous rock physical properties be well understood and a variety of measurements are being made in laboratories. In current practice, the interpretation of the geophysical field responses is assisted by combined modeling of fluid flow and seismic wave fields. The least understood link in this process, however, is the lack of knowledge on rock physical properties under the conditions encountered within a reservoir.   

Session A3: Electronic States in Graphene

Infrared Probe of the Anomalous Magneto-transport of Graphite in the Extreme Quantum Limit

We present a systematic investigation of the magnetoreflectance of highly oriented pyrolytic graphite in magnetic fields $B$ up to 18~T . From these measurements, we report the determination of lifetimes tau associated with the lowest Landau levels in the quantum limit. We find a linear field dependence for inverse lifetime 1$/$tau($B)$ of the lowest Landau levels, which is consistent with the hypothesis of a three-dimensional (3D) to 1D crossover in an anisotropic 3D metal in the quantum limit. This enigmatic result uncovers the origin of the anomalous linear in-plane magnetoresistance observed both in bulk graphite and recently in mesoscopic graphite samples. This work is a collaboration with Z.Q. Li, S.-W. Tsai, W.J. Padilla, S.V. Dordevic, K.S. Burch, and Y.J. Wang.   

Two-Dimensional Dirac Fermions in Graphene at High Magnetic Fields

Graphene, a single atomic sheet of graphite, is a monolayer of carbon atoms densely packed into a honeycomb structure. It can be viewed as either an unrolled single-wall carbon nanotube or a giant flat fullerene molecule. Advances in micromechanical extraction and fabrication techniques for graphite structures now permit such exotic 2D electron systems to be probed experimentally. It has been discovered that the electrons in graphene are two-dimensional Dirac Fermions, based on the observation of half-integer quantum Hall effect and Berry's phase of $\pi $ in the magneto-oscillations. We further investigate the transport properties of graphene in extremely strong magnetic fields. Under such condition, we observe new sets of quantum Hall states at filling factors $\nu =0,\pm 1,\pm 4$, indicating the lifting of the four-fold degeneracy of the previously observed quantum Hall states at $\nu =\pm 4(n+1/2)$, where $n $is the Landau level index. In particular, the presence of the $\nu =0,\pm 1$ quantum Hall states indicates that the Landau level at the charge neutral Dirac point splits into four sub-levels, lifting both sublattice and spin degeneracy in graphene. The quantum Hall effect at $\nu =\pm 1,\pm 4$ is studied in tilted magnetic fields at various temperatures. It has been found that $\nu =\pm 4$ are due to the lifting of the spin-degeneracy of the Landau level $n=\pm 1$ while $\nu =\pm 1$ are most likely due to the sublattice degeneracy lifting of $n=0$. Finally, the availability of large, high quality graphene crystals opens new possibilities for optical and scanning probe studies. A brief discussion of our recent experiments on Raman spectroscopy and STM will be presented.   

Electronic Confinement and Coherence in Patterned Epitaxial Graphene

Transport in ultrathin graphite films grown on single-crystal silicon carbide is dominated by the electron-doped epitaxial graphene layer at the interface and shows graphene characteristics. Epitaxial graphene provides a platform for studying the novel electronic properties of this 2D electron gas in a controlled environment. Shubnikov-de Haas oscillations in the magnetoresistance data indicate an anomalous Berry's phase and reveal the Dirac nature of the charge carriers. The system is highly coherent with phase coherence lengths beyond 1 micrometer at cryogenic temperatures, and mobilities exceeding 2.5 square meters per volt-second. In wide structures, evidence is found for weak anti-localization in agreement with recent graphene weak-localization theory. Patterned narrow ribbons show quantum confinement of electrons. Several Hall bar samples reveal anomalous magnetoresistance patterns consisting of large structured non-periodic oscillations that may be due to a periodic superlattice potential.   

Electronic properties of single and multi-layer Graphene

Graphene, a two dimensional carbon crystal with a honeycomb lattice, was discovered only two years ago. It has generated a lot of excitement in the condensed matter community because of its unusual properties: anomalous integer quantum Hall effect, universal d.c. conductivity, absence of weak localization, unusual behavior in high magnetic fields, among others. In this talk I am going to discuss the various non-Fermi liquid properties of single layer, bilayer, and multi-layer graphene. These results indicate that graphene belongs to a new class of materials with unique properties that can be used as basis for a carbon based electronics.   

Session A4: Responsive and Adaptable Polymeric Materials

Adaptive and Responsive Polymer NanoComposites

In addition to thermal-mechanical improvements of commodity plastics, polymer nanocomposite concepts offer opportunities to impart \textit{responsive} characteristics as well as enhance the performance of \textit{active} polymers, including shape memory and piezo - resistivity. Opportunities arise from 1) the utilization of the extensive polymer-nanoparticle interfacial area ($>$500 m$^{2}$/g), 2) the responsiveness of the percolative network of the nanoparticle to external fields, and 3) the impact of nanoscale compositional fluctuations on the local electric field. As an example, carbon nanotube addition to shape memory polymers increases blocking stress by 100{\%} and provides novel electrical and optical methods to trigger recovery. Similarly, the pyro-resitive character of carbon nanotube -- polyimide nanocomposites depends on the surface modification of the nanotube, displaying a positive coefficient of resistivity (resistance increase with temperature) from cryogenic to the glass transition temperature. Challenges facing characterization and the establishment of structure-property correlations will be discussed.   

Hydrophobic Hydration of Stimulus-Responsive Polyproteins Measured by Single Molecule Force Spectroscopy

We present a new procedure to reduce and analyze force-extension data obtained by single molecule force spectroscopy (SMFS). This approach allows, for the first time, to infer effects of solvent quality and minor changes in molecular architecture on molecular-elasticity of individual (bio)macromolecules. Specifically, we show how changes in the effective Kuhn segment length can be used to interpret the hydrophobic hydration behavior of elastin-like polypeptides (ELPs).Our results are intriguing as they suggest that SMFS in combination with our analysis procedure can be used to study the subtleties of polypeptide-water interactions on the single molecule level. We also report on the force-induced cis-trans isomerization of prolines, which are repeated every fifth residue in the main chain of ELPs. We present evidence for this mechanism by Monte Carlo simulations of the force-extension curves using an elastically coupled two-state system. Our results suggest that SMFS could be used to assay proline cis-trans isomerization in proteins and may thus have significant potential diagnostic utility.   

Nature's Mechanisms for Tough, Self-healing Polymers and Polymer Adhesives

Spider silk$^{2}$ and the natural polymer adhesives in abalone shells$^{3}$ and bone$^{4,5}$ can give us insights into nature's mechanisms for tough, self-healing polymers and polymer adhesives. The natural polymer adhesives in biomaterials have been optimized by evolution. An optimized polymer adhesive has five characteristics. 1) It holds together the strong elements of the composite. 2) It yields just before the strong elements would otherwise break. 3) It dissipates large amounts of energy as it yields. 4) It self heals after it yields. 5) It takes just a few percent by weight. Both natural polymer adhesives and silk rely on sacrificial bonds and hidden length for toughness and self-healing.$^{6}$ A relatively large energy, of order 100eV, is required to stretch a polymer molecule after a weak bond, a sacrificial bond, breaks and liberates hidden length, which was previously hidden, typically in a loop or folded domain, from whatever was stretching the polymer. The bond is called sacrificial if it breaks at forces well below the forces that could otherwise break the polymer backbone, typically greater than 1nN. In many biological cases, the breaking of sacrificial bonds has been found to be reversible, thereby also providing a ``self-healing'' property to the material.$^{2-4}$ Individual polymer adhesive molecules based on sacrificial bonds and hidden length can supply forces of order 300pN over distances of 100s of nanometers. Model calculations show that a few percent by weight of adhesives based on these principles could be optimized adhesives for high performance composite materials including nanotube and graphene sheet composites. \newline \newline $^{2}$N. Becker, E. Oroudjev, S. Mutz et al., Nature Materials \textbf{2} (4), 278 (2003). \newline $^{3}$B. L. Smith, T. E. Schaffer, M. Viani et al., Nature \textbf{399} (6738), 761 (1999). \newline $^{4}$J. B. Thompson, J. H. Kindt, B. Drake et al., Nature \textbf{414} (6865), 773 (2001). \newline $^{5}$G. E. Fantner, T. Hassenkam, J. H. Kindt et al., Nature Materials \textbf{4}, 612 (2005). \newline $^{6}$G. E. Fantner, E. Oroudjev, G. Schitter et al., Biophysical Journal \textbf{90} (4), 1411 (2006).   

Is experimental heteropolymer sequence design practical, or does it belong to the realm of science fiction?

In the protein folding context, theorists consider various methods of sequence design, which turns out a very useful way to look at various heteropolymer properties. Simultaneously and largely independently, there is a rather old idea to find an experimental counterpart of computational and theoretical sequence design algorithms. Here, we review some of the experiments in this direction along with some of the more recent theoretical advances and come to the guarded conclusion that full experimental realization of sequence design is possible but probably remote.   

Session A5: Mechanisms and Landscapes of Cellular Networks

Some physics problems in biological networks

Most of the interesting things that happen in living organisms require interactions among many components, and it is convenient to think of these as a ``network'' of interactions. We use this language at the level of single molecules (the network of interactions among amino acids that determine protein structure), single cells (the network of protein-DNA interactions responsible for the regulation of gene expression) and complex multicellular organisms (the networks of neurons in our brain). In this talk I'll try to look at two very different kinds of theoretical physics problems that arise in thinking about such networks. The first problems are phenomenological: Given what our experimentalists friends can measure, can we generate a global view of network function and dynamics? I'll argue that maximum entropy methods can be useful here, and show how such methods have been used in very recent work on networks of neurons, enzymes, genes and (in disguise) amino acids. In this line of reasoning there are of course interesting connections to statistical mechanics, and we'll see that natural statistical mechanics questions about the underlying models actually teach us something about how the real biological system works, in ways that will be tested through new experiments. In the second half of the talk I'll ask if there are principles from which we might actually be able to predict the structure and dynamics of biological networks. I'll focus on optimization principles, in particular the optimization of information flow in transcriptional regulation. Even setting up these arguments forces us to think critically about our understanding of the signals, specificity and noise in these systems, all current topics of research. Although we don't know if we have the right principles, trying to work out the consequences of such optimization again suggests new experiments.   

Session A6: Frontier in Computational Materials

Quantum Design of Complex Nanostructured Electronic Materials

Over the last decade, our ability to predict the fundamental properties of nanoscale building blocks such as quantum dots, wires, and slabs has improved dramatically. In particular, first principles modeling techniques can now routinely predict how the structural, electronic, optical, and transport properties of these building blocks depends on their size, shape, composition, and surface structure. In this talk we present the results of three projects designed to build upon these fundamental studies to engineer novel, nanostructured materials with tailored electronic properties. These complex, nanoscale heterostructure materials utilize both the unique properties of their nanoscale building blocks and the interactions between the constituent building blocks to engineer the ideal material properties. (i) We will describe the design of a silicon/germanium nanowire based thermoelectric material whose performance is enhanced by suppressing thermal transport and enhancing electronic transport. This is achieved by engineering the nanoscale confinement and scattering of phonons and electrons. (ii) We will describe the design of a silicon based laser, constructed from silicon nanocrystals embedded in an amorphous silicon nitride matrix. Models of the electronic states in the nanocrystal, the surrounding matrix, and the interface between the two, enable us to optimize the optical efficiency of the emission and electrically pump the laser. (iii) We will describe the use of first principles models to predict the optical response of silicon nanowires. These predictions are used to interpret the results of optical scatterometry metrology which can measure the size and surface roughness of nanoscale electronic devices produced by a combination of lithography and etching. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.   

The European Theoretical Spectroscopy Facility

The ETSF (www.etsf.eu) is being created as a permanent output of the EU-funded {\it Nanoquanta} Network of Excellence (www.nanoquanta.eu, 2004-8), which joins 10 groups and over 100 researchers in research on the theory and simulation of spectroscopy of electrons in matter, and related excited-state electronic properties including quantum transport. The ETSF is intended to contribute significantly to nanoscience and nanotechnology through the development and application of theoretical spectroscopy, involving close collaboration between theorists (the existing {\it Nanoquanta} groups together with further theoretical groups) and a new community of experimental and industrial researchers who wish to apply modern theories of spectroscopy. In this talk I shall review some of the scientific output of the project so far, including the development of new ideas and techniques in many-body perturbation theory and time-dependent density-functional theory, and their application to a variety of prototype and actual systems including quantum transport in nanostructures, optical absorption in biological molecules and advanced materials, optical properties of nanoclusters and nanotubes, non-linear optical response, and spectroscopies of complex surfaces. I shall also briefly describe the network's integration activities, including code interoperability and modularity, training of internal and external researchers, and the legal, financial and organizational preparations for the ETSF.   

The prediction of crystal structure by merging knowledge methods with first principles quantum mechanics

The prediction of structure is a key problem in computational materials science that forms the platform on which rational materials design can be performed. Finding structure by traditional optimization methods on quantum mechanical energy models is not possible due to the complexity and high dimensionality of the coordinate space. An unusual, but efficient solution to this problem can be obtained by merging ideas from heuristic and ab initio methods: In the same way that scientist build empirical rules by observation of experimental trends, we have developed machine learning approaches that extract knowledge from a large set of experimental information and a database of over 15,000 first principles computations, and used these to rapidly direct accurate quantum mechanical techniques to the lowest energy crystal structure of a material. \textit{Knowledge} is captured in a Bayesian probability network that relates the probability to find a particular crystal structure at a given composition to structure and energy information at other compositions. We show that this approach is highly efficient in finding the ground states of binary metallic alloys and can be easily generalized to more complex systems.   

Quantum-Mechanical Combinatorial Design of Solids having Target Properties

(1) One of the most striking aspects of solid state physics is the diversity of structural forms in which crystals appear in Nature. Not only are there many distinct crystal-types, but combinations of two or more crystalline materials (alloys) give rise to various local geometric atomic patters. The already rich repertoire of such forms has recently been significantly enhanced by the advent of artificial crystal growth techniques (MBE, STM- atom positioning, etc.) that can create desired structural forms, such as superlattices and impurity clusters even in defiance of the rules of equilibrium thermodynamics. (2) At the same time, the fields of chemistry of nanostructures and physics of structural phase-transitions have long revealed that different atomic configurations generally lead to different physical properties even without altering the chemical makeup. While the most widely - known illustration of such ``form controls function'' rule is the dramatically different color, conductivity and hardness of the allotropical forms of pure carbon (diamond,graphite, C60), the physics of semiconductor superstructures and nanostructures is full of striking examples of how optical, magnetic and transport properties depend sensitively on atomic configuration. (3) Yet, the history of material research has generally occurred via accidental discoveries of material structures having interesting physical property (semiconductivity, ferromagnetism; superconductivity etc.). This begs the question: can this discovery process be inverted, i.e. can we first articulate a desired target physical property, then search (within a class) for the configuration that has this property? (4) The number of potentially interesting atomic configurations exhibits a combinatorial explosion, so even fast synthesis or fast computations can not survey all. (5) This talk describes the recent steps made by solid state theory + computational physics to address this ``Inverse Design'' (Franceschetti {\&} Zunger, Nature, 402, 60 (1999) problem. I will show how Genetic Algorithms, in combination with efficient (``Order N'') solutions to the Pseudopotential Schrodinger equation allow us to investigate astronomical spaces of atomic configurations in search of the structure with a target physical property. Only a small fraction of all ($\sim $ 10**14 in our case) configurations need to be examined. Physical properties are either calculated on-the-fly (if it's easy), or first ``Cluster-Expanded'' (if the theory is difficult). I will illustrate this Inverse Band Structure approach for (a) Design of required band-gaps in semiconductor superlattices; (b) architecture of impurity --clusters with desired optical properties (PRL 97, 046401, 2006) (c) search for configuration of magnetic ions in semiconductors that maximize the ferromagnetic Curie temperature (PRL, 97, 047202, 2006).   

Computational Thermoelectrics.

For several decades the thermoelectric properties of materials have attracted moderate interest in the solid state physics community. It was believed that bulk materials such as Bi2Te3 have come close to the maximum attainable figure of merit ZT. The resulting efficiency for energy conversion and other applications was seen as insufficient to spur more detailed theoretical studies. In the 80's and 90's the expansion of material fabrication technologies allowing for the fabrication of nano-patterned systems and the theoretical prediction that ZT can reach values in nanostructures far larger than in bulk materials have spurred a renewed theoretical interest in thermoelectric properties. This presentation will offer a review of the computational efforts undertaken to achieve a quantitative description of the thermoelectric properties of nano-patterned materials. Evaluating ZT requires the computation of the electronic contribution to the electrical and thermal conductivities and the Seebeck coefficient, and the lattice contribution to the thermal conductivity. A brief overview of the methods mostly used in evaluating these transport properties will be given. Semiclassical approaches relying on a solution of the Boltzmann transport equation for both electrons and phonons will be described as well as Green-Kubo and non-equilibrium transport techniques. Examples will be given for bulk semiconductors such as silicon, germanium and bismuth telluride. Atomic level calculations of the thermoelectric properties for semiconductor nanostructures will also be presented. The lattice contribution to the thermal conductivity is of particular importance to maximize ZT for semiconductors. Beside the Boltzmann transport equation approach, other methods use the fluctuation-dissipation theorem or non-equilibrium molecular dynamics. Numerical results will be shown for bulk materials and nanostructures. Concluding remarks will offer an estimate of the currently achievable accuracy on the prediction of thermoelectric properties and will outline the path for improvements.   

Session A7: Unconventional Transport and Magnetic Properties of Hexaborides

Magneto-optical evidence of double exchange in a percolating lattice

Because of the potential technological applications, materials exhibiting colossal magnetoresistive (CMR) effects are of high current interest in solid state physics. Europium hexaboride ($EuB_{6}$) and the well known manganites, for which the onset of ferromagnetism is accompanied by a dramatic reduction of the electrical resistivity, are primary examples, that have intensively been studied. We concentrate on the series of cubic $Eu_{1-x}Ca_{x}B_{6}$, which displays interesting correlations between magnetic, transport and optical properties. Substituting $Eu$ by $Ca$ in ferromagnetic $EuB_6$ leads to a percolation limited magnetic ordering. We present and discuss magneto- optical data of the $Eu_{1-x}Ca_{x}B_6$ series, based on measurements of the reflectivity $R(\omega)$ from the far infrared up to the ultraviolet, as a function of temperature and magnetic field. Via the Kramers-Kronig transformation of $R$ we extract the complete absorption spectra of samples with different values of $x$. The change of the spectral weight in the Drude component by increasing the magnetic field agrees with a scenario based on the double exchange model, and suggests a crossover from a ferromagnetic metal to a ferromagnetic Anderson insulator upon increasing $Ca$-content at low temperatures. This work appeared in Phys. Rev. Lett. 96, 016403 (2006)   

Disentangling Surface and Bulk Electronic Structures of EuB$_6$

By means of angle-resolved photoemission, the surface and bulk electronic structures of UHV-cleaved ferromagnetic hexaboride EuB$_6$ have been disentangled to reveal both a variable density surface 2D electron gas and an exchange splitting of the boron p-bands below the bulk ferromagnetic ordering temperature of the localized Eu 4f moments. Surface-slab LDA calculations find (i) a distinct surface-related band residing in the bulk-projected bandgap along X-M, (ii) a 2D X-point electron pocket, and (iii) energy-shifted surface-atom Eu 4f states resulting from an electric dipole at the highly ionic surface. These surface-related features manifest in experiment as time dependent effects, the filling of a small X-point electron pocket of Eu 4d-character, correlated to changes in the overall B-p band structure and a splitting of the Eu 4f states. The time-dependent behavior is explained in terms of clustering of mobile surface Eu atoms on the freshly cleaved surface. Understanding and control of these surface effects then allows the bulk electronic structure to be discerned, including a pinning of the Fermi level to the bulk X-point valence band maximum and the magnitude of the valence band exchange splitting below T$_c$.   

Double exchange model and magnetic polarons in Eu-based hexaborides

In this presentation, important details of the Double Exchange model at low densities and their pertinence to the physics of ferromagnetic hexaborides will be addressed. After a brief survey of some key experiments and signatures of these compounds, it will be shown that in such systems, where itinerant electrons at extremely reduced densities interact with a dense local spin subsystem, effects of Anderson localization are paramount, providing a consistent picture of the remarkable and unusual response of materials like Eu$_{1-x}$Ca$_x$B$_6$ in magnetic, optical and transport measurements. In this context we will show how one can understand the blue shift in the plasma frequency, the enhancement of carrier density and the CMR effect upon entering the ferromagnetic phase of EuB$_6$ as effects stemming from Anderson localization mechanisms. We will provide an interpretation for the metal insulator transition that occurs upon doping, under the light of recent magneto-optical experiments. In addition, the region of stability of magnetic polarons in the low density Double Exchange Model is discussed, and shown to be consistent with experimental hints of a polaronic phase mediating the PM-FM transition in the vicinity of T$_C$.   

Magnetic polarons in EuB$_6$ and other low carrier density ferromagnets.

Magnetic polarons are formed in systems with low carrier density and large local exchange coupling between the spin background and the spin of the carrier. Magnetic polarons can be free, as in manganese pyrochlores, or bound by Coulomb interaction to impurities in the lattice, as in diluted magnetic semiconductors. EuB$_6$ is a likely candidate for the formation of magnetic polarons as revealed by spin flip Raman scattering and muon-spin rotation measurements. I will give a general perspective on magnetic polarons with special emphasis on the evaluation of the experimental evidence for magnetic polarons in EuB$_6$[1]. This work was supported by Churchill College (University of Cambridge), LPS, and NSF. \newline \newline [1] M.J. Calderon, L.G.L. Wegener, and P.B. Littlewood, Physical Review B 70, 092408 (2004).   

Session A8: Focus Session: Novel Superconductors I: Doping and Impurities in MgB2

$MgB_2$: doped or with pressure, four systems same behaviour

$MgB_2$, the intermediate $T_c$ superconductor, can be doped with carbon, aluminium and scandium and it has been also studied experimentally under pressure, in these four cases $T_c$ diminishes. In previous studies we have shown, with electronic structure calculations, that when $Mg$ is substituted with $Sc$ [$(Mg,Sc)B_2$] the drop of $T_c$ can be associated with the loss of electrical anisotropy of the $\sigma$-bands [1]. When $Mg$ is substituted with $Al$ $[(Mg,Al)B_2]$ or $B$ is substituted with $C$ [$Mg(B,C)_2$] then, with a change of doping scale, a common $T_c$ curve is obtained for both systems, comparison with the $\sigma$-$DOS$ shows that $T_c$ drop is due to $\sigma$-band-filling and to $\sigma$-band anisotropy loss [2]. In further studies we have found that both these features, $\sigma$-band anisotropy reduction and the loss of $\sigma$-band-carriers, can be associated to the drop of $T_c$ in these three doped systems [$Mg(B,C)_2$, $Mg,Al)B_2$ and $(Mg,Sc)B_2$] and in $MgB_2$ under pressure. All these studies show that: (a) with a change of doping scale then $T_c$ in both the C and Al doped systems follows the same curve which is very close to the $\sigma$-DOS; (b) for the four systems both the $\sigma$-band anisotropy and the number of $\sigma$-carriers are two fundamental physical properties of the relatively high $T_c$ in $MgB_2$. [1] J. Phys.: Condens. Matter 18 (2006) 1403-1412 [2] cond-mat/0606019   

First principles study of the electronic structure and phonon properties for Al and C-doped MgB$_2$

We have studied the structural, electronic and lattice dynamic properties of the superconducting alloys Al and C-doped MgB$_2$ within the framework of density functional perturbation theory, using a mixed-basis pseudopotential method and the virtual crystal approximation (VCA) for modeling the alloy. For both systems the structural parameters were determined on the following ranges, 0$\leq$x$\leq$1 for Mg$_{1-x}$Al$_x$B$_2$ and 0$\leq$x$\leq$0.4 for MgB$_{2(1-x)}$C$_{2x}$, finding a very good agreement between the calculated structural parameters and experimental data. The complete phonon dispersion curves were calculated for selected Al and C-concentrations. The calculated phonon bands for MgB$_2$ using the LDA and GGA approximations are compared in detail with the experimental data available in the literature. The evolution of the full-dispersion curves are analyzed as a function of Al and C-concentration, specially the E$_{2g}$-phonon mode frequency. In agreement with the experimental observed behavior, we find strong renormalization of the E$_{2g}$-mode for both Al and C-doped MgB$_2$. Additionally, we found a strong reduction of the E$_{2g}$-band dispersion with the filling of the $\sigma$-band. This research was supported by CONACYT, M\'{e}xico under Grant No. 43830-F.   

Carbon and Aluminum Doping in MgB$_{2}$. Similarities and differences

Both carbon and aluminum dope the magnesium diboride by one extra electron which leads to filling of the most important $\sigma $ band and decreasing of the transition temperature. The point-contact spectroscopy in magnetic field is used to address the evolution of two superconducting energy gaps and density of states in the doped systems with $T_{c}$'s from 39 to 22 K. The similarities and differences in the inferred \textit{interband} and \textit{intraband} scatterings introduced by these two substitutions are discussed. It is shown that the two gap superconductivity is retained in all studied cases. The carbon doping is effective in increasing of the intraband scattering mainly in the $\pi $ band. This leads to important enhancement of the upper critical field. The approaching of two gaps is stronger in the Al-doped systems but the interband scattering is yet not large enough to merge two gaps. The full merging can be expected only for higher dopings, in the samples with $T_{c}$'s below 10 -- 15 K. Al substitution does not affect strongly the intraband scattering leaving the samples in the clean limit.   

Carbon Doped MgB2 Thin Films using TMB

The most effective method to enhance the upper critical field in MgB2 is through carbon doping. In the case of thin films, ``alloying'' with carbon has resulted in enhanced Hc2 values estimated to be as high as 70 T for H parallel to ab and 40 T for H perpendicular ab [1]. ``Alloying'' refers to the in-situ Hybrid Physical-Chemical Vapor Deposition (HPCVD) of carbon containing MgB2 films using (C5H5)2Mg as the carbon source. While these films exhibit enhanced Hc2 values, there are amorphous boron- carbon phases in the grain boundaries that reduce the cross section area for superconducting current. We present here the results of our attempts to make more homogeneously carbon doped thin films using gaseuous trimethyl-boron (TMB) as the carbon source. Initial results indicate different behavior upon carbon doping using TMB from carbon-alloying. The microstructures and upper critical fields of the carbon doped films using TMB and carbon alloyed films will be compared. [1] V. Braccini et al., Phys. Rev. B 71 (2005) 012504. [2] A.V. Pogrebnyakov et al., Appl. Phys. Lett 85 (2004) 2017.   

Disorder in carbon-doped HPCVD MgB$_{2}$ thin films

Carbon-doped MgB$_{2}$ films prepared by hybrid physical-chemical vapor deposition have the highest $H_{c2}$ ($\sim $70 T at 0 K for H parallel to \textit{ab} plane) of all MgB$_{2}$ materials. We have characterized the nanoscale structure and chemistry of one such film by TEM and STEM. The C concentration in the Mg(B$_{1-x}$C$_{x})_{2}$ grains from EELS is not dramatically higher than that of C-doped bulk MgB$_{2}$, so doping does not explain the high $H_{c2}$. Instead, the doped film has a variety of forms of structural disorder at length scales down to 5 nm, which may be sufficient to explain the $H_{c2}$ of these films. These include MgB$_{2}$ domains with a 30 degree rotation about the $c$-axis, small angle rotations about $c$-axis, and a small tilt of the $c$-axis. There are also amorphous, C-rich regions between some MgB$_{2}$ domains. The amorphous phase comes from the oversupply of C during growth, which may also cause the other disorder by interrupting epitaxial film growth. This work is supported by the FRG on MgB$_{2}$, NSF DMR-0514592.   

Correlated enhancement of H$_{c2}$ and J$_{c}$ in carbon nanotube-doped MgB$_{2}$.

We achieved simultaneous enhancement of upper critical magnetic field, H$_{c2}$, and critical current density, J$_{c}$, by doping polycrystalline samples of MgB$_{2}$ with double-wall carbon nanotubes (DWCNT), a source of atomic carbon. The optimum DWCNT content from the point of view of the J$_{c}$ is in the range 2.5-10{\%} at depending on field and temperature. Record values for H$_{c2}$ (4K) = 41.9 T (with extrapolated H$_{c2}$(0) $\approx $ 44.4 T) are reached in a bulk sample with 10{\%} at DWCNT content. The measured H$_{c2}$ vs T in all samples are successfully~described using a theoretical model for a two-gap superconductor in the dirty limit first proposed by Gurevich \textit{et al}.   

Point-Contact Andreev-Reflection Spectroscopy in Neutron-Irradiated Mg$^{11}$B$_2$

We report recent results of point-contact spectroscopy (PCS) in Mg$^{11}$B$_2$ polycrystalline samples irradiated with neutrons at different fluences up to $\Phi$ = 1.4 $\cdot$ 10$^ {20}$ cm$^{-2}$. A strong depression of the bulk critical temperature $T_c$ down to about 8.7 K was observed after irradiation. The gaps $\Delta_{\pi}$ and $\Delta_{\sigma}$ were obtained from the experimental Andreev-reflection conductance curves through a two-band Blonder-Tinkham-Klapwijk fit and reported as a function of the Andreev critical temperature of the junctions, $T_c^A$. The resulting $\Delta_{\pi}$($T_c^A$) and $\Delta_{\sigma}$($T_c^A$) curves clearly show a merging of the gaps when $T_c^A <$ 9 K, which perfectly confirms the findings of recent specific-heat measurements in the same samples. ``Anomalous'' contacts with $T_c^A > T_c$ and a different dependence of the gaps on $T_c^A$ with respect to ``standard'' ones were obtained in samples irradiated at the highest fluences. The possible origin of these anomalies is discussed in terms of local current-induced annealing and/or nanoscale inhomogeneities - indeed observed by STM in the most irradiated samples.   

Reflection of two band properties in the magnetic penetration depth of ion irradiated MgB$_{2}$

Multiband superconductivity in MgB$_{2}$ has wide ranging ramifications for its transport characteristics. Using ion irradiation we have previously reported that by carefully choosing the type and density of defects, it is possible to control the inter and intra band scattering between the 2D $\sigma $ and isotropic $\pi $ bands of MgB$_{2}$. Here we report on the reflection of this defect induced modified scattering mechanism on the Meissner and mixed state penetration depth as a function of temperature, dc magnetic field, and defect density. The measurements are carried out using an ultrastable rf tunnel diode oscillator. The samples include unirradiated and those irradiated with 200 MeV Au$^{15+}$ and 100 MeV Si$^{8+}$. The fits to the superfluid density over the entire temperature range give information about the evolution of two gaps with progressive dirtying. From the mixed state measurements the bulk pinning force constant and flux flow resistivity are estimated. We also compare the superconducting properties of MgB$_{2}$ with 2H-NbSe$_{2}$ (T$_{c}$ = 7.3 K).   

Disorder induced evolution of two energy gaps in MgB2

We study disorder effect on MgB2 superconductivity using the two band model by Suhl, Matthias, and Walker. We stress the importance of the Cooper pair size effect in the response of the BCS superconductor to the perturbation: the bounded Cooper pairs see the impurities within the range of the coherence length. This effect will undermine the initial decrease of the Tc and the big energy gap due to disorder, until the resistance ratio reaches about $\sim $3. For the resistance ratio less than 3, weak localization starts to decouple electrons and phonons, leading to the significant decrease of both the Tc and the big gap. In particular, we trace the evolution of two energy gaps of MgB2 as a function of disorder. Estimating the inter-band scattering rate from the experimental data, we compare our calculations with experiments. We also calculate the transition temperature, Tc as a function of the resistance ratio.   

Effects of Magnetic and Non-Magnetic Impurities in MgB$_2$: A Point-Contact Study of Single Crystals

We studied the effects of chemical substitutions, either magnetic (Mn) or non-magnetic (Al, C), on the energy gaps of MgB$_2$ by means of directional point-contact spectroscopy (PCS) in state-of-the-art single crystals. Here we discuss two noticeable cases, i.e. Mg$_{1-x}$Mn$_{x}$B$_2$ crystals with $x$ up to 0.015, and Mg$_{1-x}$Al$_x$B$_2$ crystals with $x$ up to 0.32. In both cases, we used a pressure-less PCS technique in which a thin Au wire is put in contact with the side surface of the crystal by means of a small drop of Ag paint. The gaps $\Delta_{\sigma}$ and $\Delta_{\pi}$ were obtained through a two-band Blonder-Tinkham-Klapwijk (BTK) fit of the Andreev-reflection conductance curves of the resulting contacts. Both in Mn- and Al-doped MgB$_2$, the gaps decrease on decreasing the critical temperature of the contacts, $T_{c}^{A}$ (at which the Andreev-reflection structures disappear), but remain clearly distinct down to $T_{c}^{A}\simeq 10$ K. Once analysed within the two-band Eliashberg theory, the $\Delta_{\sigma}$ and $\Delta_{\pi}$ vs. $T_{c}^{A}$ curves give information about the effects of Mn and Al substitutions on the different scattering channels (interband and intraband, magnetic or non-magnetic). It turns out that the main effect of Mn is to increase the spin-flip scattering within the $\sigma$ band (with smaller contributions from either the $\pi-\pi$ or the $\sigma-\pi$ channels), as also confirmed by first-principle bandstructure calculations. In the case of Al, the band-filling effect is largely dominant. An increase in non-magnetic interband scattering is possible, but small enough not to give rise to gap merging. \newline \newline In collaboration with G.A. Ummarino, A. Calzolari, M. Tortello, D. Delaude, R.S. Gonnelli, Dipartimento di Fisica and CNISM, Politecnico di Torino, Italy; V.A. Stepanov, P.N. Lebedev Physical Institute, RAS, Moscow, Russia; N.D. Zhigadlo, J. Karpinski, Laboratory for Solid State Physics, ETHZ, Zurich, Switzerland; and S. Massidda, Dipartimento di Fisica, Universit\`{a} di Cagliari, Italy.   

Session A9: Superconductivity: Thermodynamic and Doping Effects

Investigation of the M\"{o}ssbauer spectrum of RuSr$_2$GdCu$_2$O$_8$ as a function of Temperature shows that there is only one type Ru site

A sample of RuSr$_2$GdCu$_2$O$_8$ was prepared with enriched $^{99}$Ru which allows us to study the temperature dependence of the M\"{o}ssbauer spectrum up 145K. The sample magnetically orders at 138K and has a transition to superconductivity at 8.7K with an onset at $\sim$13K. The spectrum at 4.2K was fit with a single-site fit. The hyperfine field is 59.4K with isomer shift which indicates that the charge state of the Ru ion is close to +5. The strength of the electric quadrupole interaction is 0.36 mm/sec with $\eta=0.2$. This spectrum is essentially identical to that found for a sample prepared with the natural $^{99}$Ru abundance. At 146K, above the magnetic transition temperature, the spectrum is fit with a pure electric quadrupole interaction of the same magnitude as at 4.2K with the same isomer shift.   

Magnetic Penetration Depth in Overdoped Tl-2201 Superconductors

Studies of the magnetic penetration depth $\lambda_{ab}$ {\it via\/} the $\mu^+$SR lineshape in the vortex state has revealed a great deal about {\sl under\/}doped cuprate superconductors, including the original confirmation of $d$-wave superconductivity. However, {\sl over\/}doped cuprates have been neglected, partly due to the difficulty of doping sufficiently to decrease $T_c$, and partly because the overdoped materials are thought to be ``ordinary Fermi liquid'' superconductors, about which many presume we already know everything. In the belief that we may {\sl not\/} know everything about these materials, the UBC group has set out to grow high quality crystals of Tl$_2$Ba$_2$CuO$_{6+\delta}$ (Tl-2201), which can be made {\sl very\/} overdoped, to the point of $T_c \to 0$. We have now used $\mu^+$SR lineshape studies to measure $\lambda_{ab}$ as a function of $T$ and $H$ for crystal mosaics with $T_c$'s of 72, 60 and 46 K. As expected, $\lambda_{ab}^{-2}(T=0)$ continues to increase with doping beyond optimal doping, but then decreases again with higher doping. We also find a strong dependence on the applied field $H$. The low-$T$ behavior of $\lambda_{ab}^{-2}(T)$ is again strongly linear, as expected for a $d$-wave superconductor.   

Nodeless $d$-wave superconducting pairing in antiferromagnetic underdoped Pr$_{2-x}$Ce$_x$CuO$_{4-\delta}$

Experimental results concerning the superconducting pairing symmetry have been contradictory in electron doped cuprates. In particular, penetration depth measurements appear to indicate the presence of an s-wave and/or a d-wave gap in different doping regimes [1]. Here, we discuss the doping and $T$-dependence of the penetration depth in Pr$_{2-x}$Ce$_x$CuO$_{4-\delta}$ (PCCO) and provide a natural explanation for the occurrence of a nodeless superconducting gap and a nonmonotonic gap variation with maximum gap near hot-spots in the underdoped system [2]. Despite the presence of a $d_{x^2-y^2}$ pairing gap, we find a crossover of the low-$T$ penetration depth from a nodeless behavior in the underdoped case to a linear-in-T behavior (characteristic of $d$-wave) as doping increases and a nodal Fermi surface pocket emerges. The present results support the coexistence of antiferromagnetism and superconductivity in the electron doped cuprates [3]. Work supported in part by the USDOE. \newline [1] M.-S. Kim {\it {et. al.,}} PRL, {\bf{91}}, 087001 (2003). \newline [2] T. Das {\it {et. al.,}} PRB, {\bf{74}}, 020506(R) (2006). \newline [3] Y. Dagan {\it {et. al.,}} PRL, {\bf{92}}, 167001 (2004).   

Small T$^{-1}_{1}$ peak near T$_{c}$ in unconventional BCS superconductors

It is usually believed that a coherence peak just below T$_{c}$ in the nuclear spin lattice relaxation rate T$_{1}^{-1}$ in superconducting materials is a signature of conventional s-wave pairing. We demonstrate that {\bf any} unconventional superconductor obeying BCS pure-case weak-coupling theory should show a small T$_{1}^{-1}$ coherence peak near T$_{c}$ ,generally with a height between 3 and 15 percent greater than the value at T$_{c}$. It is due to impurity scattering, magnetic effects, gap anisotropy and other effects that this peak has not been commonly observed.   

A Practical Algorithm for Fitting Magnetic Moment Data for Superconducting Thin Films and Multilayers in Parallel Magnetic Fields

Superconducting thin films and multilayers in DC magnetic fields applied nearly parallel to the film plane can yield spurious magnetization data dominated by extreme shape anisotropy and strong diamagnetism of a confined supercurrent. This situation may lead to highly reproducible discontinuities or apparently random ``instabilities'' when measured with SQUID magnetometers such as the ubiquitous Quantum Design MPMS, which requires samples to behave as an ideal point-dipole. We have devised an accurate multipole fitting routine for the raw SQUID voltmeter output that eliminates spurious contributions to the axial dipole moment from transverse (off-axis dipole) or non-point-dipole axial magnetizations. We demonstrate this method as applied to Nb/Ni multilayers and Nb thin films and foils of various thicknesses that probe the influence of supercurrent confinement on the non-dipole response.   

Magnetic Instabilities along the Superconducting Phase Boundary of Nb/Ni Multilayers

We report vibrating reed and SQUID magnetometer data that exhibit prominent cusps or oscillations of the SC onset temperature, $\vert \Delta $T$_{C}$(H)$\vert \quad \approx $ 0.01 to 0.7 K, for a [Nb(23nm)/Ni(5nm)]$_{5}$ multilayer (ML) in DC magnetic fields applied nearly parallel to the ML plane. The vibrating reed data exhibit additional structures below T$_{C}$ that may mark multiple SC transitions or vortex lattice rearrangements within the ML. This striking behavior would then pose new challenges for theoretical and experimental investigations of SC/FM interfaces that involve ``pi phase shifts'' of the SC order parameter and exotic (``LOFF'') pairing states. Alternatively, the anomalies may signal dynamical instabilities within a confined, strongly anisotropic Abrikosov vortex lattice.   

X-ray Structural Studies of HgBa$_2$CuO$_{4+\delta}$

In recent years, there has been mounting evidence for electronic and structural inhomogeneities in the cuprate high-temperature superconductors (HTSC). From stripe phases found in lanthanum-based cuprates to the oxygen-order-driven lattice modulations in YBa$_2$Cu$_3$O$_{7-\delta}$ and to the nanoscale electronic density-of-states ``patches" in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ and other cuprates, these inhomogeneities appear to have significant effects on the electronic, transport, and spectroscopic properties of these systems. Of all the high-T$_\textrm{c}$ materials, HgBa$_2$CuO$_{4+\delta}$ has the highest transition temperature among single-layer compounds and one of the simplest structures. Consequently, it may be the perfect candidate system to help separate the effects of extrinsic structural inhomogeneities from those that are universal and intrinsic to HTSC. To begin to address this issue, we have grown sizable, high-quality crystals of HgBa$_2$CuO$_{4+\delta}$ and carried out two structural studies: a diffuse x-ray scattering experiment, showing evidence for short-range structural displacement modulations, and a polarized extended x-ray absorption fine-structure (EXAFS) experiment on the temperature-dependent local structure around the copper and mercury atoms.   

Microscopic origin of the oxygen reduction process and its impact on superconductivity in electron-doped copper oxides

The oxygen reduction process is one of the unique processes in the electron-doped high temperature copper oxides. Superconductivity is induced when the electron-doped as grown samples are annealed in the oxygen reduced atmosphere. Many experiments show that a small amount of oxygen reduction affects the mobility of charge carriers and it suppresses the long range antiferromagnetic order especially at high doping level. However, the detailed microscopic process of oxygen reduction and its effect on superconductivity are still unknown. Our x-ray and neutron scattering data, combined with chemical and thermo-gravimetric analysis measurements in the electron-doped Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4}$ show that the microscopic process of oxygen reduction is to remove Cu deficiencies in the as-grown materials and to create oxygen vacancies in the stoichiometric CuO$_{2}$. Our results indicate that the role of annealing is to repair disorder in the CuO$_{2}$ plane induced by Cu deficiencies and to provide itinerant electrons for superconductivity.   

X-ray diffuse scattering experiments from bismuth based high T$_c$ superconductors

A detailed X-ray diffuse scattering study of the recently found two dimensional (2D) displacive short range order (SRO) superstructure, with doubled periodicity along the orthorhombic a direction from the high T$_c$ superconductors Bi$_2$Sr$_2 $CaCu$_2$O$_{8+\delta}$(BISCO-2212) is reported. The investigation has been extended to high and low temperatures for optimally doped crystals, to crystals with different doping levels and to the one layer compound Bi$_2$Sr$_2$CaCuO$_ {6+\delta}$ (Bi-2201). The most striking feature is that both, the intensity of the diffuse scattering and the extent of the 2DSRO vary with doping as the critical temperature, T$_c$. These findings show that these short range ordering features are of importance for a better understanding of high Tc materials, at least those from the BISCO family.   

Low-temperature Specific Heat in underdoped YBa$_{2}$Cu$_{3}$O$_{7}$ Single Crystals

One single crystal of YBa$_{2}$Cu$_{3}$O$_{7}$ has been post-annealed into six different doping levels in the underdoped region with T$_{c}$ ranging from 30 K to 92 K. The low temperature specific heat has been measured on these samples down to 100 mK with magnetic field applied along c-axis and a-b plane. By subtracting the specific heat measured in these two different field directions, we have successfully removed the Schottky anomaly and obtained the field induced increase of the specific heat coefficient due to Doppler shift effect in d-wave superconductors. It is found that even for the very underdoped sample (T$_{c}$=30 K), the quasiparticle density of states is always increased by applying a magnetic field. This is similar to our earlier results in very underdoped LaSrCuO single crystals leading to the expectation for a Fermi arc ground state for the pseudogap state. In addition, the field increased part $\Delta \gamma $=AH$^{0.5}$ becomes smaller towards underdoping, indicating a larger nodal gap slope. The implications of our results on the mechanism of cuprate superconductors are discussed based on the Fermi arc picture of normal state. The YBCO single crystal was provided by Prof. Xin Yao at Shanghai Jiaotong University, China. .   

Thermodynamic properties of cuprate superconductors: Singularities and Pseudogaps.

We have calculated the entropy and superfluid density of Bi-2212 from an ARPES-derived rigid energy dispersion and a model for the normal-state pseudogap. Their detailed doping and temperature dependence is found to closely mimic the experimentally measured data, thus indirectly validating the ARPES data. The doping level at which the Fermi level crosses a van Hove singularity (vHs) is determined and found to agree with that inferred from ARPES. The superfluid density is found to be linear in $T$ at the vHs crossing. Surprisingly, the doping dependence of $T_{c}$ seems to be unaffected by crossing the singularity.   

Confined vortex loops in superconductors with a magnetic core

A magnetic moment inside an extreme type II superconductor gives rise to confined vortex states in its neighborhood. We show how the presence of such states can be tracked down in the I-V characteristic curve, thus providing a simple method to their detection. The Lorentz force causes their growth and periodic evolution, passing through a long range ordered state (bulk) or an external vortex pair state (sub-micron particle). For a small magnetic moment there are exactly three confined vortex loops whereas for a large more elaborate vortex arrangements arise are possible. Their onset from the upper critical field core in sets of threes is proved to be energetically favorable over the growth of just one or two confined vortex loops independently of boundary conditions. All our results are derived in the context of the time-dependent and of the time-independent Ginzburg-Landau theory applied to a superconductor with periodic (bulk) and superconductor-insulator (sub-micron particle) boundary conditions, using three independent numerical methods.   

Session A10: Superconductivity: Electronic and Thermal Transport Properties

High Field Hall Effect and Resistivity in High-$T_{c}$ La$_{2-x}$Sr$_{x}$CuO$_{4}$

Hall effect and resistivity measurements were performed in a set of La$_{2-x}$Sr$_{x}$CuO$_{4}$ thin film samples in magnetic field up to 60T. The Sr doping, x, was varied between 0.08 and 0.22. The resistivity and Hall voltage were measured simultaneously using digital lockin technique developed at NHMFL. We find a pronounced minimum in the doping dependence of the Hall coefficient, suggesting a common phenomenon which is generic for high temperature superconductors. This Hall effect anomaly is most readily associated with a phase transition near optimal doping where superconductivity is most robust.   

In-plane resistivity and Hall effect data of La$_{2-x}$Sr$_{x}$CuO$_{4}$ in high magnetic fields

The effects of stoichiometry (Sr concentration in La$_{2-x}$Sr$_{x}$CuO$_{4 }$- LSCO) are of extreme interest in exploring the phase space of high-temperature superconductivity (HTS). Carrier doping in LSCO is determined by the Sr concentration rather than non-stoichiometric oxygen, thus controlling the carrier concentration in LSCO tends to be easier than in the other HTS cuprates. Nevertheless, precise control of Sr at a precision greater than 0.005 is extremely difficult using existing single crystal growth techniques. We use our unique MBE growth chamber to grow combinatorial thin films of LSCO with a uniform gradient of Sr concentration across a single substrate. Intense magnetic fields suppress superconductivity, revealing the underlying normal state to temperatures below 0.3K. We report the Hall effect and resistivity with an extremely fine $\sim $x=0.0002 Sr resolution in fields up to 60T.   

Low-temperature specific heat and thermal Hall conductivity in a vortex state of d-wave superconductors

We analyze the mixed state of $d$-wave lattice superconductors focusing on the quasiparticle contribution to the specific heat and the thermal Hall conductivity at intermediate magnetic fields $H_{c1}\ll H \ll H_{c2}$. In the ultra-low temperature regime $T\ll T_0\approx v_D^2/(v_F l)$ the specific heat follows a general scaling form $C[T, H=hc/el^2] =(T/v_F l) \Phi[ v_F/(Tl), v_F/v_D, k_F l]$. In this regime the specific heat exhibits oscillatory behavior as a $2\pi$-periodic function of $k_F l$: in general it has an activated form $C\propto \exp(-\Delta_m/T)$ except for a discrete set of $k_Fl$ where $\Delta_m=0$ and $C\propto T^2$. At temperatures $T_0\ll T\ll \Delta$, the $k_Fl$-oscillations become unobservable due to thermal broadening and the Simon-Lee scaling is recovered. The results of the analysis of the thermal Hall conductivity are similar: in particular, at the lowest temperatures, $\kappa_{xy}$ is an oscillating $2\pi$-periodic function of $k_Fl$. We calculate the scaling functions numerically and compare our results with the existing experimental data on the specific heat and thermal Hall conductivity.   

The Hall Number, Optical Sum Rule and Carrier Density for the $t-t'-J$ Model

Mott Hubbard systems, epitomizing strong correlations and a sensitivity to half filling, display striking departures from band theory for many measurables. E.g. consider two quantities; the Hall constant $R_H$ and the optical conductivity sum rule $\omega_P^2/8$. These are often inverted to give the carrier densities $n_H\equiv 1/ q_e c R_H$ and $n_{Op}=\frac{m}{ 4 \pi q_e^2} \omega_P^2$. There is considerable difficulty in reconciling these with $x$, the ``chemical'' estimate of density in many High $T_c$ systems[1]. We have argued previously[2] that the Hall constant is a manybody object, that need not scale simply with $x$. In this work, we compute the variables $n_H$ and $n_{Op}$ for a $t-t'-J$ model by using exact diagonalization of small clusters and different dopings $x$. We compute the Kubo formulas exactly for small clusters, and also the high frequency Hall constant for even larger systems, and obtain a strong dependence of these variables on the ratio $t'/t$. We also comment on the departure from Luttinger's theorem for the Fermi surface for these clusters, defining the same from the tower of excited states for a given wave vector for an added particle or hole. [1] W. Padilla {\em et.al.}, ~Phys. Rev. {\bf B 72}, 060511(2005). [2] B. S. Shastry, B. I. Shraiman and R. R. P. Singh, Phys. Rev. Lett.{\bf 70}, 2004(1993).   

Nernst effect as a probe of superconducting fluctuations in Nb$_{0.15}$Si$_{0.85}$

We present a study of the Nernst effect in thin films of the amorphous superconductor Nb$_{0.15}$Si$_{0.85}$ . A finite Nernst signal was resolved at temperatures well above T$_{c}$ and at relatively high magnetic fields (1). In the zero-field limit and close to T$_{c}$, our results are in very good agreement with a simple relation derived from the theory by Ussishkin, Sondhi and Huse (2) for a two-dimensional superconductor. According to the theory, the magnitude of the Nernst signal generated by the fluctuating Cooper pairs depends only on the superconducting coherence length $\xi$. Far above T$_{c}$ and/or in presence of a finite magnetic field, a departure from this relation is observed. Yet, even in this regime, the amplitude of the Nernst coefficient depends on a single length scale set by $\xi$ and by the magnetic length $l_{B}$. This observation allows to establish a phenomenological relation for the Nernst coefficient, for all magnetic fields and temperatures above T$_{c}$, which depends only on the size of the superconducting fluctuations set by $\xi$ and/or $\l_{B}$.\\ (1) A. Pourret \emph{et al.}, Nature Physics \textbf{2}, 683 - 686 (2006)\\ (2) I. Ussishkin, S. L. Sondhi and D. A. Huse, Phys. Rev. Lett. \textbf{89}, 287001 (2002)   

On the heat current in the magnetic field: Nernst-Ettingshausen effect above the superconducting transition

For maintaining gauge invariance in a magnetic field, the heat current operator should include the magnetic term. Taking this term into account, we revised calculations of the Nernst-Ettingshausen effect above the superconducting transition. We found that the fluctuations of the modulus of the order parameter do not change the particle-hole asymmetry (PHA) of the thermomagnetic effects. As in the normal state, the thermomagnetic effects in the fluctuation region are proportional to the square of PHA and, therefore, small. Magnetization currents in the electric field contribute to the charge and energy transfer, but not to the heat current. Only in this way, one can obtain the Nernst and Ettingshausen coefficients that satisfy to the Onsager relation Large Nernst effect observed in the high-temperature cuprates requires vortex-like excitations due to the phase fluctuations, which are beyond the Gaussian-fluctuation theory.   

Nernst effect and diamagnetism in a vortex liquid

When a superconductor is warmed above its critical temperature $T_c$, superconductivity is destroyed by fluctuations in the order parameter. These fluctuations are seen in a variety of experimental probes, including conductivity, diamagnetism, and the Nernst effect -- the thermoelectric analogue of the Hall effect. In this talk we will discuss a regime in which superconductivity is destroyed by phase fluctuations arising from a dilute liquid of mobile vortices. The local superconducting correlations in this state lead to unusual properties, which are theoretically captured by a thermally fluctuating XY model in which amplitude fluctuations remain effectively frozen. We find that the Nernst effect and diamagnetic response differ dramatically from those arising from Gaussian fluctuations -- in particular, a more rapid decay with temperature is obtained. We predict a rapid onset of Nernst effect at a temperature $T_{\rm onset}$, and show that this scale tracks $T_c$ rather than the pairing temperature. We predict a close quantitative connection with diamagnetism -- the ratio of magnetization to transverse thermoelectric conductivity $\alpha_{xy}$ reaches a universal value at high temperatures. We compare our results to Nernst effect measurements on the underdoped cuprates, and interpret these results in terms of a dilute vortex liquid over a fairly wide temperature range above $T_c$.   

Anomalous quasiparticle thermal transport in the superconducting state of ultra pure URu$_2$Si$_2$ single crystals

In heavy fermion superconductor URu$_2$Si$_2$, although it is believed that superconductivity in this material ($T_c\sim1.5$ K) is unconventional, details of the superconducting gap structure are still unknown. To investigate the quasiparticle transport in the superconducting state of URu$_2$Si$_2$, the thermal conductivity $\kappa$ is measured in ultra pure single crystals with residual resistivity ratio $\sim600$. In zero field, $\kappa/T$ shows a steep increase below $T_c$, indicating that the quasiparticle mean free path is strongly enhanced in the superconducting state. A finite residual term of $\kappa/T$ as $T\rightarrow0$ is clearly resolved, together with a $T^2$ dependence at very low temperatures. With applying magnetic field, thermal conductivity grows rapidly at low magnetic fields, and exhibits a $\sqrt{H}$-dependence. These results strongly indicate a presence of line nodes in the superconducting gap function. We found that $\kappa/T$ exhibits a sudden drop at upper critical field, which has never been observed in any superconductors. We discuss this unusual behavior of thermal conductivity in the context of anomalously large $\omega_c\tau(>1)$ and giant magnetoresistance observed in this material.   

Low Temperature Heat Transport in the superconducting skutterudite PrOs$_4$Sb$_{12}$: Evidence for nodes in the superconducting gap

Thermal conductivity measurements were performed on single crystal samples of the superconducting skutterudite material PrOs$_4$Sb$_{12}$ both as a function of temperature and as a function of magnetic field applied perpendicular to the heat current. In zero magnetic field we find clear evidence for residual electronic conduction as the temperature tends to zero Kelvin which is consistent with the presence of nodes in the superconducting gap. The field dependence of this electronic conductivity shows a rapid rise immediately above H$_{c1}$, increasing by a factor 10 in 100 mT ($\sim$ 0.05 H$_{c2}$). This is consistent with a semi-classical theory based on a Doppler-shift of the quasiparticle spectrum through coupling to the superfluid flow around magnetic vortices.   

Probing the nodal metal in LBCO with heat transport

The cuprate superconductor La$_x$Ba$_{2-x}$CuO$_4$ (LBCO) has a near-zero minimum in the superconducting transition temperature at $x=1/8$. This is accompanied by the emergence of static one-dimensional spin and charge ordering in ``stripes'' [1]. Spectroscopic measurements at the same doping in the normal state have shown that a gap with d-wave symmetry is present in the single particle spectrum [2]. One possible origin of this gap is the destruction of the coherence of the superconducting ground state by phase fluctuations, suppressing $T_c$ while leaving gapped but ``uncondensed'' Cooper pairs and nodal quasiparticles. We present measurements of the thermal conductivity of LBCO at very low temperature in both superconducting and field-induced nodal metal states. [1] P. Abbamonte et al., {\em Nature Physics} {\bf 1}, 155 (2005) [2] T. Valla et al., {\em Science.} 10.1126/1134742 (2006)   

One Dimensional Superconducting Transition in Quasi-Two-Dimensional Stripes

We investigate the nature of the superconducting transition in NbN ultrathin nano stripes where the thickness of the stripe (4 nm) is about or less then the coherence length, and the width (100 nm) is significantly larger then the coherence length. It is well known that in micro stripes the resistive state below the Berezinskii-Kosterlitz-Thouless transition is produced by dissociated vortex-antivortex pairs. However, our data clearly demonstrates that in such structures the resistive state is formed due to one-dimensional phase slip centers (PSCs) at low current densities. Our analysis shows that the resistive state is actually a result from the competition between the PSCs and two-dimensional vortices. At low currents, the PSC mechanism prevails over the contribution from vortices over a broad temperature range. At higher currents, current induced unbinding of vortex-antivortex pairs contributes the most to resistivity, however this effect is limited by electron heating. From this analysis we will develop a current-temperature phase diagram for superconducting nano stripes.   

Thermal Expansion at the Superconducting Phase Transition in Nb

Thermal expansion is an important thermodynamic quantity that is difficult to measure with sufficient precision to observe electronic phase transitions such as the normal to superconducting transition. Thermal expansion data will be presented on the superconducting to normal phase transition of Nb ($T_c$ = 9.27 K), obtained with a novel quartz dilatometer cell. Surprisingly, only one prior report of this measurement has been published.$^{*}$ This report does not clearly show the predicted jump at $T_c$. Thermal expansion data can be used to compute the pressure derivative of $T_c$, and this analysis will be presented. $^{*}$ White, G.K., $\textit{Croyogenics}$ $\textbf{2}$, 292 (1962).   

On the Nature of the Superconducting Transition in YBCO

In the high-Tc superconductor YBCO, a transition was observed from a hexagonal FLL at low magnetic field (parallel to the c-axis) to a square configuration at high fields. Also seen was a rapid decrease in the Bragg intensity at low temperature (T). It has been the general belief that both the symmetry change and the T-dependence behaviour was due to the d- wave nature of high-Tc superconductivity. However, we observed that the fall-off in intensity with increasing temperature depended on the strength of the applied external field and that excellent fits to this T-dependence could be obtained by simply multiplying the temperature dependence of the familiar Ginzburg-Landau two-fluid model, appropriate for high-kappa materials conventional superconductors, by an exponential factor exp(-aT), with the field-dependent variable `a' being the only free parameter. The impact of these observations on the symmetry of the order parameter will be discussed.   

Session A11: Magnetic Phase Transitions

Competing magnetic fluctuations in Sr$_3$Ru$_2$O$_7$ probed by Ti doping

The bilayered ruthenate Sr$_3$Ru$_2$O$_7$ shows itinerant metamagnetic quantum criticality which has been cited as a textbook example. In this talk we report the effect of nonmagnetic Ti$^{4+}$ impurities on the electronic and magnetic properties of this material. Small amounts of Ti suppress the characteristic peak in magnetic susceptibility near 16 K and result in a sharp upturn in specific heat. The metamagnetic quantum phase transition and related anomalous features are quickly smeared out by small amounts of Ti. These results provide strong evidence for the existence of competing magnetic fluctuations in the ground state of Sr$_3$Ru$_2$O$_7$. Ti doping suppresses the low temperature antiferromagnetic interactions that arise from Fermi surface nesting, leaving the system in a state dominated by ferromagnetic fluctuations.   

Effect of Magnetic Field on Electronic Nematic Order in a Bilayer System: Application to Sr$_{3}$Ru$_{2}$O$_{7}$

Recent experiments on the bilayer compound Sr$_{3}$Ru$_{2}$O$_{7}$ suggest the existence of an electronic liquid-crystal phase. A possible explanation for the unusual behavior observed in this material is provided by an electronic nematic theory. Within this framework, a bilayer system undergoes multiple phase transitions and exhibits strong transport anisotropy. The model also incorporates an external in-plane magnetic field to study the effect on metamagnetic transitions and anisotropic transport. Details of our numerical calculations will be presented.   

Magnetic Phase Transition and Magnetic Structure of Ca$_{3}$Ru$_{2}$O$_{7}$

Ca$_{3}$Ru$_{2}$O$_{7}$ shows exciting physical properties, including a bulk spin-valve behavior and orbital ordering.$^{[1-3]}$ We have investigated the magneto-transport properties and the magnetic structure of this material using high-quality Ca$_{3}$Ru$_{2}$O$_{7}$ single crystals grown by a floating-zone (FZ) method. From magnetoresistivity measurements, we observe that the previously reported metamagnetic transition at $\sim $6T for $H//a$ axis consists of two separate transitions occurring at 5.9 and 6.5T, respectively. The first transition is extremely sharp with the transition width less than 1 Gauss, corresponding to the bulk spin-valve behavior, while the second transition has a finite width which is likely associated with the change of orbital polarization. Our elastic neutron scattering measurements on FZ-grown Ca$_{3}$Ru$_{2}$O$_{7}$ single crystals confirm the magnetic structure suggested by previous works,$^{[2, 4]}$ i.e., the magnetic moments align ferromagnetically within the double layers and antiferromagnetically between the double layers. 1. X.N. Lin et al., Phys. Rev. Lett., 95, 017203 (2005). 2. D.J. Singh and S. Auluck, Phys. Rev. Lett., 96, 097203 (2006). 3. J.F. Karpus, et al., Phys. Rev. Lett., 93, 167205 (2004). 4. Y. Yoshida, et al., Phys. Rev. B, 72, 054412 (2005).   

Specific Heat of (Ca$_{1-x}$Sr$_{x})_{3}$Ru$_{2}$O$_{7}$ Single Crystals

We have measured the specific heat of crystals of (Ca$_{1-x}$Sr$_{x})_{3}$Ru$_{2}$O$_{7 }$using ac- and relaxation-time calorimetry. Special emphasis was placed on the characterization of the N\'{e}el (T$_{N}$=56 K) and structural (T$_{c}$ = 48 K) phase transitions in the pure, x=0 material. While the latter is believed to be first order, detailed measurements under different experimental conditions suggest that all the latent heat (with L $\sim $ 0.3 R) is being captured in a broadened peak in the effective heat capacity. The specific heat has a mean-field-like step at T$_{N}$, but its magntitude ($\Delta $c$_{P }\sim $ R) is too large to be associated with a conventional itinerant electron (e.g. spin-density-wave) antiferromagnetic transition, while its entropy is too small to be associated with full ordering of localized spins. The T$_{N}$ transition broadens with Sr substitution while its magnitude decreases slowly. On the other hand, the entropy change associated with the T$_{c}$ transition decreases rapidly with Sr substitution and is not observable for our x=0.58 sample.   

In-plane anisotropy of magnetoresistivity of tri-layered ruthenate Sr$_4$Ru$_3$O$_{10}$

The tri-layered ruthenate Sr$_4$Ru$_3$O$_{10}$ exhibits intriguing magnetic properties; its ferromagnetic transition at $T_c$ $\approx$ 105 K is followed by an additional magnetic phase transition at $T^*$ $\approx$ 50 K [1,2]. Below $T^*$, a first order metamagnetic transition is induced by a magnetic field applied in the plane. We have recently measured the in-plane angular dependence of magnetoresistivity of this material at various magnetic fields and temperatures. Our data reveal that the in-plane anisotropy of magnetoresistivity undergoes a transition from two-fold to four-fold symmetry across the metamagnetic transition of Sr$_4$Ru$_3$O$_{10}$. Such a transition can be well interpreted in terms of a multiple-band effect which involves the coexistence of ferromagnetic and metamagnetic bands.\\* $[1]$ G. Cao $et$ $al.$, Phys. Rev. B \textbf{68}, 174409 (2003). \\* $[2]$ Z.Q. Mao $et$ $al.$, Phys. Rev. Lett. \textbf{96}, 077205 (2006).   

Long Range Order in Orbital Model

We investigate the existence of N\'eel type long range order (LRO) in an orbital model which is highly anisotropic and frustrated. The model originated from magnetic materials such as LaMnO$_3$ where orbital degrees of freedom play important role. In the system described by the two-fold degenerate $e_g$ orbitals, due to the Kugel-Khomskii superexchange, the orbital degrees of freedom are represented by quantum pseudo-spin 1/2 operators. By applying the reflection-positivity method developed by Dyson, Lieb, and Simon, and adopting appropriate numerical variational method to obtain good estimations on the energy density and correlation functions, we are able to rigorously prove the existence of long range order in this orbital model on the square lattice.   

Orbital order and spin waves in the Kugel-Khomskii model

The Kugel-Khomskii model, introduced in the seventies, attempts to describe transition metal oxides in which orbital degeneracy plays an important role in ground state properties. The model provides a qualitative description of pseudocubic perovskites like LaTiO$_3$ and YTiO$_3$ in which the three $t_{2g}$ d-orbitals are thought to be active at low energy. We investigate the cubic $t_{2g}$ Kugel-Khomskii model in the limit of strong electron-electron interaction (on-site Hubbard U). We use perturbation theory with small hopping parameter (t/U) to derive an effective large pseudospin Hamiltonian with 6 degrees of freedom on each site (2 spins X 3 orbitals). In this model the $t_{2g}$ orbital structure combined with cubic symmetry leads to hopping that depends on both the orbital label and the bond direction. We find the classical (mean-field) ground state manifold systematically and derive a spin wave theory to account for quantum fluctuations. The theory proceeds beyond leading order in order to capture the coupling between the spin and orbital degrees of freedom of the system. This approach leads to better understanding of the quantum-mechanical ground state, it's energy and symmetries.   

Optical spin waves in magnetite

For the last 70 years, the microscopic origin of the Verwey transition in magnetite (Fe$_{3}$O$_{4})$ was thought to be charge-ordering, although this has been disputed of late, bringing renewed interest in this system. The spinel structure of magnetite contains two different iron sites; A (stable valence, Fe$^{3+})$ and B (mixed valence, Fe$^{2.5+})$, with charge ordering of Fe$^{2+}$/Fe$^{3+}$ species occurring on the B-site. As the spin waves are expected to be sensitive to charge ordering, the optical spin waves were measured above and below the Verwey transition by inelastic neutron scattering. The optical spin waves propagating on the A-site sublattice ($\sim $115 meV) are unchanged at the transition. The spin waves propagating on the B-site sublattice ($\sim $75 meV) are $\sim $5 meV stiffer and broader in the metallic phase. The results are interpreted as evidence of B-site double exchange in the metallic phase.   

Electronic Raman scattering in Magnetite

Raman spectra of optimally doped magnetite (Fe$_{3}$O$_{4})$ single crystals reveal broad electronic background extending up to 900 wavenumbers ($\sim $110 meV). Redistribution of this background is observed when sample is cooled below the Verwey transition temperature (T$_{V}$= 123K). In particular, spectra of the low temperature phase show diminished background below 300 wavenumbers followed by an enhancement of the electronic background between 300 and 400 wavenumbers with subsequent decrease of the background below 400 wavenumbers. Such redistribution may be assigned to an opening of the charge gap at about 350 wavenumbers (43 meV). The value of the gap is within the range of the photoemission data on freshly fractured magnetite sample.   

Resonant x-ray scattering of the Bi$_{1-x}$Sr$_{x}$MnO$_{3}$ (x$\le $0.5) charge-ordered phases

Charge-orbital ordering (CO-OO) in Bi$_{1-x}$Sr$_{x}$MnO$_{3}$ (x=0.3, 0.5) have been studied by resonant x-ray scattering (RXS) at the Mn K edge. Strong resonances were observed at the Mn K-edge for weak superstructure (h00), (0k0) and forbidden (h/200), (0k/20) reflections with h, k odd within the \textit{ab} plane (\textit{Ibmm} setting) in both single crystals. Additional (hk0) and (hk/20) with k odd have also been studied. The azimuth angle and polarization dependence of the resonant intensity for this set of reflections point out to a structural transition at the T$_{COO}$ that stabilizes an checkerboard ordering of two non-equivalent Mn atoms with different local geometrical structures and a very small charge segregation for both x=0.5 and x=0.3 compounds. We can conclude that A$_{1-x}$B$_{x}$MnO$_{3}$ tends to order in a checkerboard pattern independently of the nature of the A and B atoms and for x even far from 0.5. Furthermore, the electronic states of the two non-equivalent Mn atoms are far from the ionic (+3 and +4) species.   

Effect of Charge Ordering on Phonon Spectra of La$_{1/3}$Sr$_{2/3}$FeO$_{3-\sigma }$

La$_{1/3}$Sr$_{2/3}$FeO$_{3-\delta }$ (LSFO) compounds are reported to have an unusual magneto-structural transition at low temperatures. Below $\sim $210$K$, it is proposed that charge disproportionation occurs according to 3Fe$^{3.67+}=>$2Fe$^{3+}$+Fe$^{5+}$, and the different iron valences order in the pattern 3+, 3+, 5+ along the body diagonal [111]$_{c}$.$_{ }$Simultaneously, LSFO undergoes antiferromagnetic ordering and a slight distortion in crystal structure from cubic to rhombohedral. Inelastic neutron scattering was used to determine the effect of the charge ordering on the phonon spectra. We find that the high frequency oxygen phonons ($\sim $80 meV) soften above the transition by several meV. The result and relationship between the charge ordering and the phonon softening are discussed.   

Pressure-Induced Quantum Criticality in Cr

Diamond anvil cell high-pressure techniques are used in concert with high resolution magnetic x-ray diffraction to probe the quantum critical regime of the elemental itinerant antiferromagnet Chromium. The antiferromagnetic order is suppressed by an applied pressure of $\sim $6 GPa in the zero-temperature limit. We perform high-resolution measurements of both the charge- and spin-density-wave order parameters as the system is tuned through this magnetic phase transition. The results illustrate the effects of quantum fluctuations and enhanced dimensionality on a canonical correlated electron system.   

High Pressure Probes of Magnetic Quantum Phase Transitions

Magnetic susceptibility and electrical transport measurements in concert with diamond anvil cell techniques permit access to magnetic quantum critical points impossible to access by other means. We combine a continuously variable high-pressure cell with an optical system for in situ pressure calibration and Raman capability that can be cooled to pumped helium temperatures. With this system, we investigate the P-T phase diagram of the spin-density wave antiferromagnet chromium. We discuss its quantum critical behavior along with the possibility of alternative correlated phases as the magnetic order is suppressed in the zero-temperature limit.   

Influence of the antiferromagnetic spin density wave on the magnetoresistance of Cr

We have performed magnetotransport measurements on Cr films that are 350, 56, 43 and 18 nm thick. The magnetoresistance with the field perpendicular to the film plane shows a clear increase below the Neel temperature and is accompanied by an anomalous negative magnetoresistance at the Neel temperature. The orbital magnetoresistance satisfies the Kohler's rule in the paramagnetic state but violates it in the Neel state. The Hall resistance shows temperature dependence in the paramagnetic state, which was previously suggested to be indicative of a pseudogap [1]. We explain the above phenomena by the evolution of the electronic structure due to the formation of antiferromagnetic spin density wave, the influence of antiferromagnetic domain walls, and the existence of more than one scattering time. [1] ``Quantum phase transition in a common metal'', A. Yeh, Y-A. Soh, J. Brooke, G. Aeppli, T. F. Rosenbaum, and S. M. Hayden, Nature (London) \textbf{419}, 459 (2002).   

Thermomagnetic Studies of K$_{2}$NaCrO$_{8}$

There has been renewed interest in the search for new model quantum spin systems that can exhibit BEC of magnons. K$_{2}$NaCrO$_{8}$ is one of the simplest spin systems available since $S=\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 2$} $ and $I$ = 0. Specific heat ($C_{p})$ measurements indicate that this material orders antiferromagnetically at $T_{N} \quad \sim $ 1.7 K in zero-field [1]. Application of an external magnetic field pushes the $C_{p}$ maximum to lower temperatures. Torque and AC susceptibility measurements show that the transition temperature is rapidly suppressed around 7.4 T, with no hysteretic behavior, implying the presence of a quantum phase transition. Measurements are underway to map the phase boundary in the $T \quad \to $ 0 K, B $\sim $ 7.4 T region and extract the critical exponent ($\alpha )$ from the relation $k_{B}T_{c} \quad \approx $ (B$_{c}$-B)$^{\alpha }$ . [1] B. Cage, N. S. Dalal, \textit{Chem. Mater.} \textbf{13}, 881 (2001).   

Session A12: Focus Session: Spin Hall Effect

Generating Spin Currents in Semiconductors with the Spin Hall Effect

There is a growing interest in exploiting electron spins in semiconductor nanostructures for the manipulation and storage of information in emergent technologies based upon spintronics and quantum logic. Recently we have explored two mechanisms for electrically generating spin polarization in non-magnetic materials: current-induced spin polarization and the spin Hall effect. Current-induced spin polarization results in spins being polarized by the internal magnetic field arising from spin-orbit coupling, and the spin Hall effect refers to the generation of a spin current transverse to a charge current in the absence of an applied magnetic field. Recent measurements in ZnSe reveal that both of these effects are robust to room temperature\footnote{N. P. Stern, S. Ghosh, G. Xiang, M. Zhu, N. Samarth, and D. D. Awschalom, \textit{Phys. Rev. Lett.} \textbf{97}, 126603 (2006)}. Although spin current is difficult to measure directly, the spin Hall effect creates spin accumulation at the edges of a channel which has been measured in bulk epilayers of n-doped semiconductors and in two- dimensional hole and electron systems. More recently, we investigate spin currents generated by the spin Hall effect in GaAs structures that distinguish edge effects from spin transport\footnote{V. Sih, W. H. Lau, R. C. Myers, V. R. Horowitz, A. C. Gossard and D. D. Awschalom, \textit{Phys. Rev. Lett.} \textbf{97}, 096605 (2006).}. We fabricate mesas with transverse channels to allow spins to drift into regions in which there is minimal electric current. Using optical techniques, we observe the electrical generation of a transverse spin current, which can drive spin polarization nearly 40 microns into a transverse channel. Using a model that incorporates the effects of spin drift, we determine the transverse spin drift velocity from the magnetic field dependence of the spin polarization. These results reveal opportunities for an electrical spin source in non-magnetic materials.   

Persistent Spin Helix

Spin-orbit coupled systems generally break the spin rotation symmetry. However, for a model with equal Rashba and Dresselhauss coupling constant (the ReD model), and for the {\$}[110]{\$} Dresselhauss model, a new type of SU(2) spin rotation symmetry is discovered. This symmetry is robust against spin-independent disorder and interactions, and is generated by operators whose wavevector depends on the coupling strength. It renders the spin lifetime infinite at this wavevector, giving rise to a Persistent Spin Helix (PSH). We obtain the spin fluctuation dynamics at, and away, from the symmetry point, and suggest experiments to observe the PSH.   

Topological Insulators in Three Dimensions

We study three dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where the QSH effect is distinguished by a single $Z_2$ topological invariant, in three dimensions there are 4 invariants distinguishing 16 ``topological insulator'' phases. There are two general classes: weak (WTI) and strong (STI) topological insulators. The WTI states are equivalent to layered 2D QSH states, but are fragile because disorder continuously connects them to band insulators. The STI states are robust and have surface states that realize the 2+1 dimensional parity anomaly without fermion doubling, giving rise to a novel ``topological metal'' surface phase. We show that the $Z_2$ invariants can be easily determined for systems with inversion symmetry. This allows us to predict specific materials are STI's, including semiconducting alloy Bi$_{1-x}$ Sb$_x$ as well as $\alpha-$Sn and HgTe under uniaxial strain.\newline \newline 1. Liang Fu, C.L. Kane, E.J. Mele, cond-mat/0607699. \newline 2. Liang Fu, C.L. Kane, cond- mat/0611341.   

Skew-scattering contribution in Rashba-type 2D systems with short-range scalar impurity potential.

There is a renewed interest in the anomalous Hall effect (AHE) motivated by the fabrication of materials that are both ferromagnetic and semiconducting, diluted magnetic semiconductors (DMS). Experimental and theoretical studies have shown that the skew-scattering contribution can have a dominant role in magnetotransport, especially in the low-impurity-concentration limit. The Hamiltonian describing Rashba-type systems is sufficiently simple to allow analytical solutions, yet it has the features of a typical DMS: (1) spin-orbit coupling, (2) more than one band with momentum-dependent Berry's curvature, and (3) it allows for inter- and intra-band scattering on impurities. We estimate skew-scattering contribution to two-dimensional Rashba-coupled systems in the leading order of expansion in disorder strength. We consider short-range disorder potentials and derive the general formula for arbitrary spin-orbit coupling through a high-order Born approximation.   

Low field phase diagram of spin-Hall effect in the mesoscopic regime

When a mesoscopic two dimensional four-terminal Hall cross-bar with Rashba and/or Dresselhaus spin-orbit interaction (SOI) is subjected to a perpendicular uniform magnetic field $B$, both integer quantum Hall effect (IQHE) and mesoscopic spin-Hall effect (MSHE) may exist when disorder strength $W$ in the sample is weak. We have calculated the low field `phase diagram' of MSHE in the ($B, W)$ plane for disordered samples in the IQHE regime. For weak disorder, MSHE conductance $G_{sH}$ and its fluctuations \textit{rmsG}$_{sH}$ vanish identically on even numbered IQHE plateaus, they have finite values on those odd numbered plateaus induced by SOI, and they have values $G_{sH}=1/2$ and \textit{rmsG}$_{sH}=0$ on those odd numbered plateaus induced by Zeeman energy. For moderate disorder, the system crosses over into a regime where both $G_{sH}$ and \textit{rmsG}$_{sH}$ are finite. A larger disorder drives the system into a chaotic regime where $G_{sH}=0$ while \textit{rmsG}$_{sH}=0$ is finite. Finally at large disorder both $G_{sH}$ and \textit{rmsG}$_{sH}$ vanish. We present the physics behind this `phase diagram'.   

Quantum spin Hall phase and surface spin current in Bi and Sb

In the quantum spin Hall (QSH) phase, the bulk is gapped while edge states are gapless and carry spin currents. Experimental studies for the QSH phase are called for. To search for candidates of the 2D QSH phase, we relate the spin Hall conductivity in insulators with magnetic response of the orbital magnetization to the Zeeman field. In this respect, bismuth is promising since it is a strong diamagnet enhanced by spin-orbit coupling. For a 2D (111)-bilayer bismuth, we calculate the $Z_2$ topological number, the band structure for the strip geometry, the spin Chern number, and the parity at the time-reversal symmetric wavenumbers. We predict that the (111)-bilayer bismuth will be a QSH phase [1]. On the other hand, it was proposed recently that 3D bismuth is a simple insulator, and not the QSH phase, by parity consideration [2]. Transition from the 2D QSH topological phase to the 3D simple insulator phase is described by gradually increasing inter-bilayer hopping, thereby band-touching occurs at high- symmetry points and parities of the wavefunctions are exchanged. Similar discussion applies for Sb, where 2D bilayer is a simple insulator and 3D bulk is the QSH phase. Finally, we compare the theory with the ARPES data showing surface spin-splitting (spin current) for various surfaces of Bi and Sb. [1] S. Murakami, cond-mat/0607001 (to appear in Phys. Rev. Lett.). [2] L. Fu, C. L. Kane, cond-mat/0611341.   

Mesoscopic Spin Hall Effect

We investigate the spin Hall effect in ballistic chaotic quantum dots with spin-orbit coupling. We show that a longitudinal charge current can generate a pure transverse spin current. While this transverse spin current is generically nonzero for a fixed sample, we show that when the spin-orbit coupling time is short compared to the mean dwell time inside the dot, it fluctuates universally from sample to sample or upon variation of the chemical potential with a vanishing average. For a fixed sample configuration, the transverse spin current has a finite typical value $\simeq e^2 V/h$, proportional to the longitudinal bias $V$ on the sample, and corresponding to about one excess open channel for one of the two spin species. We discuss spin current correlations and noise.   

Spin torque contribution to the frequency dependent spin Hall conductivity in spin-orbit coupled systems

The spin Hall effect in spin-orbit coupled systems has lately attracted great attention. Since the electron spin is not a conserved quantity in spin-orbit coupled systems, the conventional form for the spin current operator turn out to be ill-defined. A fundamental issue is then a proper definition of spin current in such systems. Recently J. Shi et. al. [1] introduced an unambiguous and proper definition of spin current which adds to the conventional part, a spin source term (spin torque) associated to the spin processional motion. In this work, using the linear response Kubo formalism, and employing the new definition for the spin current operator, we study the frequency dependent spin Hall conductivity for a two dimensional electron gas in the presence of Rashba and Dresselhaus spin-orbit coupling. We show that the optical spectrum of the charge and spin conductivity changes dramatically when the proper definition is used, as new and strong resonances appear. It is shown that the spin torque contribution to the spin Hall conductivity clearly dominates over the conventional part. These results may encourage experimentalists to measure the spin Hall current and/or spin accumulation in the frequency domain in such systems, as to establish the vality of the new definition of the spin current operator. [1] J. Shi, P Zhang, D. Xiao and Q Niu, Phys Rev. Lett \textbf{96}, 076604 (2006)   

Search for the Persistent Spin Helix in a 2-Dimensional Electron Gas

The persistent spin helix is an infinitely long-lived helical spin density wave that is predicted to occur in 2-dimensional electron systems with equal-strength Rashba and Dresselhaus spin-orbit coupling [Bernevig \textit{et al}., cond-mat/0606196]. The infinite lifetime of the helix would result from the combined effects of diffusion and precession in the spin-orbit effective field. These effects would also greatly enhance the lifetime of spin excitations at the helix wave vector in systems where Rashba $\ne $ Dresselhaus. We use the transient spin grating technique to search for this effect in GaAs quantum wells. In these experiments, two non-collinear, orthogonally polarized pump pulses from a Ti:Sapphire oscillator generate a holographic spin grating in the interference region on the sample. The subsequent decay of the spin grating is monitored by diffraction of a time-delayed probe pulse. The wave vector of the spin grating can be tuned by varying the angle between the interfering pump beams, making this technique ideally suited for observing the persistent spin helix.   

Berry Curvature and the $Z_2$ Topological Invariants of Spin-Orbit-Coupled Bloch bands.

The (``anomalous'') integer quantum Hall effect can occur in non-interacting models of band insulators with broken time-reversal- ($T$-)symmetry where the sum of Chern invariants of occupied bands of Bloch states is non-zero. These topological invariants can be computed from the zeroes of certain functions in the Brillouin zone (BZ), but have a simpler formulation as BZ-integrals of Berry curvature. Recently, Kane and Mele found that $T$-invariant 2D systems with strong spin-orbit coupling possess a ``$Z_2$'' ($+$ or $-$) analog of the Chern invariant, which they formulated in terms of zero-counting arguments (3D generalizations have also been found). I give an alternate formulation in terms of Berry-curvature integrals, in the case that spatial-inversion- ($I$-)symmetry is broken, but $T$-symmetry is not. In 2D, such bands generically form a genus-5 2-manifold, with antipodal points paired by Kramers degeneracy: the $Z_2$ invariant is obtained by integration over a Kramers-distinct half-manifold; the 3D case is similar. I also discuss the case of doubly-degenerate bands with unbroken $I$-symmetry: despite recent suggestions, it does not appear that the $Z_2$ invariant of such systems can be obtained purely from knowledge of the parity quantum numbers at $T$-invariant points in the BZ.   

Quantum Spin Hall Effect in HgTe in a Magnetic Field

Recently, the quantum spin Hall effect has been proposed in HgTe quantum wells. It has been shown that this system exhibits the quantum spin Hall effect and the Hamiltonian is analogous to two copies of the quantum anomalous Hall effect. Here we examine the features of this system in a strong magnetic field. We use an analytic transfer matrix formalism to study the system on a lattice in a strip geometry in the presence of a strong perpendicular magnetic field. We characterize the bulk band structure and edge states for various applied field strengths and discuss possible experimental signatures of the quantum spin Hall effect. We also discuss possible discrepancies between the continuum and lattice picture.   

Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells

We show that the Quantum Spin Hall Effect, a state of matter with topological properties distinct from conventional insulators, can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the electronic state changes from a normal to an ``inverted'' type at a critical thickness d$_c$. We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss the methods for experimental detection of the QSH effect.   

Session A13: Focus Session: Multiferroics I

Magnetic Symmetry of Two-Dimensional Multiferroics

Hexagonal rare earth manganites are multiferroic materials which exhibit triangular antiferromagnetic ordering in the basal plane which can be characterized by two-dimensional (2D) magnetic symmetry. Reduced dimensionality is also desirable for achieving large (usually nonlinear) magnetoelectric coupling at higher temperatures. Indeed, the magnetization in BaMnF$_4$ orders two dimensionally below the transition temperature with a change in the b-axis dielectric constant. Moreover, there can be phase transitions between different 2D magnetic phases. From this perspective we study two dimensional magnetic (or color) symmetry, enumerate 2D magnetic space groups and illustrate their role in multiferroic phase transitions.   

Rotation of orbital stripes and the consequent charge-polarized state in Pr(Sr$_{,}$Ca)$_{2}$Mn$_{2}$O$_{7}$

Nano-scale self-organization of electrons is ubiquitously observed in correlated-electron systems such as complex oxides of transition metals. The phenomenon of charge ordering (CO) or the formation of charge stripes, as observed for layered-structure cuprates and nickelates, is one such example. Among them, the CO in the manganites is closely tied to the orbital degree of freedom of $3d$ electrons, leading to the staggered orbital ordering (OO) or the formation of orbital stripes in the layered structure. Here, we present the phenomena of thermally-induced rotation of the orbital stripes by 90 degrees for bilayered manganite Pr(Sr$_{1-x}$Ca$_{x})_{2}$Mn$_{2}$O$_{7}$(x=0.9) with half hole-doping, i.e., a 1:1 ratio of Mn$^{3+}$/Mn$^{4+}$ [1]. The rotation of orbital stripes and the consequent CO coupled with the underlying lattice distortion were found to produce the charge-polarized state, as also evidenced by its activity of optical second harmonic generation. [1] Y. Tokunaga \textit{et al}., Nature Materials, doi:10.1038/nmat1773 (2006).   

Structural changes related to dielectric anomalies in RFe$_{2}$O$_{4}$ (R=Lu and Y).

RFe$_{2}$O$_{4}$ (R=Lu and Y) have a characteristic rhombohedral structure ith the space group R-3m, in which the hexagonal double-layers of Fe-O ions are sandwiched by Lu-O layers. In addition, the average valence of Fe ions is Fe$^{2.5+}$, which implies that Fe$^{2+}$ and Fe$^{3+}$ ions occupy the equivalent site on the hexagonal layers with equal density. Recently, a regular arrangement of Fe$^{2+}$ and Fe$^{3+}$ in the hexagonal plane (charge ordering) is suggested on the basis of the anomalous dielectric behavior in YFe$_{2}$O$_{4.}$ Thus, we investigated structural change due to the charge ordering in RFe$_{2}$O$_{4}$ (R=Lu and Y) mainly by transmission electron microscopy. We found characteristic superlattice reflections at (1/3 1/3 1/2)-type positions at room temperature in YFe$_{2}$O$_{4}$. It is suggested that the diffuse streaks are due to the charge ordering in the three-dimensional hexagonal plane. We examined structural change by obtaining the electron diffraction (ED) patterns in the warming process and found that successive structural phase transition takes place around 220K. It is considered that these transitions should be characterized as the change of the charge ordering pattern in the hexagonal plane and are strongly correlated to the anomalous dielectric properties found in YFe$_{2}$O$_{4}$.   

X-ray Magnetic Circular Dichroism Investigation of Fe Valence Ordering in Multiferroic LuFe$_2$O$_4$

A new mechanism of ferroelctricity that is based on the iron valence ordering in a charge frustrated lattice has been reported for LuFe$_2$O$_4$. In this compound, a ferroelectric transition occurs at 330 K and ferrimagnetic order develops below 250 K. The ferroelectric polarization shows a sharp increase at the ferrimagnetic ordering temperature suggesting that the two order parameters are coupled. X-ray magnetic circular dichroism (XMCD) at the Fe K edge and at Lu L$_{2,3}$ edges has been measured in LuFe$_2$O$_4$ using 4-ID-D beamline at Advanced Photon Source. Two clear peaks are seen in the Fe K-edge XMCD suggesting that the magnetism of Fe is associated with two types of Fe sites. Fe K edge XMCD probes the 4p shell, thus it is sensitive to different charge states and gives an indirect measure of the Fe magnetism through 3d-4p hybridization. The observed double peak structure in the XMCD is an indication of charge ordering of Fe$^{2+}$ and Fe$^{3+}$ in the ferrimagnetic state. XMCD is also observed at Lu L$_{2,3} $ edges suggesting a small induced Lu 5d moment. Funded by US Dept. of Energy.   

Spin-Charge-Orbital States and Electric Polarization in Multiferroic RFe$_2$O$_4$

Layered iron oxides RFe$_2$O$_4$ (R: rare-earth ion) is recognized to be an electronic ferroelectric and multiferroic compounds. Crystal structure of this compound consists of stacked FeO triangle layers. Charge and spin states have been studied by the electron and neutron diffraction experiments. Long range charge and spin orders characterized by the momentum (1/3, 1/3) appear around 320K and 250K, respectively, in LuFe$_2$O$_4$. Electric polarization is induced around the charge ordering temperature of Fe$^{2+}$ and Fe$^{3+}$, and is enhanced around the magnetic ordering temperature. We examine theoretically spin-charge-orbital structures and electric polarization in RFe$_2$O$_4$. We suggest that Fe$^{2+}$ ion has the doubly degenerate orbital degree of freedom. Effective Hamiltonian for spin, charge and orbital degrees of freedom is derived. Numerical analyses with the multi-canonical Monte-Carlo simulation and the mean-field approximation show that the electric polarization is attributed to the charge order with momentum (1/3, 1/3). A magnitude of the polarization is enhanced around the magnetic ordering temperature due to the coupling between spin and charge. Conventional orbital order is not expected from the numerical calculation, and possible orbital states at low temperatures are discussed.   

Charge ordering and ferroelectricity in magnetite

Magnetite Fe3O4 is one of the most fascinating material in solid state physics. Besides being the first magnetic material known to the mankind, it is also the first example of an insulator-metal transition in transition metal oxides -- the famous Verwey transition [1]. One usually connects this transition with the charge ordering of Fe$^{2+}$ and Fe$^{3+}$. However the detailed pattern of CO in Fe$_{3}$O$_{4 }$is still a matter of debate. Another aspect, which is not so widely known and which did not yet receive sufficient attention, is that below T$_{V}$, besides being completely spin polarised, magnetite apparently is also \textit{ferroelectric} (FE) [2]. Thus it seems that magnetite, besides being the first magnetic material and the first transition metal oxide with an insulator-metal transition, is also the first \textit{multiferroic} material. Using the idea of a coexistence of site-centred and bond-centred charge ordering [3], I suggest a novel type of ordering in magnetite which explains the observed FE in Fe$_{3}$O$_{4}$ and which agrees with the structural data. \newline [1] Verwey E.J.W., Nature \textbf{144}, 327 (1939) \newline [2] Rado G.T. and Ferrari J.M., Phys.Rev.B \textbf{12}, 5166 (1975); Kato K. and Iida S., J.Phys.Soc.Japan \textbf{50}, 2844 (1981) \newline [3] Efremov D.V., van den Brink J. and Khomskii D.I., Nature Mater. \textbf{3}, 853 (2004)   

Lattice and Magnetic Effects on Multiferroic Transitions in Garnets

The possible presence of ferroelectricity in a magnetically ordered state has attracted considerable attention particularly in ABO$_{3}$ and AB$_{2}$O$_{5}$ systems with B = Mn. Evidence for strong coupling of the two order parameters has been provided in the so-called multiferroics, where the field-induced polarization leads to a giant magnetoelectric effect and a magneto-dielectric effect. It was recently shown that the ferrimagnetic garnet crystal of Tb$_{3}$Fe$_{5}$O$_{12}$ exhibits a large magnetodielectric response as well when a very small magnetic field is applied (1). To understand the origin of the high sensitivity of the dielectric effect in garnets, we investigated the crystal and magnetic structures of Tb$_{3}$(Fe/Ga)$_{5}$O$_{12}$ using pulsed neutron diffraction. The garnet crystal appears to be very close to a lattice instability and high-resolution diffraction showed that the lattice gradually changes symmetry from cubic to rhombohedral with cooling over a wide temperature range. At the same time, magnetic diffuse scattering is observed that goes away by 15 K. The role of the lattice and of local distortions in the magnetic polarization and the coupling of the magnetostriction to the dielectric effect will be discussed. (1) N. Hur \textit{et al, }Appl. Phys. Lett. \textbf{87}, 042901 (2005).   

Magnetoelectric coupling in multiferroic materials from first principles

The combination of magnetic and ferroelectric properties in a single material is very appealing both because of the interesting coupling effects that emerge as well as due to a variety of technological applications that can be envisaged. Computational methods based on density functional theory have made invaluable contributions to the present understanding of such magnetoelectric multiferroics. In this talk I will show how we use these methods to understand the intriguing properties of presently known multiferroics and to design new multiferroic materials with more desirable properties. In particular, I will focus on the coupling between structural distortions and so-called ``weak'' magnetic order that is mediated by the Dzyaloshinskii-Moriya interaction, and I will discuss the possibility of electric-field induced magnetization switching in prototypical multiferroic systems such as BiFeO$_3$ and BaNiF$_4$.   

First-principles Investigation of Ground State Magnetic Structure and Effective Exchange Interaction in GaFeO$_3$

Among many multiferroic materials, GaFeO$_3$ has attracted much attention due to its large magnetoelectric effect and the unique magneto-electric, magneto-optic, and piezoelectric properties. We report our first-principles calculations on the electronic and magnetic structures of multiferroic GaFeO$_3$. Based on the LDA+U density-functional theory by employing a linear-combination-of-localized-pseudo-atomic orbitals (LCPAO) method, GaFeO$_3$ in its ideal structure is shown to be antiferromagnetic. Through calculations of effective exchange interactions among Fe atoms at either Ga or Fe sites in GaFeO$_3 $, it is concluded that net magnetic moments observed in experiments may arise from the Fe substitution at the Ga sites. Total energy calculations show that the site disorder among Fe and Ga sites is quite feasible, which is consistent with experiments. Unquenched orbital magnetic moment of Fe is found to exist possibly due to the broken inversion symmetry at the Fe site with the distortion of surrounding oxygens. The calculated orbital magnetic moments are discussed in comparison with the results of recent X-ray magnetic circular dichroism measurement.   

Systematic investigation of rare-earth doped BiFeO$_{3}$ thin films using composition spreads

(1) Department of Materials Science and Engineering, University of Maryland, USA (2) University of New South Wales, AU (3) Center for Superconductivity Research, University of Maryland, We have systematically investigated compositionally varied rare-earth (RE) doped BiFeO$_{3}$ thin films using the combinatorial approach. Epitaxially grown (Bi$_{1-x}$RE$_{x})$FeO$_{3}$ composition spread thin films were fabricated by laser molecular beam epitaxy on SrTiO$_{3}$ (001) substrates with an SrRuO$_{3}$ buffer layer. Transmission electron microscopy of the films showed that homogeneous epitaxial films were obtained throughput the composition range. Structural properties of (Bi$_{1-x}$RE$_{x})$FeO$_{3}$ was mapped using scanning x-ray diffraction, and structural transitions were observed at various compositions. In some compositions, substantial enhancement in ferroelectric properties was observed at the structural transition: increase in the dielectric constant, increase in the piezoelectric response, and decrease in the coercive field were observed, while high polarization is maintained. Detailed dependence of various properties on composition variation will be discussed. Work supported by NSF DMR 0094265, DMR 0231291, MRSEC DMR-00-0520471 and the W. M. Keck Foundation.   

Exchange bias between ferromagnetic metals and multiferroic BiFeO$_{3}$, LuMnO$_{3}$, and TbMnO$_{3}$

We are using exchange bias at ferromagnet layer/multiferroic interfaces to study the nature of magnetism in multiferroic materials. Co 5 nm layers have been deposited by sputtering on surfaces of epitaxial BiFeO$_{3}$ and TbMnO$_{3}$ thin films and on LuMnO$_{3}$ single crystals. Epitaxial BiFeO$_{3}$ and TbMnO$_{3}$ films were prepared by PLD. Magnetic properties of the Co/multiferroic bilayers are measured using SQUID, VSM, MOKE and XMCD. In BiFeO$_{3}$, we find that the bilayers exhibit exchange bias even at room temperature. In the TbMnO$_{3}$ system, increasing of coercive field and exchange bias was also clearly observed below the N\'eel temperature. In LuMnO$_{3}$, we observe positive exchange bias as well as switching of the sign of the exchange bias depending on the cooling procedure. This behavior may be related to the frustration in Mn spins. Difference in the exchange bias behavior between different multiferroic materials will be discussed. The effect of electric field on exchange bias is currently under investigation. Supported by ONR N000140110761, ONR N000140410085, NSF DMR 0094265, DMR 0231291, MRSEC DMR-00-0520471, and the W. M. Keck Foundation.   

Charge ordering as alternative to Jahn-Teller distortion

It was pointed out in the seminal paper of Jahn and Teller that a partially occupied degenerate molecular level, often a doubly degenerate $E_{g}$ level in a cubic ligand field, is unstable against a distortion that splits the level and lowers the total energy of the occupied states. Since then, this effect has been commonly found in solids where it takes a form of a \textit{cooperative} Jahn-Teller (JT) effect (orbital ordering), when the crystal lattice distorts coherently so as to lift orbital degeneracy at each site or, in band language, to split an entire band ($e.g.$, $e_{g}$) and thus open a gap at the Fermi level. Upon the gradual delocalization of degenerate electrons, the JT distortion and corresponding orbital ordering becomes less and less favorable, but, as we show, below a crossover region exists with the possibility of lifting degeneracy not by an \textit{orbital ordering}, but by a \textit {charge ordering} (CO): an electron can be transferred from one ion to another, so that, say, the doubly degenerate $e_{g}$ level on one site will be fully occupied, and on the other site empty. In this paper we demonstrate, experimentally and by first principles calculations, that just such a ``JTCO'' effect actually occurs in the rare earth nickelates such as YNiO$_{3}$ and LuNiO$_{3}$. Apparently this novel phenomenon can also take place in other similar systems.   

Session A14: Focus Session: Spin Dependent Tunneling I

Spectroscopic Studies on epitaxially grown Fe/MgO/Fe magnetic tunnel junctions on W(100)

In these days, there is a big interest in epitaxial Fe/MgO/Fe MTJ systems in the TMR issues. We investigated electronic states and magnetic behaviors of epitaxially grown Fe/MgO/Fe on W(100) at different MgO thicknesses using XAS, MCD, XPS, SRPES, and discussed a few noticeable phenomena in this system. First, XAS and MCD spectra at Fe $L_{2,3}$-, O $K-$, and Mg $K-$edges varies as a function of MgO thickness. Second, in MgO/Fe/W(100), the magnetic hysteresis curve suddenly changes at a certain MgO layer thickness, probably due to a developed strain at the MgO/Fe interface. Finally, in Fe/MgO/Fe/W(100), an antiferromagnetic and a ferromagnetic interlayer coupling between two Fe ferromagnetic layers were observed for different MgO layer thicknesses, and we determined the spin polarization of the density of states.   

Electronic structure of sputter deposited MgO(100) tunnel barriers in magnetic tunnel junction structures exhibiting giant tunneling magnetoresistance

Giant tunneling magnetoresistance (TMR) in magnetic tunnel junctions formed with crystalline MgO tunnel barriers [1] have potential applications in a wide variety of spintronic devices. However, the relationship of the TMR to the detailed chemical and electronic structure of the MgO barrier and its interfaces with the ferromagnetic electrodes is not yet fully understood. We have carried out valence band photoemission spectroscopy and x-ray absorption spectroscopy to characterize the chemical state and electronic structure of sputter deposited, highly oriented, MgO (001) barriers and its interfaces with ferromagnetic electrodes. A large band gap of $\sim $7.5 eV is found even for ultrathin MgO layers. This is consistent with barrier heights found from fitting current versus voltage curves providing that very small effective electron masses are used. We discuss the role of thin Mg interface layers that we have used to reduce oxidation of the underlying ferromagnetic layer during the MgO layer formation [1]. [1] S. S. P. Parkin, C. Kaiser, A. Panchula, P. M. Rice, B. Hughes, M. Samant, S.-H. Yang, Nature Materials 3, 862 (2004).   

Influence of disorder on tunnel magnetoresistance

In spite of recent success in observing large values of tunnelling magnetoresistance (TMR) in epitaxial FeCo$|$MgO$|$FeCo magnetic tunnel junctions (MTJ's), the values reported are still two orders of magnitude lower than those predicted by first-principles transport calculations for ideal, defect-free MTJ's. In this talk, we present results of a systematic study of the influence of roughness and leads disorder on TMR in a FeCo$|$vacuum$|$FeCo model system. Our study is based upon a tight-binding muffin-tin orbital (TB-MTO) implementation of the Landauer-B\"{u}ttiker scattering theoretical formulation of transport. Disorder is included in the transport calculation using large lateral supercells. In our study we found that in case of ideal, perfectly ordered systems, the values of TMR comparable in size to those predicted by others in which the mechanism responsible is the very effective transmission through resonant states close to the Fermi level for the minority spin channel. Roughness is found to quench these resonances leading to a drastic reduction of TMR to values comparable to those seen in experiment. Leads disorder is found to quench the TMR but less strongly than roughness.   

First-principles prediction of high Curie temperature for ferromagnetic bcc-Co and its relation to Co/MgO/Co magnetic tunnel junctions

We determine from first principles the Curie temperature of bulk Co in the ground state hcp phase and the metastable fcc and bcc phases. For fcc-Co we found a Curie temperature of $T_{\mathrm{C}}(\mbox{fcc-Co})=1280$~K, in reasonable agreement with experimental results. For bcc-Co, a Curie temperature of $T_{\mathrm{C}}(\mbox{bcc-Co})=1400$~K is predicted. This suggests that bcc-Co/MgO/bcc-Co tunnel junctions offer high tunneling magnetoresistance ratios even at elevated temperatures, giving them an advantage over Fe/MgO/Fe junctions. $T_{\mathrm{C}}(\mbox{bcc-Co})$ appears robust under tetragonalization upon epitaxial growth on MgO, in contrast to Fe for which $T_{\mathrm{C}}(\mbox{bcc-Fe})$ is found to drop by more than 20\% (from 970~K to 750~K) upon such a tetragonalization. We find that FeCo alloys have an even higher $T_{\mathrm{C}}$, as high as 1660~K for ordered FeCo. We discuss the origin of these effects in terms of the electronic structure and densities of states. The Curie temperatures are calculated by mapping {\it ab initio} results to a Heisenberg model, which is solved by a Monte Carlo method.   

Theory of the spin-orbit induced anisotropy in the tunneling magnetoresistance of magnetic tunnel junctions.

We investigate the effects of the spin-orbit interaction on the tunneling magnetoresistance of magnetic tunnel junctions. We propose a theoretical model in which the two-fold symmetry of the tunneling anisotropic magnetoresistance (TAMR) effect, observed in Fe/GaAs/Au tunnel junctions, originates from the interference between Dresselhaus and Bychkov-Rashba spin-orbit couplings at the interface between the ferromagnetic (Fe) region and the GaAs tunnel barrier. Bias induced changes of the Bychkov-Rashba spin-orbit coupling can result in a flipping of the axis of the two-fold symmetry of the TAMR. The theoretical calculations are in good agreement with recent experiments [1]. \newline \newline [1] J. Moser, A. Matos-Abiague, D. Schuh, W. Wegscheider, J. Fabian, and D. Weiss, cond-mat/0611406.   

Bias induced inversion of the tunneling magnetoresistance

Demand for high density at low cost two-terminal nonvolatile memory devises has boosted research interest in electroresistive phenomena where conductivity exhibits voltage--induced resistance jump up to several orders in magnitude. NiO based junctions are particularly promising because of its high ON/OFF ratio and simple constituents. We report low temperature transport properties of electrochemically synthesized Ni/NiO/CoNi/NiO/Co magnetic double barrier tunneling junction (MTJ) in nanowires with diameter of 70nm, and NiO barrier thickness of about 2 nm. Resistance bi-stability of double NiO nanojunctions is observed and reaches 100{\%}. We observe the \textit{sign inversion }of the tunnel magnetoresistance upon resistance switching from low-resistance (LR) to high-resistance (HR) state, indicating a new resonant tunneling path promoted by an applied voltage bias. Thus our MTJ shows multifunctional properties with four resistance states which can be manipulated by applied electric and magnetic fields. This device can be used as a four-state logic gate or memory cell with multifunctional properties. The interpretation in terms of occupation-driven metal-insulator transition in one of the two junctions is proposed, explaining switching of the resistance and the magnetoresistance.   

Evidence for WKB Failure in Contemporary Magnetic Tunnel Junctions

This work describes evidence for the failure of the WKB approximation in state-of-the-art magnetic tunnel junctions. Surprisingly, the tunneling conductance of three varieties of CoFeB/MgO/CoFeB magnetic tunnel junctions depends quadratically on the applied voltage to anomalously high biases: the parabolic conductance persists to 2~V, greater than half the theoretical MgO barrier height. Within the framework of WKB, these data imply unphysical barrier parameters. We show that the origin of this breakdown is a distribution of barrier thicknesses consistent with experimentally feasible interfacial roughness, possibly in conjunction with the tunneling electron sensing the MgO band structure. Additionally, well defined and reproducible bias-dependent conductance oscillations are observed in CoFeB/MgO/NiFe devices. These oscillations are mediated by the reflection of tunneling electrons from the sharp MgO/NiFe interface, which allows electron standing waves to form within the MgO barrier. The oscillation amplitude is enhanced in the antiparallel state, which gives rise to oscillations of the tunneling magnetoresistance. A model employing spin-split free electron bands and the exact solution to the Schr\"{o}dinger equation demonstrates qualitative agreement with the data. This work implies that using existing WKB-based models may lead to physically incorrect barrier parameters for contemporary tunnel junctions, which may underscore the imminent necessity for first principles analyses of contemporary tunneling devices with textured or epitaxial barriers, MgO or otherwise.   

Highly charged ion modified magnetic structures

Highly charged ions (HCIs) deposit large amounts of energy very locally in small areas of only a few square nanometers per HCI impact. This allows for the modification of nanometer sized areas and the creation of nanosized features on impact surfaces. We have used highly charged ions such as Xe$^{44+}$ to modify ultrathin oxide barriers in magnetic tunnel junctions (MTJs) in order to locally change their electrical properties. We have been able to drastically reduce the resistance area (RA) product of our Co/Al-Ox/Co MTJs. While the magnetoresistance of HCI modified MTJ is also reduced, we created a new hybrid magnetic field sensor composed of tunnel and metallic junctions. We have analyzed the properties of individual HCI created conduction channels through ensemble measurements. Generalizing this approach, HCIs can be used to create hybrid materials through the introduction of nanometer sized electric or magnetic channels. This could be a useful tool to probe materials properties and physics on the nanometer scale.   

Tunneling anisotropic magnetoresistance in Ni break junctions

Anisotropic magnetoresistance (AMR) is the difference in resistance as the magnetization direction is changed with respect to the direction of current flow. We will present results of first-principles calculations of AMR in Ni nanowires. It is known that in the ballistic regime the conductance of a magnetic nanowire changes in steps of $e^{2}$/$h$ as the angle of the magnetization changes with respect to the axis of the wire.[1] This ballistic AMR (BAMR) effect originates from the spin-orbit coupling which can change the number of bands crossing the Fermi energy ( $E_{F}$ ) as the magnetization direction is changed. We extend this consideration to the case of a break junction, where transport occurs via tunneling. We find a significant dependence of the tunneling conductance on the magnetization direction, an effect known as tunneling AMR (TAMR). We find that states localized at the electrode tips near the break are broadened by the spin-orbit interaction and contribute significantly to the tunneling. The position with respect to $E_{F}$ and broadening of these states depend strongly on the orientation of magnetization. Our results bear a striking resemblance to recent experimental results [2], clearly indicating an origin different from the one proposed previously.[2] This work is supported by Seagate Research and Nebraska NSF-MRSEC. [1] J. Velev et al. PRL \textbf{94}, 127203 (2005), [2] K. Bolotin et al. PRL \textbf{97}, 127202 (2006).   

Magnetoresistance in Boron Carbide junctions

The properties of thin insulator layers are crucial to the performance of magnetic tunnel junctions. Commercial requirements are a device with a high tunnel magnetoresistance (TMR) with low cost and high stability. At present the vast majority of barriers are made from amorphous Al$_{2}$O$_{3}$ and crystalline MgO. The TMR value depends not only on the spin-dependent electronic structure of the electrodes, but on the metal-insulator interface. Oxide-type barriers may suffer from local vacancies and other type of defects, resulting in oxygen diffusion, making the TMR value unstable with time. We present TMR results obtained on a non-oxide barrier, boron carbide (B$_{10}$C$_{2})$ for applications in magnetic tunnel junctions. This low $Z $inorganic material can be grown by plasma enhanced chemical vapor deposition (PECVD) without pinholes in the ultra thin film regime. PECVD grown boron carbide is an excellent dielectric with resistivities in the range of 10$^{7}$ ohm-cm, with a band gap that can be adjusted from 0.7 eV to 1.9 eV by altering the boron to carbon ratio and to band gap values well above 2.7 eV by adding phosphorus. This creates a unique opportunity for experimental study of a broad spectrum of phenomena, related to the dielectric properties of the barrier.   

Inelastic Electron Tunneling Spectroscopy of a Molecular Magnetic Tunnel Junction.

We present the results of systematic measurements of molecular magnetic tunnel junctions (MTJs). In this study, we fabricated molecular-monolayer based MTJs and show that inelastic electron tunneling spectroscopy (IETS) can be utilized to characterize such junctions to investigate the existence of desired molecular species in the device area and to study the reported bias-dependence of junction tunneling magnetoresistance (TMR). Temperature-dependent current-voltage characterizations have been performed on the fabricated molecular MTJ with octanethiol as the molecular tunnel barrier. Tunneling transport has been observed at T $<$ 50K. IETS measurement at T = 4.2 K revealed spectra signatures due to $\nu $(Ni-S), $\nu $(C-S), and $\delta _{s}$(CH$_{2})$ vibrational modes, thus confirming the presence of the molecular species confined inside the ferromagnetic-octanethiol magnetic tunnel junctions. TMR measurements have been carried out and spin-dependent tunneling transport has been observed. A bias-dependence of the tunneling resistance has been observed. IETS measurements at different magnetic field suggest that the like cause of the TMR bias-dependence is inelastic scattering due to molecular vibrations.   

Towards Fully Organic Tunnel Junctions

Quantum mechanical tunneling through ultrathin (25 A) insulating materials has been experimentally verified since the 1950's. Only recently, has tunneling through organic based materials and single molecules occurred from inorganic metallic injectors. We present here our effort focused on fabrication and characterization of an all organic tunnel junction where the injector is a conducting polymer and discuss the subtle difference which stem from polaronic metal.   

Session A15: Focus Session: Spin Freezing on Frustrating Lattices

Magnetic diffuse scattering in Tb3Ga5O12 and Tb3Al5O12 garnets

In geometrically frustrated systems, long-range magnetic ordering is usually suppressed down to very low temperatures. While in the so-called spin liquid phase, magnetic diffuse scattering is observed. The physical origin of such scattering is not well understood. Using neutron scattering and DC, AC magnetic susceptibility measurements on Tb3Ga5O12 and Tb3Al5O12, we observed magnetic diffuse scattering and unusual paramagnetic behavior. The M-T curve at high magnetic field does not coincide with the one at low fields below $\sim $10 K. This indicates that magnetic correlations are gradually developing around that temperature. The nonlinear response of the AC susceptibility suggests that the diffuse scattering may originate from critical scattering, which has also been observed in frustrated spinel systems. This might indicate the realization of soft (magnon) modes in the spin liquid phase.   

Spin glass freezing in the disorder-free pyrochlores A$_{2}$Sb$_{2}$O$_{7 }$(A = Mn, Co, Ni)

The pyrochlores in the series A$_{2}$Sb$_{2}$O$_{7}$ (A = Mn, Co, Ni) have been synthesized and characterized as exhibiting spin glass transitions at T$_{G }$= 41, 4.5 and 2.6 K (for A = Mn$^{2+}$ S = 5/2, Co$^{2+}$ S = 3/2, and Ni$^{2+}$ S= 1 respectively) despite the lack of chemical disorder. Since the Curie-Weiss temperature remains essentially constant for all members in the series ($\theta $ = -40 K), the frustration index for these materials increases significantly as the moment size is reduced from f = 1.1 (Mn) to 9.3 (Co) to 14.6 (Ni). There is also a corresponding change in the spin dynamics measured by the shift in the AC susceptibility signal as a function of frequency. These new materials provide an avenue to investigate the effect of quantum fluctuations on the Heisenburg pyrochlore lattice in the low spin limit, and show that there is a dramatic change in the spin dynamics as the quantum regime is approached   

Low temperature specific heat of geometrically frustrated Gd$_2$Sn$_2$O$_7$

Previous measurements of the specific heat of Gd$_2$Sn$_2$O$_7$ showed a $T^2$ power law below a strongly first-order phase transition, though there was some indication of a deviation from this power law below 500 mK\footnote{P. Bonville \emph{et al.} J. Phys.: Cond. Mat. {\bf 15}, 7777 (2003).}. Theory has predicted that anisotropy due to the dipolar interaction leads to a gapped spin wave spectrum resulting in an exponential specific heat as $T$ approaches 0.\footnote{A. G. Del Maestro and M. J. P. Gingras, J. Phys.: Cond. Mat. {\bf 16}, 3339 (2004).} We will present specific heat measurements to below 100 mK. Preliminary results show a deviation from the $T^2$ law which supports the above theoretical model.   

Slow spin relaxation and zero point entropy in diluted and stuffed rare earth pyrochlores

Work on the cooperative paramagnet ${Tb}_{2}{Ti}_{2}{O}_{7}$, and on the spin ices ${Dy}_{2}{Ti}_{2}{O}_{7}$ and ${Ho}_{2}{Ti}_{2}{O}_{7}$ has exposed new avenues of study into the nature of excitations and ordering in geometrically frustrated magnetic systems. Here, we will present low temperature AC susceptibility, magnetization, and heat capacity data on these materials, and on their diluted and stuffed variants, formed either by replacing some magnetic rare earth ions with non-magnetic $Y$ or $Lu$, or by replacing some $Ti$ with magnetic $Ln$ ions. Experimental results on diluted ${Tb}_{2}{Ti}_{2}{O}_{7}$ and ${Dy}_{2}{Ti}_{2}{O}_{7}$ will be discussed, which indicate the existence of slow spin relaxations ($\tau\geq0.001 s$) in both systems, but with opposing characters [1,2]. For the stuffed materials, we will show that additional $Ln$ ions cause the effective magnetic interaction to become stronger and increasingly antiferromagnetic. Additionally, low temperature AC susceptibility and heat capacity data will be presented to compare the different effects of stuffing on the ground states of the materials [3]. \newline \newline [1] \textit{Phys. Rev. Lett.} \textbf{96}, 027216 (2006). \newline [2] \textit{Phys. Rev. Lett.} \textbf{91}, 107201 (2003). \newline [3] \textit{Nature Phys.} \textbf{2}, 249 (2006).   

Effective Thermodynamics of Artificial Spin Ice

We analyze the effective thermodynamics of artificial spin ice: a recently realized lattice of nanoscale single-domain ferromagnetic islands that are arrayed along the edges of a square lattice[1]. After demagnetization, the moments in this model system have a static disordered configuration similar to the frozen state of the spin ice materials. We demonstrate that this athermal state has extensive degeneracy and we introduce a formalism that can predict both the entropy and an effective temperature. The theory also predicts the populations of local states and short-distance correlations of this ice-like system with no adjustable parameters. \newline \newline References: \newline [1] R.~F. Wang, C.~Nisoli, R.~S. Freitas, J.~Li, W.~McConville, B.~J. Cooley, M.~S. Lund, N.~Samarth, C.~Leighton, V.~H. Crespi and P.~Schiffer, Nature (London) {\bf 439}, 303.   

Dynamics of Artificial Kagome `Spin Ice' In Geometrically Frustrated Permalloy Nano Structures

Thin films of ferro-magnetic material with lithographically designed geometries can be used as an analog for the study of spin ice or frustrated systems. Here we study the magnetic structure and magnetization dynamics of permalloy thin films in a frustrated, hexagonal geometry using Transmission Lorentz Microscopy. The permalloy films are evaporated through patterns defined by conventional electron beam lithography to form single domain elements. These elements interact absent the effects of inhomogeneity and disorder associated with multi-domain magnetic elements and their grain structures. The mapping of in-plane magnetic moments through Lorentz microscopy show these magnetic structures to be governed by spin ice rule usually found in Kagome lattice systems. The switching process of these magnetic structures is observed using in-situ application of magnetic fields. The spin ice rule is shown to be valid as the exchange energy between elements is minimized in this artificially designed geometry.   

Quantum Antiferromagnet on a Hyper-kagome Lattice: Applications to Na$_4$Ir$_2$O$_8$

Motivated by the intriguing low temperature paramagnetic behaviour recently observed in the Mott insulator Na$_4$Ir$_2$O$_8$, we study the quantum antiferromagnet Heisenberg model on a hyper-kagome lattice. Employing a large N generalization of the Schwinger boson description of spin systems uniquely suited to frustrated lattices, we find various closely competing phases for the ground state. Implications of our results for Na$_4$Ir$_2$O$_8$ are also discussed.   

Classical antiferromagnet on a hyper-kagome lattice

Motivated by recent experiments on Na$_4$Ir$_3$O$_8$ [Takagi, unpublished], we study the classical antiferromagnet on a frustrated three-dimensional lattice obtained by selectively removing one of four sites in each tetrahedron of the pyrochlore lattice. This ``hyper-kagome'' lattice consists of corner-sharing triangles. We present the results of large-$N$ mean field theory and Monte Carlo computations on $O(N)$ classical spin models. We find the classical ground states to be highly degenerate. Nonetheless, at low temperatures, nematic order emerges via ``order by disorder'' in the Heisenberg model ($N$=3), representing the dominance of coplanar spin configurations. Above this transition, the spin-spin correlations show a dipolar form which can be understood to arise from a generalized ``Gauss' law'' constraint. Implications for future experiments are discussed.   

Spin Glass Order Induced by Dynamic Frustration

It is generally believed that both frustration and disorder are essential ingredients in the formation of a spin glass ground state. It was therefore surprising that PrAu$_2$Si $_2$ was reported to show all the characteristics of a spin glass, even though it is a stoichiometric compound with a well-ordered crystal structure. We report on inelastic neutron scattering measurements of the crystal field excitations, which show that PrAu $_2$Si$_2$ has a singlet ground state and that the exchange coupling is extremely close to the critical value to induce magnetic order. We propose that fluctuations of the crystal field levels are enough to destabilize the induced moments and prevent phase-coherent long-range order, and that spin glass freezing results from this dynamic frustration rather than any intrinsic static disorder.   

Spin dynamics in LiY$_{0.998}$Ho$_{0.002}$F$_4$ via $^{19}$F NMR and $\mu$SR

The $^{3+}$Ho ion doped into the host LiYF$_4$ is a single-ion magnet demonstrating slow dynamics at the avoided level crossings (ALCs) in the hyperfine-coupled electronuclear Zeeman diagram. We have studied $^{19}$F NMR and $\mu$SR in dilute LiY$_{0.998}$Ho$_{0.002}$F$_4$ to probe these dynamics and find clear evidence for an increase in the spin-lattice relaxation rate {\it{1/T$_1$}} at field values corresponding to ALCs using both techniques. We will discuss using these signatures as probes to measure the tunnel splitting $\Delta$ and the level broadening, as well as the onset of magnet correlations for increasing Ho concentration.   

Session A16: Ab-initio Theory of Spin Dependent Properties

Electronic structure theory of wide gap dilute magnetic semiconductors

The recent exciting reports that wide gap semiconductors, most notably ZnO, TiO$_2$ and GaN, when doped with transition metal elements, may have Tc's that are higher than room temperature have attracted great interest. When interpreted with care, highly precise first principles FLAPW calculations such as used here\footnote{E.Wimmer,H.Krakauer,M.Weinert,A.J.Freeman, PRB {\bf 24}, 864(1981)}, are now providing insights into the nature of their strong ferromagnetism (FM). Here, we present an analysis to the electronic structures of several typical wide gap DMS's and illustrate how first principles calculations can lead to correct predictions of their magnetic properties for both Cr:TiO$_2$ and Mn:GaN. The results demonstrate the importance of defect compensation in the determination of the magnetism. A comparison between Mn:ZnO and Co:ZnO highlights the fundamental difference in their electronic structures which explains why their FM is dependent on carriers of different polarity. Correct predictions of their magnetism are found to be due to the correct treatment of the LDA band gap problem. Finally, we provide semi-quantitative discussions of Co doped TiO$_2$, and illustrate why it is highly non- trivial to fully explain its FM based on first principles calculations.   

Spin-driven transition metal clustering in the wide-gap ferromagnetic semiconductor Cu$_2$O:Co

Cu$_2$O is a prototype material for p-type transparent conductive oxides, and a host material for diluted magnetic semiconductors. Using local density-functional supercell calculations we study (1) the origin of p-type behavior of pure Cu$_2$O, and (2) the short and long range magnetic interactions of Co atoms substituting Cu. We find that (i) Cu vacancies produce holes, which O vacancies are not able to destroy thus explaining the natural p-typeness, (ii) a single Co induces a fully occupied and localized level near midgap. This would suggest Co--Co magnetic interactions to be weak because there is no energy gain in magnetic coupling. Nevertheless, (iii) we find that Co--Co pairs lead to a huge ferromagnetic stabilization energy and binding energy, both of around 0.5~eV/pair. This dimerization is accompanied by strong lattice relaxation and symmetry breaking together with level splitting. Both clustering and ferromagnetism are caused by the fact that the bonding states of the previously unoccupied levels become occupied and are lower in energy relative to the antibonding levels of previously occupied levels. Such binding is allowed only for Co atoms with the same spins, leading to ferromagnetism (albeit short ranged).   

Mechanism of ferromagnetism in wide band gap semiconductors

Several wide bandgap semiconductors/oxides doped with small concentrations of transition metal impurities have been found to exhibit ferromagnetism at temperatures higher than room temperature. As the typical dopant concentrations are far below the percolation threshold associated with nearest neighbor cation coupling, a picture of ferromagnetism has been proposed which attributes an important role played by the intrinsic defects which are present in these materials. We have considered several examples of the most common defects found in GaN and ZnO, and examined within ab-initio calculations how their presence modifies ferromagnetism. Some defects, such as Ga-vacancies in GaN favor strongly spin polarised configurations with exchange splittings as large as 1 eV. However, the exchange splittings are quenched if the defect induced levels are below the transition-metal induced levels. We consider various scenarios for the location of the defect induced levels and the transition metal levels and identify the regime of defect enhanced ferromagnetism and examine various features of this regime.   

First-principles Investigation of the Neutral and Charged Embedded Clustering in Mn doped GaN: Revisited

Based on extensive density functional theory calculations, the spatial distribution and magnetic coupling of Mn atoms in Mn:GaN has been re-investigated by doping up to 5 Mn atoms in large supercells, where both the neutral and selected charged valence states are studied. The Mn atoms are found to have a tendency to form substitutional embedded clusters with the long-range wurtzite structure maintained. While for neutral pair-doping, the coupling is ferromagnetic regardless of the distance and orientation of Mn atoms, for the experimentally observed oxidation charged state $\rm Mn^{2+} $($d\rm^{5}$), antiferromagnetic coupling becomes favorable. Furthermore, for both neutral and negatively charged states, for larger (than pair) cluster configurations, states containing antiferromagnetic coupling are always favored. The size of supercell and the atomic relaxation are found important. The electrical conductivity of Mn:GaN depends sensitively on the valence charged states, where the oxidation states $\rm Mn^{2+}$($d\rm^{5}$) exhibit highly insulating character as observed in experiments. Our results highlight the intrinsic complex nature in transition metal doped dilute magnetic semiconductors, and can rationalize some hitherto puzzling experimental observations.   

Heusler clusters

Heusler alloys are known for their bulk properties, for example the magnetic shape-memory Ni$_2$MnGa [1]. Using first principles simulations, based on the real space pseudopotential method implemented in PARSEC [2], we examine Heusler alloy clusters. Clusters with various Ni-Mn-Ga compositions are examined in the size from 15 up to 113 atoms. Clusters with compositions being the closest to the stoichiometric Ni$_2$MnGa are the most stable. The geometry of tetrahedral coordination in Heusler structures is energetically favorable. In order to retain this coordination, clusters have to be symmetrically shaped. This implies that even in very small clusters the structure is bulk-like. However, the electronic densities of states do not show Kohn-like anomalies at the Fermi level, that are characteristic for bulk Ni-Mn-Ga alloys. [1] P. Entel, V. D. Buchelnikov, V. V. Khovailo et al. J. Phys. D: Appl. Phys. 39, 865 (2006) [2] http://www.ices.utexas.edu/parsec/   

Control of Magnetic Order in Monolayer Films by Substrate Tuning

Surprisingly, antiferromagnetic order has recently been observed in a monolayer (ML) film of Fe on W(001) [1] and a novel, nanoscale magnetic structure has been discovered for a ML Fe on Ir(111) [2] showing the crucial influence of the substrate. Here, we therefore propose to tailor exchange interactions in magnetic monolayer films by tuning the adjacent non-magnetic substrate. Using first-principles calculations based on density functional theory, we demonstrate a ferromagnetic-antiferromagnetic phase transition for one ML Fe on a Ta$_{x}$~W$_{1-x}$(001) surface as a function of the Ta concentration. At the Ta concentration of the transition, the nearest-neighbor exchange interaction becomes negligible and exchange terms beyond nearest-neighbors and higher order spin interactions beyond the Heisenberg Hamiltonian become crucial. In this regime, the accessible magnetic phase space is dramatically enhanced, and we study complex magnetic order such as spin-spiral states, multiple-$q$ states, or even disordered local moment states. [1] A.\ Kubetzka, {\sl et al.}, Phys.\ Rev.\ Lett.{\bf 94}, 087204 (2005). [2] K.\ von Bergmann, {\sl et al.}, Phys.\ Rev.Lett.\ {\bf 96}, 167203 (2006).   

Linear scaling \textit{ab initio} approach to the electronic structure calculation for L1$_{0}$-FePt nanoparticles embedded in FePt random alloy

Magnetic nanostructures present substantial theoretical challenges due to the need to treat the electronic interactions quantum-mechanically whilst dealing with a large number of atoms. In this presentation, we show a direct quantum mechanical simulation of~magnetic nano-structures made of spherical L1$_{0}$-FePt nanoparticles, with diameter within 2.5 nm $\sim $ 5 nm, embedded in an fct-FePt random alloy. The calculation is performed using the locally self-consistent multiple scattering method, a linear scaling \textit{ab-initio} all-electron method capable of treating tens of thousands of atoms. We found that there exists a screening region below the surface of each nanoparticle which essentially screens out the effect of the external random alloy to keep the physical properties of the interior region unchanged from the bulk of L1$_{0}$-FePt. Interestingly, the depth of this screening region is independent of the size of the nanoparticles we have investigated. We will show a non-collinear electronic structure calculation for the nano-structure and discuss the exchange coupling between the nanoparticle and the surrounding random alloy.   

Surface magnetism of Fe/W(110): an ab-initio study of the substrate effects

The pseudomorphic monolayer of Fe grown on a W(110) surface is very interesting from the point of view of magnetism. In studies of the surface magneto-crystalline anisotropy, the Fe monolayer on top of a W substrate has become the system of choice, since (a) the growth of the first Fe monolayer is pseudomorphic, (b) the W substrate has a large spin-orbit coupling, and (c) the interface anisotropy is the strongest ever observed. This makes the Fe monolayer on a W substrate a good candidate for an {\em ab initio} benchmark investigation of how the properties of the magneto-crystalline anisotropy are influenced by the substrate. Our investigation is done as a function of the substrate thickness (up to 8 layers). Analyzing the magnetocrystalline anisotropy energies, we find stable (with respect to the number of substrate layers) in-plane easy and hard axes of magnetization along the [1$\bar{1}$0]- and [001]-directions, respectively, reaching a value in good agreement with experiment for thick substrates. Additionally, the magnetic spin- and orbital moments, and the density of the Fe $d$-states are analyzed at different numbers of substrate layers as well as with respect to the direction of magnetization, confirming recent observations that ``Hund's 3rd rule is broken'' for the W substrate.   

Giant magneto-crystalline anisotropies in transition-metal monowires

The magneto-crystalline anisotropy energy (MAE) proved to be crucial for stability of magnetism in low-dimensional structures against thermal fluctuations. Here, we report on magnetic properties of free standing $3d$, $4d$, and $5d$ transition-metal (TM) monowires, paying special attention to the influence of spin-orbit interaction, revealing its utter importance for magnetism in these structures. The calculations were performed with the one-dimensional (1D) version of the full-potential linearized augmented plane-wave (FLAPW) method. The new 1D-FLAPW scheme [1] is extremely fast and allows a natural treatment of structures with 1D geometry. We present equilibrium interatomic distances, spin- and orbital moments, and the values of MAE. Across the series the easy axis of magnetization oscillates between two possible directions: perpendicular and along the wire axis. The largest values of the MAE occur at the end of the series. Giant values of 30-100 meV/atom can be obtained upon stretching of $4d$- and $5d$-TM wires. Certain chains change the magnetization direction upon wire stretching, opening new perspectives in controlling the spin-dependent ballistic conductance in these structures [2]. [1] Y.Mokrousov {\sl et al.}, Phys.\ Rev.\ B\ {\bf 72}, 045402 (2005), [2] Y.Mokrousov {\sl et al.}, Phys.\ Rev.\ Lett.\ {\bf 96}, 147201 (2006)   

Qualitative aspects of magnetism formation in Gd and its compounds

Using highly precise full-potential electronic structure calculations, we study the formation of magnetism in gadolinium. By manipulating the 4f-shell magnetic moments in a large supercell, the interplay between on-site and off-site contributions to the spin polarization of valence electrons is analyzed. Qualitative features of exchange coupling are discussed, and the limitations of model RKKY-like approaches are demonstrated. We also analyze the magnetization density distribution in ferromagnetic hcp Gd which, unlike transition- metal ferromagnets, shows a strongly inhomogeneous, directional structure in the interstitial region. The qualitative features revealed in this study are very generic, and we discuss their relevance to other rare-earth elements and their compounds.   

First-principles Calculation of Atom-scale Magnetic Interaction

The advance of manipulating atoms on surfaces by STM has made it possible to study atomic magnetism. It has been shown that STM can build chains of magnetic atoms and measure magnetic excitation of such chains [1]. This new technique has potential application to explore the limits of magnetic data storage, by engineering the energy required to flip the collective orientation of a small number of magnetically coupled atoms. We have applied GGA+U to determine the atomic spin and calculate the exchange coupling J (several meV) for Mn chains on a CuN/Cu(100) surface. Our spin-density analysis shows that Mn atoms in such a surface preserve their atomic spins S=5/2. To demonstrate the potential to engineer the coupling between atomic spins, we calculate the J's for the Mn dimers atop Cu atoms and atop N in the CuN layer, and find the Cu-site dimer has its J twice as large as the N-site. The local structures of the Mn dimers on these two sites determined by relaxation account for this difference in J.The charge transfers between Mn and its neighboring atoms are also calculated. [1] C. F. Hirjibehedin, C. P. Lutz, A. J. Heinrich, Science \underline {312}, 1021 (2006).   

Ab-initio determination of magnetic properties of Fe-Co nanoclusters on Cu(100).

By making use of the fully-relativistic screened Korringa-Kohn-Rostoker method supplemented by the embedded cluster method the spin and orbital magnetic moments as well as the magnetocrystalline anisotropy energy (MAE) of Fe-Co nanoclusters of different sizes are explored as a function of the cluster composition. The MAE and magnetic moments are found to vary strongly in dependence on the concentration of Fe and Co atoms as well as on specific arrangements of atoms within the clusters. Consequently the easy magnetization axis can be tuned by controlling the cluster composition. In contrast to clusters of a pure material there exist additional contributions to the anisotropy in the surface plane due to the two different atomic species.   

Magnetism of small Co clusters as a probe of \textit{ab initio} theory

We report \textit{ab initio} calculations of the electronic and magnetic properties of small Co clusters. We performed pseudopotential-based and all-electron calculations. In view of the ``unwritten theorem'' that electron localization enhances the electronic correlations, we have also considered the LDA+U functional, which is tailored for the strong-correlation problem associated with, e.g., partially-filled $d$ shells. As a result of the weak dependence of the total energy on the calculated magnetic moment, the latter is very sensitive to the method employed. Thus, the magnetic moments obtained in the all-electron and pseudopotential calculations are quite different. Furthermore, the on-site Hubbard $U$ enhances the magnetic moment significantly. The available experimental data for the magnetic moment of small clusters [Billas et al., Science \textbf{265}, 1682 (1994)] are consistent with this enhancement.~ Additional Stern-Gerlach measurements for smaller clusters would, in combination with our \textit{ab initio} results, constitute a direct determination of the $U$ for these prototypes of correlated-electron behavior. (*) Supported by NSF Grant ITR DMR-0219332 (+) Managed by UT-Battelle for the U.S. DOE under contract DE- AC05-00OR22725   

Non-collinear magnetism in Permalloy ($\mathrm{Ni}_{0.8} \mathrm{Fe}_{0.2}$)

Permalloy is an important material in a wide variety of magnetic systems, most notably in GMR read-heads. However, despite this great interest its properties are not fully understood. For an in depth analysis of important physical properties as e.g. electric transport or magnetic anisotropy a detailed understanding of the distribution of magnetic moments on an atomic level is necessary. Using our first principles Locally Self-consistent Multiple Scattering (LSMS) method we calculate the magnetic ground state structure for a large super-cell model of Permalloy. Our code allows us to solve both the usual non-relativistic Schr\"odinger equation as well as the fully relativistic Dirac equation and to find the magnitude and direction of the magnetic moments at each atomic site. While the non-relativistic calculation yields a collinear ground state in accordance with previous calculations, we find the ground state for the fully relativistic calculation to be slightly non-collinear. We also investigate the influence of variations in the iron concentration on the distribution of magnetic moments. Research sponsored by DOE-OS and BES-DMSE under contract number DE-AC05-00OR22725 with UT-Battelle LLC. The calculations presented were performed at the Center for Computational Sciences (CCS) at ORNL and at the National Energy Research Scientific Computing Center (NERSC).   

Session A17: Charged and Ion - Containing Polymers

Solvent effects on polyelectrolyte charge and conformation in solution

We study partially quaternized poly(2-vinyl pyridine) in a wide range of solvents, with chloride or iodide counterions. Dielectric spectroscopy (conductivity) determines the effective charge on the polymer, which increases systematically with solvent dielectric constant, but is significantly smaller than the Manning prediction for strongly charged polyelectrolytes in high dielectric constant solvents. Small-angle X-ray scattering and specific viscosity are used to provide two independent measures of the correlation length. The results motivate us to include ion solvation effects and both ion-dipole and dipole-dipole attraction effects in the `solvent quality' of the Dobrynin scaling model. For instance, the stronger dipole of condensed iodide makes ethylene glycol a poor solvent, while it is a good solvent for the polymer with chloride counterions.   

Electrostatic Properties of an Entirely Hydrophilic Polyelectrolyte.

A new of class of polyelectrolyte ionenes is described, one with an entirely hydrophilic backbone of quaternized nitrogens connected by polyoxyethylene spacers of controlled length. The chemistry of these pegylated ionenes yields solubility at constant charge density in solvents of varying dielectric constant; it also allows for controlled variation of polyelectrolyte charge density through choice of monomers. Such features make the new ionenes ideal model polyelectrolytes on which to test theories for electrostatic properties of polyelectrolytes. In particular, we report on the use of electrophoresis to measure effective charge density for different charge spacings and dielectric constants. In conformance with previous results for aliphatic ionenes, we find counterion condensation for pegylated ionenes at conditions different than classical predictions. Counterion condensation -- a constant effective charge density - is encountered in univalent electrolyte by the lowering of dielectric constant even when the dimensionless charge density is less than unity; conditions for the condensation depend on counterion identity (size). Additional studies on various anionic polyelectrolytes dissolved in nonaqueous solvents reproduce the same trends, suggesting their universality.   

Formation, Structure and Electrochemical Impedance Analysis of Microporous Polyelectrolyte Multilayers

Microporous networks are of interest as electrolyte materials, gas separation membranes and catalytic nanoparticle templates. Here, we create microporous polyelectrolyte networks of tunable pore size and connectivity using the layer-by-layer (LBL) technique. In this method, a film is formed from the alternate adsorption of oppositely charged polyelectrolytes from aqueous solution to create a cohesive thin film. Using poly(ethylene imine) (PEI) and poly(acrylic acid) (PAA), LBL thin films of variable composition and charge density were assembled; then, the films were treated in an acidic bath, which ionizes PEI and de-ionizes PAA. This shift in charge density induces morphological rearrangement realized by a microporous network. Depending on the assembly pH and acidic bath pH, we are able to precisely tune the morphology, which is characterized by atomic force microscopy and scanning electron microscopy. To demonstrate the porous nature of the polyelectrolyte multilayer, the pores were filled with non-aqueous electrolyte (i.e. ethylene carbonate, dimethyl carbonate and lithium hexafluorophosphate) and probed with electrochemical impedance spectroscopy. These microporous networks exhibited two time constants, indicative of ions traveling through the liquid-filled pores and ions traveling through the polyelectrolyte matrix.   

Influence of humidity and crystallization time on the conductivity of nanoparticle-filled solid polymer electrolytes

The purpose of this study is to investigate two conditions that influence the conductivity of solid polymer electrolytes [SPEs]: humidity and crystallinity. SPEs cannot currently be used in solid-state lithium ion batteries because low room-temperature conductivity precludes effective application. Many modifications have been made to improve the conductivity; however, conductivity results vary widely for the same system investigated within different studies. One explanation is that SPE conductivity is extremely sensitive to experimental conditions which are often not reported. We investigate the consequence of humidity on conductivity, and the time at which conductivity is measured following sample preparation. Specifically, we choose nanoparticle-filled SPEs as an example to demonstrate that various conclusions can be made regarding the influence of nanoparticles on conductivity, depending on the experimental conditions.   

Counterion Effects on Ion Mobility and Mobile Ion Concentration of Doped Polyphosphazenes and Polyphosphazene Ionomers

Previous investigations have shed some light on the ion conduction process in polymer electrolytes, yet ion transport is still not well understood. Here, upon the application of a physical model of electrode polarization to two systems with nearly identical chemical structure, one composed of an ionomer (MI) with a single mobile cation, and the other a salt-doped polymer (M+S) with mobile cation and mobile anion, quantitative comparison of the conductivity parameters is achieved. The polymer electrolyte chemistries of both MI and M+S are based on poly(methoxyethoxy-ethoxy phosphazene) (MEEP). The glass transition was found to be an important factor governing the conductivity and ion mobility. However, even accounting for the glass transition, the mobility of ions in the M+S system is 10 times larger than that in the MI system, which must arise from faster diffusion of the anion than the cation. Values for mobile ion concentration are also approximately 10 times higher in M+S than MI. These differences originate from free volume available for diffusion and local environment surrounding the ion pairs, demonstrating that the location of the ion pairs in the polymer matrix has a crucial effect on both conductivity parameters. Research supported by NSF Polymers Program.   

Ion mobility and mobile ion concentration in PEO-based polyurethane ionomers

The conductivity of a series of single-ion conducting polyurethane ionomers, based on poly(ethylene oxide) (PEO) segments and containing Li$^{+}$ and Na$^{+}$ cations, was studied using dielectric spectroscopy. The application of a physical model of electrode polarization allows the separate determination of the ion mobility and the mobile ion concentration as a function of temperature. The influence of temperature, type of mobile cation, and water content on the parameters determining the ionic conductivity was investigated, in order to contribute to the understanding of the mechanisms of ion conduction. The conductivity is also discussed in relation to the glass transition and dielectric relaxation processes of the materials. The results are compared to those of previous studies on PEO-based polyester ionomers having a closely related chemical structure.   

Conformational structures in dry ionomers

The molecular architecture of polymer electrolyte membranes (PEM), which consist of hydrophobic and hydrophilic segments, leads to its own self-assembled structure through a partial phase segregation. Controlling these structures is necessary for improving the performance of fuel cells. We have used computer simulation to analyze the relationship between the hydrophilic cluster structure and the parameters describing the pendant side chains in dry Nafion-like materials. We investigate the morphology of a dry PEM system within different coarse-grained models: a free-proton model, a dipolar model for side chains, and a branched-chain model. We conclude that the free-proton model, where the proton-proton correlations are decoupled from the sulfonate-sulfonate correlations, has the potential to explain the experimentally observed conformational structures of PEM. We find that the geometry of domains with a high concentration of sulfonate groups depends only weakly on the form of the distance-dependent dielectric permittivity, but strongly depends on the partial charge and monomeric unit sequence distribution along the ionomer chain. We predict a nanophase separation with a lamellar-like morphology in ionomers carrying a divalent salt.   

Water Diffusion in Ultrathin Ionomer Thin Films: Neutron Reflectivity Study

The mechanism of penetration of solvents into ionic random co-polymers is a key to formation of polymeric membranes with selective transport. The pathways of diffusion depend on molecular parameters including the chemical structure, ionic strength and conformation of the polymer. The penetration of water into thin (on the order of magnitude of several R$_{g}$'s) highly rigid sulfonated polyphenlylene films, supported on SiOx substrate as a function of time was investigated by neutron reflectometry. The ionomer films were exposed to saturated vapor and to liquid water and reflectometry patterns were recorded until equilibrium was reached. Increase thickness due to swelling was observed in both cases whereas exposure to vapors results in reversible changes and contact with bulk water, transform the film permanently. The onset of the diffusion is Fickian, however the distribution of the solvent within in the film is not uniform. Clear interfacial segregation is denoted.   

Nanoscale Morphology of Sulfonated Polystyrene Ionomers

We have applied our scanning transmission electron microscopy (STEM) methods to investigate the size, shape and spatial distribution of the ionic, nanoscale aggregates in poly(styrene-\textit{ran}-styrene sulfonate) (P(S-SS$_{x}))$ ionomers. This analytical electron microscopy method minimizes phase contrast that can obscure nano-scale features and accentuates differences in atomic number. We recently reported quantitative agreement between STEM and X-ray scattering results in a Cu-neutralized poly(styrene-\textit{ran}-methacrylic acid) (SMAA) ionomer with respect to the size of the ionic aggregates and their number density. For this study, P(S-SS$_{x})$ ionomers were prepared by solution neutralizing with metal acetates, solution casting, and annealing. Initial STEM results from P(S-SS$_{0.019})$ fully neutralized with Zn indicate a uniform distribution of monodisperse spherical aggregates. Combining direct imaging and X-ray scattering of P(S-SS$_{x})$ ionomers, we will investigate the effect of cation type and level of neutralization.   

Morphology and Proton Transport in Polyimide-Polysiloxane Segmented Copolymers

Sulfonated polyimides are fuel cell candidates due to their good mechanical, chemical, and thermal stability, and their relatively high proton conductivity. Here we report the one-pot synthesis of sulfonated polyimide-polysiloxane segmented copolymers through the reaction of a dianhydride with a mixture of three diamines: a non-ionic aromatic diamine (4,4'-oxydianiline), a sulfonated diamine (4,4'-diamino-2,2'-biphenyldisulfonic acid), and a telechelic diamino polysiloxane. The presence of ionic clusters that are covalently connected to hydrophobic siloxane groups lead to interesting morphologies, swelling behavior, and proton transport characteristics. Equilibrium water sorption studies of cast films show that the presence of siloxane segments does not interfere with water swelling, suggesting microphase-segregation. TEM analysis shows evidence of phase-segregation in sulfonated polyimides and reveals that siloxane segments strongly affect ionic clustering.   

Morphological Study of Model Poly(Ethylene-Acrylic Acid) Ionomers

We have synthesized \textit{linear} poly(ethylene-co-acrylic acid) (EAA) copolymers with precisely and randomly placed acid groups using ADMET (acyclic diene metathesis) and ROMP (ring opening metathesis polymerization). In the acid form, the EAA copolymers with precisely placed acid groups exhibit the typical orthorhombic PE crystal structure along with a new layered structure. The layered structures are more pronounced at lower acid content and have spacings consistent with the separation between acid groups; at 9.5mol{\%} acid the layer-to-layer spacing is 2.53 nm. Given the PE crystal lamellae spacing determined by SAXS, each PE lamellae contains 2 to 6 acid-rich layers. The EAA copolymers with random acid groups do not exhibit well-developed layered structures. When these linear EAA copolymers are neutralized with zinc acetate in solution, STEM and X-ray scattering are used to characterize the Zn-rich ionic aggregates. Preliminary results have indicated that the ionic interactions dominate and disrupt the acid-acid layered structure even at partial neutralization.   

Proton Conducting Membranes from Fluorinated Poly(Isoprene)-\textit{block}-Sulphonated Poly(Styrene): Structure and Transport Properties.

Proton Conducting Membranes used in Fuel Cells typically comprise of ionomers, having hydrophobic backbones and hydrophilic acid bearing side chains. Cell Efficiencies are determined by membrane morphology amongst other factors. Our work is aimed at optimizing the morphology and ultimately properties of our relatively cheaper fluorinated Poly(Isoprene)-block-sulphonated Poly(Styrene) block copolymer ionomer membranes, made from post polymerization modified PS-PI. Samples have been synthesized with two levels of sulphonation of polystyrene units (25mol{\%} and 50mol{\%}), and two counterions (Cesium and proton). Analysis of our membranes has been carried out using SAXS/SANS, Gravimetry, Diffusion Cells and Electrochemical Impedance Spectroscopy. SAXS and SANS data have shown a 63{\%} increase in domain spacing upon soaking the 50mole{\%} Acid form with heavy water for 16hours at 60oC. This sample also had a water uptake value of 595{\%} and an order of magnitude less methanol permeability than Nafion{\texttrademark} 112 at ambient temperature.   

Polyelectrolyte Interfacial Swelling and Film Stability

The phase stability of polyelectrolytes at interfaces and in thin films are of fundamental interest for the fabrication of high resolution features by photolithography. In this process, a latent chemical image is formed within a thin polymer film by exposure to light and subsequently resolved by selective dissolution. The selective dissolution occurs at a polyelectrolyte copolymer gradient comprised of hydrophilic (weakly acidic) and hydrophobic groups. The balance between the hydrophobicity and hydrophilicity (degree of ionization) controls the film stability when exposed to an aqueous hydroxide solution. The average copolymer content that dissolves away can be understood by phase diagrams, but a residual material that swells, but does not dissolve, occurs within the gradient interface. Controlling this swelling amplitude and depth is of technological interest to prepare high fidelity features of ever smaller dimensions. Contrast variant neutron reflectivity and quartz crystal microbalance quantify this nanometer-scale spatial distribution of polyelectrolyte and aqueous base. The swelling spatial extent measured during in situ dissolution, water rinse, and drying implies the polymer profile is dynamic on the nanometer scale. The profile control by ionic strength and charge valence will also be discussed.   

ATRP-derived functional polymers for electronic applications

Traditionally, the controlled synthesis of functional polymers has been challenging due to the incompatibility of chemical functional groups with the propagating active centers during polymerizations. This barrier, however, has been overcome with the development of atom transfer radical polymerization (ATRP). Using this technique, in combination with ring-opening polymerization, we have successfully synthesized well-defined block copolymers containing polypentafluorostyrene (PPFS) and polylactide (PLA). Acid-catalyzed degradation of the PLA block yields PPFS films with nanoscale pores whose size and spacing are tunable through control of the diblock copolymer molecular weight and composition. The introduction of porosity to PPFS films lowers the dielectric constant, useful as isolation for interconnects. In addition, we used ATRP to synthesize well-defined homopolymers of and block copolymers containing poly(2-acrylamido-2-methyl-1-propanosulfonic acid). We used these polymers as templates for the subsequent polymerization of aniline (PANI) to create water-dispersible, directly patternable polymer conductors for thin film electronics. We can tune the conductivity of PANI through control over the molecular characteristics of the polymer acid template.   

The nature of water in hydrated acid-form Nafion membranes

The nature of water in perfluorinated membranes in the acid form (Nafion) was quantified at several hydration levels by dielectric relaxation spectroscopy. Two different experimental setups were used to probe both the low frequencies (10$^{-2}$-10$^7$ Hz, -50 to 25$^{\circ}$C) and the microwave region (0.045-26 10$^9$Hz, 25 to 45$^{\circ}$C). The competition between sulfonic-group/water attraction and water/water hydrogen-bonding, in addition to confinement effects, give rise to three states of water, manifested through distinct dynamical behaviors: The cooperative relaxation time distribution of free (isotropic) water networks is identified as the fastest process, whereas water molecules strongly bound to the charged sulfonic groups correspond to the lowest frequencies. A third relaxation mode is also observed with relaxation times at high frequencies close to the bulk water, which is attributed to ``loosely'' bound water. These water states can be correlated with the respective Nafion phase separated morphologies and the corresponding proton conductivities.   

Session A18: Photophysics of Electronic Polymers

Identification of the Possible Defect States in Poly(3-hexylthiophene) Thin Films

We find evidence for a gradual change in the electronic properties of regioregular poly(3-hexylthiophene) thin films with temperature. The conduction properties appears to be mediated by hopping conduction dominated by a low density of defects states within the highest occupied molecular orbital to lowest unoccupied molecular orbital gap, not by a change in band gap. The possible origins of a low density of defects states within the highest occupied molecular orbital to lowest unoccupied molecular orbital gap are suggested. A number of ``chemical'' defects, impurities and structural defects can contribute to features in photoemission for regioregular poly(3-hexylthiophene). A density of states within the highest occupied molecular orbital to lowest unoccupied molecular orbital gap may affect the transport properties of regioregular poly(3-hexylthiophene) and like polymers. These gap electronic states are not expected in the perfectly ordered polymer.   

Ab intio study of ladder-type metallic polymers

The electronic structure of recently synthesized ladder-type polythiophene polymer is studied with density-functional theory based calculations. It is found, in the local density approximation (LDA) that upon a simple substitution of the sulfur atoms by nitrogen and boron atoms, the band structure of the resulting polymer (called LPPyB) exhibits bands overlap between the occupied and the unoccupied states that is characteristic of metallic systems. The band structure is further validated by GW calculations confirming the assessment of the LDA results. Calculations using the B3LYP functional, which contains exact exchange, show a different electronic behavior, a small HOMO-LUMO band gap of 0.67 eV is obtained. In order to better assess the energy gap of the polymer, a TDDFT (Time-dependent density-functional theory) study of the LPPyB was performed on olygomers and verifies the metallic structure of this polymer. Other calculations were done using TDDFT on different polymers to validate the last result. In parallel, similar electronic properties were computed on an isoelectronic polymer of LPPyB, having the atomic structure of the ladder- type polythiophene, with only one sulfur atom replaced by a boron atom.   

Illumination induced metastable polaron-supporting phase in poly p-phenylene- vinylene films

We found a new illumination induced metastable polaron-supporting phase in pristine films of a soluble derivative of poly-p-phenylene vinylene (MEH-PPV). In the pristine, un-illuminated MEH-PPV phase $A$, the polymer films do not show any long-lived photogenerated polarons. Prolonged UV illumination, however, was found to induce a reversible, metastable phase $B$, characterized by its ability to support the existence of abundant long-lived photogenerated polarons. In the dark, films of phase $B$ revert back to the original phase A within about thirty minutes at room temperature. Relying on the well-established ubiquitous reversible photoinduced cyclization of diarylethenes into dihyrophenanthrene derivatives, we propose a reversible mechanism in which UV illumination creates metastable deep defects that substantially increase the photogenerated polaron lifetime.   

Ultrafast and Nonlinear Optical Spectroscopies of Excited States in Pristine and Doped $\pi $-Conjugated polymers

A variety of ultrafast and optical nonlinear spectroscopies were applied to pristine and doped $\pi $-conjugated polymers, for elucidating the excited states energy levels and primary photoexcitation species in these materials. These spectroscopies include fs pump-probe photomodulation (PM), two-photon absorption (TPA), photoluminescence up-conversion (PL(t)), and electroabsorption (EA); as well as THz time domain spectroscopy (THz-TDS). The $\pi $-conjugated polymers include derivatives of PFO, PPV and PT, as well as t-(CH)$_{x}$; doping includes fullerene molecules, as well as heavily doping with strong acceptors. The results have been analyzed in terms of the exciton picture advanced by Mazumdar et al. The primary photoexcitations are singlet excitons of which PM spectrum is composed of two strong photoinduced absorption bands in the mid and near ir spectral range, that are correlated with a stimulated emission band and PL(t). These bands are in agreements with transitions from the lowest exciton with odd symmetry into higher lying excitons with even symmetry, as revealed by TPA and EA spectroscopies. Polaron excitations are also formed and are characterized by two PA bands in the mid-ir range, and correlated ir-active vibrations. Surprisingly t-(CH)$_{x}$ is not different from many other $\pi $-conjugated polymers, except that the primary polarons recombine at a later time to form charged solitons. In fullerene-doped polymers the primary singlet excitons are trapped and undergo ultrafast nonradiative decay in doping-related defects, and this explains in part the weak cw PL in these compounds. In heavily doped polymers with strong acceptors the ground state no longer is neutral, but rather contains substantial amount of free charge carriers characterized by the Drude free carrier response in the THz to mid ir spectral ranges.   

Temperature dependence and anisotropy of charge-carrier mobilities in crystalline durene

We report on the theoretical analysis of charge-carrier mobilities in durene crystals. The crystal is studied with DFT methods to examine structural, vibrational, and electronic properties. On that basis we employ a Holstein-Peierls model (see Hannewald et al. PRB \textbf{69}, 075211 (2004); PRB \textbf{69}, 075212 (2004)) to simulate the temperature dependence of the mobilities. The relation between the anisotropy of electron/hole mobilities and the band structure as well as lattice vibrations is discussed.   

Ultrafast polarization memory dynamics of photoexcitations in $\pi $-conjugated polymers.

For better understanding ultrafast photoexcitation dynamics in $\pi $-conjugated polymers, we study the polarization memory dynamics in the pump/probe photomodulation (PM) spectrum of these materials. The transient PM spectrum of polymers contain singlet excitons with prominent photoinduced absorption (PA) band, stimulated emission and photobleaching bands in the near ir/visible spectral range; polarons with PA bands in the mid- and near-ir; and polaron pairs in the visible range. Each of these spectral feature shows polarization memory, P(t) where the PM signal with parallel pump/probe polarizations is $\sim $ twice larger than with perpendicular polarizations. P(t) has a specific dynamics for each photoexcited species, and, in addition it also depends on the excitation pump photon energy. Results for MEH-PPV films and solutions will be thoroughly discussed, in comparison with the photoluminescence efficiency.   

Experimental Determination of Charge/Neutral Branching Ratio in $\pi $-Conjugated Polymers by Broad-band Ultrafast Spectroscopy$^{1}$

We demonstrate a reliable method of determining the branching ratio, $\eta $ of photogenerated charge (polarons) to neutral (excitons) photoexcitations in various $\pi $-conjugated polymer films and solutions using femtosecond ultrafast spectroscopy with broad spectral range from 0.14 to 2.7 eV. We found that both excitons and polarons are instantaneously photogenerated, but $\eta $ critically depends on the film nanomorphology, which, in turn controls the interchain coupling. In films, $\eta $ varies between 1{\%} for derivatives of poly(p-phenylene vinylene) casted from chloroform solution, to more than 30{\%} for regio-regular poly-3-hexyl thiophene. Our results show that charge photogeneration quantum efficiency in these materials is an interchain process; and this has ramifications for their use in solar cell applications. $^{1}$Supported in part by the DOE.   

In-situ characterization of the mesophase of a high performance semiconducting polymer

Poly(2,5-bis(3-alkylthiophen-2yl)thieno[3,2-b]thiophene) is a semiconducting polymer with exceptional hole mobility in thin film transistors upon annealing into a mesophase. We have identified the structural motifs of both the mesophase and the high performance, thermally processed film with a variety of in-situ techniques: NEXAFS, spectroscopic ellipsometry (SE), and IR absorption. Upon cooling from the mesophase, the films exhibit pi-stacked lamella with molecular terraces (AFM) with a high degree of order of the conjugated backbone (NEXAFS). The side chains are well ordered (IR) and interdigitated, which may be a driving factor in the growth of large crystals. Upon re-heating, the side chains (IR) and conjugation length (SE) monotonically disorder until entry into the mesophase which is characterized by highly disordered side chains and moderate torsional disorder of the backbone but near ideal in-plane order of the polymer long axis. Side-chain order is reestablished upon re-cooling into the ordered phase. The hysteresis of the side chain order mimics the DSC of powders. As-cast films exhibit greater disorder in all degrees of freedom; entry into the mesophase is necessary to achieve high order. The spectroscopic data can be correlated with in-situ mobility measurements.   

Electro-optic Measurements in Single-Crystal Films of a Combination of Materials Involving DAST and IR-125

Single crystal films of a combination of materials involving DAST and a dye molecule IR-125 have been prepared using the modified shear method. X-ray diffraction results indicate a [001] orientation of the film similar to a DAST single-crystal film. The electro-optic measurements of the DAST-IR125 films have been performed using field induced birefringence in the cross polarized geometry at 633 nm and 1550 nm. A modulation of 14 percent has been observed in a single pass through the film for a field of 1 Volt/micron at 633 nm. The results indicate exceptionally high electro-optic coefficients at both of the wavelengths (633 and 1550 nm).   

Nonlinear Refractive Index in a Novel Nano-optical Material Based on the Nonconjugated Conductive Polymer, Poly($\beta$-pinene)

Two-photon absorption in a novel nano-optical polymer based on the nonconjugated conductive polymer, iodine-doped poly($\beta $-pinene) has been recently reported. In the present report, we will discuss measurement of the nonlinear refractive index (n$_{2})$ of iodine-doped poly($\beta $-pinene). The measurement has been made using 150 fs pulses from a Ti:Sapphire laser. Time-resolved measurement has been made using pump-probe technique in which the phase change in the probe beam was measured from the intensity-induced birefringence while the pump pulse was overlapped. The measured value of the nonlinear refractive index is larger than 10$^{-5}$cm$^{2}$/MW at 800 nm. The results show that the measured n$_{2}$ is of electronic origin. This exceptionally large magnitude of n$_{2}$ has been attributed to the special electronic structure of doped poly($\beta $-pinene) confined in a sub-nanometer domain.   

Quadrupolar dyes for NLO applications: solvent-induced symmetry breaking and huge TPA cross-sections in aggregates

Quadrupolar dyes, where electron donor (D) and acceptor (A) groups are linked by $\pi$-conjugated bridges to yield symmetrical structures (D-$\pi$-A-$\pi$-D or A-$\pi$-D-$\pi$-A) are intensively studied for TPA applications. In an essential-state model for the solvated dyes, symmetry-broken dipolar solutions are found for either the ground or the one-photon excited state. Dyes are accordingly classified in three different classes, with distinctively different spectroscopic behavior. The model provides useful guidelines for the design of molecules for TPA applications and represents a general frame to understand energy transfer processes in multipolar molecular systems. [1] The same essential state model applies to aggregates of quadrupolar dyes. Relaxing the dipolar approximation for electrostatic intermolecular interactions, bound-biexcitons appear with important spectroscopic consequences. Specifically, the large TPA cross-section of quadrupolar dyes is amplified by orders of magnitude as a result of aggregation. [1] F. Terenziani, A. Painelli, C. Katan, M. Charlot, M. Blanchard-Desce, {\it J. Am. Chem. Soc.} {\bf 2006}.   

Infrared probe of charge dynamics in single crystal rubrene organic field-effect transistors

We report on infrared (IR) spectroscopy of charge dynamics in organic field-effect transistors based on single crystal rubrene. IR microscopy measurements show uniform charge injection over macroscopic length scales of several millimeters in these devices. IR measurements uncover anisotropic optical conductivities of these transistors in agreement with earlier transport studies. The field-induced electronic excitations in rubrene reveal optical constants with the Drude-like form and low effective masses. I will discuss several new aspects of the charge dynamics in organic molecular crystals uncovered by this work.   

Session A19: Focus Session: New Frontiers in Imaging I

Mobile NMR: Measuring Pixels, Images, and Spectra

The vision of bringing nuclear magnetic resonance out of the lab to the doctor's office, the chemical reactor, or the manufacturing site is becoming reality with the development of mobile NMR. Pioneered for well logging in the oil industry, the concept has been explored for materials testing in a more systematic way since the introduction of the NMR-MOUSE. This is a small, one-sided access NMR sensor which acquires the information of one pixel from a particular spot of a large object. As the sensor explores the stray-fields of a permanent magnet and an rf coil, the magnetic fields are inhomogeneous and the sensitive volume is limited to the region, where both fields are orthogonal and the Larmor frequency lies within the excitation bandwidth. By shaping the magnet and the coil geometries, the shape of the sensitive volume can be tailored to a thin slice or a larger volume a certain distance away from the sensor surface. In the first case, there is a strong field gradient in the depth direction, and in the second case, a homogeneous sweet spot of the field profile is desired. The first case is suitable for measuring high-resolution depth profiles, while the second case is suitable for chemical shift resolved spectroscopy and volume imaging. The basic concepts of open and closed mobile NMR sensors will be discussed along with applications from testing polymer products, cultural heritage, medical tissue, and rock cores.   

Ex-Situ Spectroscopic MRI

Spectroscopic magnetic resonance imaging of a sample placed outside of both the radio frequency and the imaging gradient coils is presented. The sample is placed in a field with a permanent one-dimensional inhomogeneity. The imaging gradients used for phase encoding are designed to produce a static field that depends only on the transverse direction, uncoupling the effects associated with the single-sided nature of these coils. Two-dimensional imaging coupled with chemical shift information is obtained via the ex situ matching technique. Open-saddle geometry is used to match the static field profile for chemical shift information recovery.   

Nuclear magnetic resonance imaging with 90-nm resolution

Using magnetic resonance force microscopy (MRFM), we demonstrate two-dimensional nuclear magnetic resonance imaging (MRI) with 90-nm lateral resolution for $^{19}$F nuclei in calcium fluoride. In terms of detectable volume, this represents a 60,000 fold improvement over the highest resolution conventional MRI. The high sensitivity of our measurement is achieved using a custom-made silicon cantilever with a 60-$\mu$N/m spring constant and a nanometer-scale FeCo magnetic tip that produces magnetic field gradients up to 14 G/nm. The spin manipulation protocol, called cyclic CERMIT, uses low duty cycle cantilever-driven adiabatic reversals to manipulate statistical spin polarization and generate a detectable cantilever frequency modulation. Work is underway to further improve measurement sensitivity, including the development of an efficient RF source aimed at reducing cantilever temperatures during imaging into the low millikelvin range. This and other improvements may allow MRFM to push deeper into the nanometer range.   

Imaging Contrast Effects in Alginate Microbeads

We have investigated the use of alginate gel microbeads as contrast agents for the study of suspension flows in complex geometries using nuclear magnetic resonance (NMR) imaging. These deformable particles can provide imaging contrast to rigid polymer particles in a bimodal suspension (two particle sizes). Microbeads were formed of crosslinked alginate gel, with or without trapped oil droplets. Crosslinking of the aqueous sodium alginate solution or the continuous phase of an oil-in-water emulsion occurred rapidly at gentle processing conditions. The alginate microbeads exhibit both spin-spin relaxation time (T2) contrast and diffusion contrast relative to both the suspending fluid and rigid polystyrene particles. Large alginate emulsion microbeads flowing in the abrupt, axisymmetric expansion geometry can be clearly distinguished from the suspending fluid and from rigid polymer particles in both spin-echo and diffusion weighted imaging. The alginate microbeads, particularly those containing trapped emulsion droplets, offer potential as a positive contrast agent in multiple NMR imaging applications.   

Spin Sorting: Apparent Longitudinal Relaxation without Spin Transitions

Nuclear spins experience forces in the presence of a magnetic field gradient. The forces cause the spin-up and spin-down nuclei to move in opposite directions, resulting in a flow of longitudinal magnetization. The effect can generate local longitudinal spin magnetization, though it does not involve transitions (flipping) of spins. This phenomenon, spin sorting, competes with true spin-lattice relaxation and is generally not observable when T$_{1}$ is short. We present our calculations of the longitudinal magnetization of diffusing spins with long T$_{1}$ ($^{3}$He) in magnetic field gradients and compare the calculations with experimental results. We show that the longitudinal spin magnetization due to spin sorting can be dominant at short times in such a system. We also show how this phenomenon can potentially be used to generate nuclear magnetizations larger than thermal equilibrium.   

Spin-Exchange Optical Pumping of Solid Alkali Compounds

Spin-exchange optical pumping of noble gases has been used for many years to create highly non-equilibrium spin populations, with applications ranging from fundamental physics[1] to medical imaging[2]. In this procedure, angular momentum is transferred from circularly-polarized laser light to the electron spins of an alkali vapor and ultimately to the nuclei of a gas such as $^3$He or $^{129}$Xe. Here we show experimentally that a similar process can be used to polarize the nuclei of a solid film of cesium hydride which coats the walls of an optical pumping cell. We present nuclear magnetic resonance (NMR) data which demonstrate that the nuclear polarization of $^{133}$Cs in CsH can be enhanced above the Boltzmann limit in a 9.4-Tesla magnetic field. Possible spin-exchange mechanisms will be discussed, as well as the extension of this technique to other compounds. \newline [1] T.~W.~Kornack, R.~K.~Ghosh, and M.~V.~Romalis, Phys. Rev. Lett.~\emph{95}, 23080 (2005). \newline [2] M.~S.~Conradi, D.~A.~Yablonskiy, et al., Acad. Radiol.~\emph{12}, 1406 (2005).   

Hyperpolarized water as an authentic magnetic resonance imaging contrast agent.

Water itself in a highly 1H spin-polarized state is proposed as a contrast agent free contrast agent to visualize its macroscopic evolution in aqueous media by magnetic resonance imaging (MRI). Hyper-polarization suggests an ideal contrast mechanism to highlight the ubiquitous and specific function of water in physiology, biology and materials because the physiological, chemical and macroscopic function of water is not altered by the degree of magnetization. We present an approach that is capable of enhancing the 1H MRI signal by up to two orders of magnitude, instantaneously, under ambient conditions, at 0.35 Tesla, by utilizing highly electron spin-polarized nitroxide radicals that are covalently immobilized onto a porous, water-saturated, gel matrix. The continuous polarization of radical-free flowing water allowed us to distinctively visualize vortices in model reactors and dispersion patterns through porous media utilizing the remotely enhanced liquids to obtain unusually high image contrast (RELIC).   

Latest Developments in Dynamic MRI of Multi-Phase Systems

In recent years there has been increasing interest in applying magnetic resonance techniques in areas of engineering and chemical technology. Central to many engineering applications is the need to characterise both hydrodynamics and chemical reaction in optically opaque three-dimensional environments; thus MRI is uniquely well-suited to such studies. This presentation addresses the application of MRI techniques which have sufficiently fast data acquisition times that unsteady state processes can be imaged. The presentation will take as a theme the imaging of physical and chemical phenomena occurring within heterogeneous catalytic reactors - these systems are, typically, packings of catalytically active particles through which gas and liquid flow causing chemical conversion as the reactants interact with the surface of the catalyst. The overall aim of our work is to use MRI to provide information such that we can understand the coupling of hydrodynamics and chemical kinetics in complex porous structures. Two particular areas will be addressed: ultra-fast MRI for studying hydrodynamics, with typical data acquisition times of 10-20 ms for a 2D velocity image, and polarisation enhancement techniques for chemical mapping.   

Session A21: Focus Session: Physics Education Research

Physics, Math, and Making Sense: Understanding how brains learn science

Recent developments in neuroscience, cognitive science, and behavioral science are helping physics education researchers develop a theoretical understanding of physics teaching and learning. This understanding helps in two ways. 1). We can make sense of the way students respond (often inappropriately) to our instruction. 2). We can learn to appreciate the difficulties we have as instructors in unpacking and identifying critical components of our own knowledge. Building on observations of student learning in introductory and advanced physics, I identify critical components for teaching physics with math that are often overlooked in traditional instruction.   

Reducing the gender gap in the physics classroom

We investigated whether the gender gap in conceptual understanding in an introductory university physics course can be reduced by teaching with interactive engagement methods that promote in-class interaction, reduce competition, foster collaboration, and emphasize conceptual understanding. To this end, we analyzed data from the introductory calculus-based physics course for non-majors at Harvard University taught traditionally or using different degrees of interactive engagement. Our results show that teaching with certain interactive strategies not only yields significantly increased understanding for both males and females, but also reduces the gender gap. The greater the interaction, feedback, collaboration, and emphasis on understanding, the greater the reduction in the gender gap. In the most interactively taught courses, the pre-instruction gender gap is gone at the end of the semester.   

Addressing Gender Disparity in Introductory Physics Courses: Are existing reforms enough?

Previously researchers have reported that by transforming teaching practices in introductory physics, it is possible to eliminate the disparity in achievement of males and females on measures of conceptual learning. [1] We follow-up on the studies of the original researchers by comparing achievement of male and female students on measures of conceptual learning in the introductory physics courses at a large public research university. Just as the original authors find, we observe that reform teaching practices, such as the use of Peer Instruction [2] increase the learning gains of all students in introductory physics. Additionally, we observe a significant reduction in this gender gap in learning gains in some but not all of our transformed courses. Notably, however, the gender gap does not completely disappear in any of our courses. In addition to discussing learning gains, we analyze shifts in student beliefs [3] and examine correlations between student beliefs and learning gains. \newline \newline [1] Lorenzo, M et al. (2006).Am. J. Phys. 74(2): 118-122 \newline [2] Mazur, E. (1997). Peer Instruction (Prentice Hall). \newline [3] Adams, W.K et al. Physical Review, ST:PER. 2,1,010101.   

Sustaining Educational Innovation: engaging traditional faculty in transformed practices

Over the past five years CU Physics has engaged in an experimental study of what it means to transform our introductory physics sequence to employ the tools and practices shown to be productive by physics education research. We have previously reported on the successful transformation of the courses to make them student centered, interactive and post high learning gains on conceptual surveys. [1] In an effort to understand the long-term potential of these course transformations, we now examine what happens when the course is transferred to new faculty. We demonstrate that it is possible to maintain high learning gains with new faculty and find two critical factors that contribute to the sustained success of these course transformations: 1) faculty background and beliefs and 2) particular curricular materials and practices selected to use. We also present a model (the Learning Assistant program) designed for sustaining these reforms and for increasing student interest and retention in teaching. [2] \newline [1] N.D. Finkelstein and S.J. Pollock, ``Replicating and Understanding Successful Innovations: Implementing Tutorials in Introductory Physics'' \textit{Physical Review, Spec Top: Physics Education Research,} 1, 010101 (2005). [2] V.Otero, N.D. Finkelstein, R. McCray, and S. Pollock, ``Who is Responsible for Preparing Science Teachers?'' \textit{Science. }\textbf{313}(5786), 445-446 (2006).   

Development and assessment of research-based tutorials on heat engines and the second law of thermodynamics

The Physics Education Group has been investigating student ability to apply the second law of thermodynamics to cyclic devices such as heat engines and refrigerators. Students enrolled in courses ranging from algebra-based introductory physics to a junior-level thermodynamics course were asked if certain specified processes could occur. Their responses revealed several conceptual difficulties, including the failure to recognize the relevance of the second law to various problems. These findings informed the development of two tutorials to supplement instruction in standard undergraduate courses. Student performance on examination questions indicates that both tutorials can help improve understanding.   

Research as a guide for developing curricula on wave behavior at boundaries

The Physics Education Group at the University of Washington has been developing research-based instructional materials on mechanical waves and physical optics.* As a part of this ongoing process, we continue to assess and refine existing tutorials. In particular, we are focusing on tutorials designed to help students apply boundary conditions to the propagation and refraction of periodic waves. Pretest and post-test results are being used to inform curriculum modifications and to assess the effectiveness of the revised materials. Specific examples of persistent student difficulties will be presented. * Tutorials in Introductory Physics, L.C. McDermott, P.S. Shaffer and the Physics Education Group at the University of Washington, Prentice Hall (2002)   

Changes in Student Models of Force and Motion in Activity-Based Physics

With a three-year FIPSE grant, it has been possible at the University of Nebraska at Kearney (UNK) to develop and implement activity-based introductory physics at the algebra level. Many misconceptions about motion and force persist after instruction. Pretest and posttest responses on the ``Force and Motion Conceptual Evaluation'' (FMCE) are analyzed to determine the models that students use. Responses are divided into expert model (correct answer), student model (common incorrect answer), and null model (all other answers) categories. Students are categorized as being in an expert state (mostly expert model answers), a mixed state (a combination of expert model answers, student model answers, and null model answers), or a student state (mostly student model answers). The change (if any) of state is identified for each student. The changes are analyzed to determine the effectiveness of activity-based instruction.   

Analysis of shifts in students' reasoning regarding electric field and potential concepts

Students' reasoning regarding the relationships among electric fields, forces, and equipotential line patterns was explored using pre- and post-test responses to selected multiple-choice questions on the Conceptual Survey of Electricity and Magnetism. Students' written explanations of their reasoning, provided both pre- and post-instruction, allowed additional assessment of the changes in their thinking. The data indicate that although students largely abandon an initial tendency to associate stronger fields with wider equipotential line spacing, many of them persist in incorrectly associating electric field magnitude at a point with the electric potential at that point. Analysis of the data also illustrated that the accuracy of specific multiple-choice responses in reflecting student thinking can be strongly time dependent. In our sample, a strong and consistent pattern of correct answers on a specific question (administered before instruction) was demonstrated to provide a highly misleading impression of students' understanding.   

The role of representation when solving physics problems

Physics problems can be represented in a number of different ways, including mathematical, graphical, pictorial, or verbal formats. In a series of studies of large-lecture introductory physics courses at the University of Colorado, we have investigated the effect of problem representation on student performance and what factors influence how students use and learn to use representations appropriately. We have found that student performance can vary strongly with representation, that giving students a choice in representational format of their physics problems can have strong effects on performance, both positive and negative, and that students in a PER-informed course may develop a broader set of representational skills than those in a traditional course.   

Andes: An intelligent homework helper

Andes (www.andes.pitt.edu) is an intelligent tutor homework system designed for use as the homework portion of an introductory physics course. It encourages students to use good problem solving techniques and provides immediate feedback on each step of a problem solution along with hints on request. I will discuss how Andes works, from a student perspective, and present research demonstrating its effectiveness as a pedagogical tool. Then, I will discuss using Andes as a tool for conducting education research, briefly reviewing several studies conducted using Andes. Finally, I will show how logs of student solutions to Andes problems can be used to develop cognitive models of student learning.   

Scientific Assistant Virtual Laboratory (SAVL)

The Scientific Assistant Virtual Laboratory (SAVL) is a scientific discovery environment, an interactive simulated virtual laboratory, for learning physics and mathematics. The purpose of this computer-assisted intervention is to improve middle and high school student interest, insight and scores in physics and mathematics. SAVL develops scientific and mathematical imagination in a visual, symbolic, and experimental simulation environment. It directly addresses the issues of scientific and technological competency by providing critical thinking training through integrated modules. This on-going research provides a virtual laboratory environment in which the student directs the building of the experiment rather than observing a packaged simulation. SAVL: * Engages the persistent interest of young minds in physics and math by visually linking simulation objects and events with mathematical relations. * Teaches integrated concepts by the hands-on exploration and focused visualization of classic physics experiments within software. * Systematically and uniformly assesses and scores students by their ability to answer their own questions within the context of a Master Question Network. We will demonstrate how the Master Question Network uses polymorphic interfaces and C{\#} lambda expressions to manage simulation objects.   

Should we teach the Bohr model?

Some education researchers have claimed that we should not teach the Bohr model of the atom because it inhibits students' ability to learn the true wave nature of electrons in atoms. Although the evidence for this claim is weak, many in the physics education research community have accepted it. This claim has implications for how we present atoms in classes ranging from elementary school to graduate school. We present results from a study designed to test this claim by developing curriculum on models of the atom, including the Bohr model and the Schrodinger model. We examine student descriptions of atoms on final exams in reformed modern physics classes using various versions of this curriculum. Preliminary results show that if the curriculum does not include sufficient connections between different models, many students still have a Bohr-like view of atoms, rather than a more accurate quantum mechanical view. We present further studies based on an improved curriculum designed to develop model-building skills and with better integration between different models. We will also present a new interactive computer simulation on models of the atom designed to address these issues.   

Student application of integration when considering P-V diagrams

As part of work on teaching and learning in upper-level undergraduate thermodynamics courses, we are exploring student connections between the physics and the underlying mathematics, which is required for productive reasoning about thermal and statistical physics. Previous results on the teaching and learning of the First Law of Thermodynamics document indiscriminate application of the concept of \textit{state function}, e.g., both to internal energy and to work. We have developed questions devoid of physical context that probe student understanding of the relevant principal math concepts in a manner completely analogous to the physics questions used by previous researchers. We have administered these questions in upper-level undergraduate thermodynamics courses. Comparison of student performance on these analogous physics and math questions shows a distinction between conceptual physics difficulties and difficulties with application of the underlying mathematics. Data will be presented from physics, chemistry and engineering students.   

Session A22: Focus Session: Econophysics

Effect of citation patterns on network structure

We propose a model for an evolving citation network that incorporates the citation pattern followed in a particular discipline. We define the citation pattern in a discipline by three factors. The average number of references per article, the probability of citing an article based on it's age and the number of citations it already has. We also consider the average number of articles published per year in the discipline. We propose that the probability of citing an article based on it's age can be modeled by a {\it lifetime distribution}. The lifetime distribution models the citation lifetime of an average article in a particular discipline. We find that the citation lifetime distribution in a particular discipline predicts the topological structure of the citation network in that discipline. We show that the power law exponent depends on the three factors that define the citation pattern. Finally we fit the data from the Physical Review D journal to obtain the citation pattern and calculate the total degree distribution for the citation network.   

Counting solutions for the CDMA multiuser MAP demodulator

We evaluate the average number of locally minimal solutions for maximum-a-{\it posteriori} (MAP) demodulation in code-division multiple-access (CDMA) systems [1]. For this purpose, we use a sophisticated method to investigate the ground state properties for the Sherrington-Kirkpatrick-type (i.e. fully connected) spin glasses established by Tanaka and Edwards [2] in 1980. We derive the number of locally minimal solutions as a function of several parameters which specify the CDMA multiuser MAP demodulator. We also calculate the distribution function of the energies for the locally minimum states. We find that for a small number of chip intervals (or equivalently a large number of users) and large noise level at the base station, the number of local minimum solutions becomes larger than that of the SK model [3]. This provides us with useful information about the computational complexity of the MAP demodulator [4]. \\ \\ $[1]$ T. Tanaka, Europhys. Lett. {\bf 54} (4), 540 (2001). \\ $[2]$ F. Tanaka and S.F. Edwards, J. Phys. F: Metal Phys. {\bf 10} 2769 (1980). \\ $[3]$ D. Sherrington and S. Kirkpatrick, Phys. Rev. Lett. {\bf 35}, 1792 (1975). \\ $[4]$ J.P.L. Hatchett and J. Inoue, in preparation.   

A Weibull distribution with power-law tails that describes the first passage time processes of foreign currency exchanges

A Weibull distribution with power-law tails is confirmed as a good candidate to describe the first passage time process of foreign currency exchange rates. The Lorentz curve and the corresponding Gini coefficient for a Weibull distribution are derived analytically. We show that the coefficient is in good agreement with the same quantity calculated from the empirical data. We also calculate the average waiting time which is an important measure to estimate the time for customers to wait until the next price change after they login to their computer systems. By assuming that the first passage time distribution might change its shape from the Weibull to the power-law at some critical time, we evaluate the averaged waiting time by means of the renewal-reward theorem. We find that our correction of tails of the distribution makes the averaged waiting time much closer to the value obtained from empirical data analysis. We also discuss the deviation from the estimated average waiting time by deriving the waiting time distribution directly. These results make us conclude that the first passage process of the foreign currency exchange rates is well described by a Weibull distribution with power-law tails.   

A new perspective on Quantum Finance using the Black-Scholes pricing model

Options are known to be divided into two types, the first type is called a call option and the second type is called a put option and these options are offered to stock holders in order to hedge their positions against risky fluctuations of the stock price. It is important to mention that due to fluctuations of the stock price, options can be found sometimes deep in the money, at the money and out of the money. A deep in the money option is described when the option's holder has a positive expected payoff, at the money option is when the option's holder has a zero expected payoff and an out of the money option is when the payoff is negative. In this work, we will assume the stock price to be described by the well known Black-Scholes model or sometimes called the multiplicative model. Using Ito calculus, Martingale and supermartingale theories, we investigated the Black-Scholes pricing equation at the money (X(stock price)= K (strike price)) when the expected payoff of the options holder is zero. We also hedged the Black-Scholes pricing equation in the limit when delta is zero to obtain the non-relativistic time independent Schroedinger equation in quantum mechanics. We compared the two equations and found the diffusion constant to be a function of the stock price in contrast to the Bachelier model we have worked on earlier. We solved the Schroedinger equation and found a dependence between interest rate, volatility and strike price at the money.   

Evolution of Trading strategies

We attempt to classify the trading strategies of agents in the London Stock Exchange into broad categories. Our study is based on that that identifies the member of the exchange associated with each transaction. Based on the evolution of the inventory (holdings of the stock) as a function of time, we use clustering methods to classify the strategies into several groups. We study how these groups evolve in time and attempt to correlate the membership of the groups with other market properties, such as price volatility.   

The Product Space and its Consequences for Economic Growth

In this paper, we test the assumption underlying the foundational models of trade that there always exist products through which countries can express their endowments and technology. We map the `space' of products in the world, and find it to be quite heterogeneous, with a central core and outer periphery. Moreover, we show that the way countries develop comparative advantage is far from random, and that the empirical rules observed herein predict, together with the structure of the product space, explain the lack of convergence in international income levels. Some developing countries produce in the periphery of the product space with few opportunities for diversification, whereas others have developed capabilities easily deployable in a wide range of products creating a path to convergence.   

Stochastic volatility of financial markets as the fluctuating rate of trading: an empirical study

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades $N$ is found to be approximately Gaussian. The probability distribution of $N$ for a given time interval $\Delta t$ is non-Poissonian and has an exponential tail for large $N$ and a sharp cutoff for small $N$. Combining these two distributions produces a nontrivial distribution of log-returns for a given time interval $\Delta t$, which has exponential tails and a Gaussian central part, in agreement with empirical observations.\\ Reference: physics/0608299.   

Using behavioral statistical physics to understand supply and demand

We construct a quantitative theory for a proxy for supply and demand curves using methods that look and feel a lot like physics. Neoclassical economics postulates that supply and demand curves can be explained as the result of rational agents selfishly maximizing their utility, but this approach has had very little empirical success. We take quite a different approach, building supply and demand curves out of impulsive responses to not-quite-random trading fluctuations. Because of reasons of empirical measurability, as a good proxy for changes in supply and demand we study the aggregate price impact function $R(V)$, giving the average logarithmic price change $R$ as a function of the signed trading volume $V$. (If a trade $v_i$ is initiated by a buyer, it has a plus sign, and vice versa for sellers; the signed trading volume for a series of $N$ successive trades is $V_N(t) = \sum_{i=t}^{i=t+N} v_i$). We develop a ``zero-intelligence" null hypothesis that each trade $v_i$ gives an impulsive kick $f(v_i)$ to the price, so that the average return $R_N(t) = \sum_{i=t}^{i=t+N} f(v_i)$. Under the assumption that $v_i$ is IID, $R(V_N)$ has a characteristic concave shape, becoming linear in the limit as $N \to \infty$. Under some circumstances this is universal for large $N$, in the sense that it is independent of the functional form of $f$. While this null hypothesis gives useful qualitative intuition, to make it quantitatively correct, one must add two additional elements: (1) The signs of $v_i$ are a long-memory process and (2) the return $R$ is efficient, in the sense that it is not possible to make profits with a linear prediction of the signs of $v_i$. Using data from the London Stock Exchange we demonstrate that this theory works well, predicting both the magnitude and shape of $R(V_N)$. We show that the fluctuations in $R$ are very large and for some purposes more important than the average behavior. A computer model for the fluctuations suggests the existence of an equation of state relating the diffusion rate of prices to the flow of trading orders.   

Modelling Limit Order Execution Times from Market Data

Although the term ``liquidity'' is widely used in finance literatures, its meaning is very loosely defined and there is no quantitative measure for it. Generally, ``liquidity'' means an ability to quickly trade stocks without causing a significant impact on the stock price. From this definition, we identified two facets of liquidity -- 1.execution time of limit orders, and 2.price impact of market orders. The limit order is an order to transact a prespecified number of shares at a prespecified price, which will not cause an immediate execution. On the other hand, the market order is an order to transact a prespecified number of shares at a market price, which will cause an immediate execution, but are subject to price impact. Therefore, when the stock is liquid, market participants will experience quick limit order executions and small market order impacts. As a first step to understand market liquidity, we studied the facet of liquidity related to limit order executions -- execution times. In this talk, we propose a novel approach of modeling limit order execution times and show how they are affected by size and price of orders. We used q-Weibull distribution, which is a generalized form of Weibull distribution that can control the fatness of tail to model limit order execution times.   

The Influence of Signed Order Volume on Stock Prices

Using data from the London Stock Exchange we investigate the influence of signed transaction order volume on current and future price changes. (Buy orders are given a positive sign, sell orders a negative sign). Empirical studies have shown that transaction order signs display long memory. Because buying tends to move the price up and selling tends to move the price down, this creates a puzzle regarding efficiency -- if transaction order signs are highly predictable, why aren't prices predictable? We show that efficiency is maintained by correlated fluctuations in the response of prices to orders. We also study whether or not this is an important effect causing clustered volatility in price changes, i.e. the tendency of the magnitude of price changes to be temporally correlated.   

Is clustered volatility essential to understand heavy tails in financial markets?

Heavy tails are observed in the returns of stocks even for transaction by transaction data. We study the tail exponents and quantiles of the heavy tails for stock returns: first for transaction by transaction data, second after aggregating over $n$ transactions. In order to separate out the effect of clustered volatility, we repeat our analysis after shuffling the transaction sequence and look for variation in tail exponents and quantiles for shuffled vs. original (unshuffled) data.   

Persistent Patterns in Trading Firms' Actions

To understand the dynamics of price formation in financial markets, we take the approach of investigating the actions of market participants. We examine the impact of the participating firms on the price and find that different firms have different patterns of impact. Each firm can be representative of many traders with different trading habits and strategies but nevertheless we observe statistically significant differences in the firms' market impacts. We also investigate a method of clustering the firms based on a simplified conception of strategies. We find consistent clusters and patterns in firm strategies and show that these relations are statistically significant.   

Universality of Tail Exponents of Price Changes?

We study the tail exponents of the distribution of logarithmic price changes in financial markets, and investigate the conjecture that they are universal with an exponent near three. Using data from the London Stock Exchange, we construct the empirical distributions of price returns on several different time scales and study their variation as a function of parameters such as trading volume and tick size (the minimal unit of price variation).   

Session A23: Focus Session: High Pressure I - Earth and Planetary Materials

Characterization of Jupiter's Interior with First Principles Computer Simulations

We report results from recent investigations of the interior structures of Jupiter using density-functional molecular dynamics (DFT) simulations of dense fluid hydrogen-helium mixtures [1]. The equation of state (EOS) is derived on a grid of temperature and density points spanning Jupiter's interiors. The properties of both fluids in dynamic shock compression experiments are compared [2]. Based on the DFT-EOS, we derive models for the interior of giant planets. Our models update the suite of models that were based on the widely used Saumon-Chabrier-Van Horn (SCVH) EOS. Unlike SCVH, the computed DFT-EOS does not predict any first-order thermodynamic discontinuities associated with pressure-dissociation and metallization of hydrogen. Deviations of the DFT-EOS from SCVH are up to about +/- 5{\%} depending on the pressure. As a result our models predict a significantly larger rocky core for Jupiter than SCVH. We will discuss inferred core mass and make predictions for properties of core. [1] J. Vorberger, I. Tamblyn, B. Militzer, S.A. Bonev, ``Hydrogen-Helium Mixtures in the Interiors of Giant Planets,'' cond-mat/0609476. [2] B. Militzer, PRL 97 (2006) 175501. Supported by NASA PGG04-0000-0116 and NSF Grant 0507321.   

High pressure bonding properties of hydrogen

There has been considerable experimental and theoretical effort to describe the transition in hydrogen from a molecular to non-molecular fluid. Resolution of discrepancies that continue to exist between different investigations of hydrogen is expected to have significant implications in fields such as planetary science. We have preformed three sets of first-principles simulations, constant density, pressure, and temperature, in order to study the molecular, non-molecular, and transition regimes of the hydrogen (deuterium) phase diagram. Constrained and unconstrained bond length simulations were used to examine changes that occur in the inter-atomic potential upon disassociation. By forcing the destruction of molecules in the molecular regime, and by considering the catalyzing effect of single hydrogen atoms, we have probed the mechanisms that drive this transition. Finally, spatial distributions of species surrounding molecules at the time of dissociation have provided insight into the structure of the liquid.   

Computational study of the Hydrogen equation of state using the Coupled Electron-Ion Monte Carlo method

We study the equation of state of liquid Hydrogen at Mbar pressures, in the regime of pressure dissociation/ionization, using the Coupled Electron-Ion Monte Carlo (CEIMC) method. Our aim is to accurately describe the crossover from the molecular to the atomic regime. The CEIMC method is based on the Born-Oppenheimer approximation and consists of a Monte Carlo simulation of the ionic degrees of freedom (either with path integals or classical Metropolis) using a potential energy surface obtained from a zero temperature QMC method. The electronic calculation is done using either Variational Monte Carlo or the more accurate Reptation Quantum Monte Carlo. A Slater-Jastrow wavefunction is used, with an analytical RPA Jastrow term and one-body orbitals obtained from a fast band structure calculation. Recently, we incorporated backflow corrections to the orbitals obtained from DFT. This results in a much improved wavefunction over the entire crossover regime. We report preliminary results using this new wavefunction. We also compare our results with recent calculations obtained using Born-Oppenheimer Molecular Dynamics.   

First-principles study of the effect of helium on the onset of dissociation in liquid hydrogen

The molecular to non-molecular liquid-liquid phase transition that occurs in high-temperature/high-pressure hydrogen has been speculated to be first-order-like, where the onset of dissociation occurs abruptly. However, a small concentration of non-interacting particles, specifically helium, has been postulated to retard and smooth the transition. To study this transition in hydrogen and hydrogen-helium mixtures we performed a series of large-scale Born-Oppenheimer molecular-dynamic simulations. Additionally, we have studied the electronic properties of hydrogen-helium mixtures by using hybrid density functional theory to analyze snapshots from our molecular dynamics simulations. The simulations show that the transition is smooth and continuous without any indication of any first-order-like behavior. The simulations also predict that small concentrations of helium have a significant effect on the phase transition; most notably, the pressure profile is much smoother, and the band gap closes at a higher temperature, for the hydrogen-helium mixtures relative to pure liquid-hydrogen. This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.   

Equation of state and electronic structure of liquid Helium at high pressure

As the second most abundant element, the properties of fluid Helium form an important part of our understanding of stellar and giant planetary structure. Yet the physics of Helium at pressure-temperature conditions characteristic of these bodies is uncertain. We perform first principles molecular dynamics simulations of fluid Helium over a wide range of pressure ($< 1$ Gbar) and temperature ($< 5$ eV). The simulations are based on finite-temperature density functional theory in the generalized gradient approximation, and are performed in the canonical ensemble with a Nose thermostat. We find that both temperature and compression have a strong influence on the electronic structure as revealed by the band gap. At a density of 1 g cm$^{-3}$ the band gap varies from 20 eV for the static crystal to 0 for the fluid at 4 eV. The gap is closed at all temperatures for density greater than 20 g cm$^{-3}$. We find that the equation of state varies smoothly through the band gap closure transition with no indication of a high-order phase transformation. The decrease in band gap with increasing temperature at constant density results from enhanced mixing of 1s- and 2s-like states with increasing disorder (i.e., enhanced vibrational amplitudes and melting) that has profound implications for understanding the deep interiors of planets.   

Liquid-liquid transitions in low-Z materials: Parallel with high-pressure solid phase transitions

First-principles molecular dynamics simulations reported in [1] predict structural and electronic transitions in dense liquid sodium that are responsible for its exotic melting curve. In this talk, the possibility for observing similar behavior in other low-Z materials will be discussed. Results from ab initio calculations of several materials will be presented and compared with sodium. [1] Jean-Yves Raty, Eric Schwegler and Stanimir A. Bonev, submitted.   

Probing Dense States of Hydrogen and Oxides in Giant Planets using Multiple and Single- Shock Compression and Laser-Pulse-Heated Diamond-Anvil Cells.

Pressures and temperatures of hydrogen on adiabats deep in gas giants are achieved using a shock wave reverberating between incompressible oxide anvils and by pulsed heating in a diamond-anvil cell. At 100 GPa in gas giants, temperature varies from $\sim $20,000 K in hot Jupiters down to $\sim $1,000 K in cold Jupiters. The Hugoniot curve of hydrogen crosses these adiabats at $\sim $15 GPa and $\sim $4,000 K for Jupiter and $\sim $100 GPa for hot Jupiters, both at compressions of $\sim $4 fold. Reverberating shocks and diamond cells produce compressions up to $\sim $12 fold. Since dense hydrogen has a huge diffusion coefficient, experiments must be done sufficiently slowly that hydrogen is in thermal equilibrium and sufficiently fast that hydrogen remains in the cell. Dynamic experiments occur within this constraint. DAC experiments require heating by multiple laser pulses each of $\sim $100 ns duration. Pressures and temperatures achieved by multiple shock compression are tuned by variation of the density of oxide anvils. An oxide (Gd$_{3}$Ga$_{5}$O$_{12})$ has been found that is stiffer than diamond above 100 GPa. This oxide will enable higher pressures and lower temperatures in metallic fluid hydrogen by multiple shock and might be representative of new oxide phases in deep interiors of giant extrasolar rocky planets. Experiments and systematics will be described.   

Coherent anti-Stokes Raman Spectroscopy Study of Highly Compressed Deuterium

High density ($>$ 0.3 mol/cm$^{3})$ hydrogen and its isotopes have been studied intensely over the past three decades. Although many spectroscopic methods have been applied, none utilizes a multiphoton technique. Coherent anti-Stokes Raman Spectroscopy (CARS) has now been applied to samples over one megabar for the first time to accurately determine the density at which the bandgap of deuterium is 4.66 eV. This method yields very precise Raman shifts, linewidths and third order polarizability ratios since it avoids the problems associated with strain induced diamond fluorescence above a megabar. The pressure dependent third order polarizability ratios can indicate the location of the bandgap. We will present evidence for extrapolating the metallization pressure using these results and the implications on the phase diagram. This work has been supported by the LDRD and PDRP programs at Lawrence Livermore National Laboratory, University of California under the auspices of the U.S. Department of Energy under Contract No. W-7405-ENG-48.   

Simple Molecular Systems at High Pressures and Temperatures.

Knowledge of the elastic, optical and vibrational properties of materials under extreme conditions of high pressure and temperature is crucial for interpreting the results of seismological and planetary observations, for materials science, and for improving our understanding of fundamental physics and chemistry under such conditions. We will present the results of Raman, infrared, and x-ray diffraction measurements of hydrogen, water, nitrogen, and oxygen under conditions of high static pressure and temperature in the diamond anvil cell. High temperatures were generated mainly by laser heating, but also using internal resistive heating. These studies revealed novel phase transitions, complex phase diagrams, unexpected chemical transformations and also helped to established the behavior of interatomic interactions in molecular materials. We thank the following individuals for contributing to this work: N. Goldman, L. Fried, C. Mundy, J. Zaug, R. J. Hemley, E. Gregoryanz, C. Sanloup, M. Somayazulu, Y. Meng, N. Guignot, M. Mezour.   

Bonding Changes in Compressed Carbon Dioxide: A New Stishovite-like Phase of CO$_{2}$

At ambient conditions, carbon dioxide (CO$_{2})$ is a prototypical molecular system, with strong covalent O=C=O molecular bonds and relatively weak quadrupolar interactions between molecules. At high pressures and temperatures, CO$_{2}$ transforms to a series of solid polymorphs with differing crystal structures, intermolecular interactions and chemical bonding. In particular, two fully covalent (extended) solid phases have been reported above 40GPa, with characteristics analogous to SiO$_{2}$ polymorphs. First, CO$_{2}$-V (above 40GPa and 1500K), consists of a network of corner sharing CO$_{4}$ tetrahedra and is structurally similar to SiO$_{2}$ tridymite$^{1}$. And, recently, an extended-solid amorphous phase (\textit{a-carbonia}), similar to amorphous silica, has been reported at room temperature above 40GPa$^{2}$. Here, we present a new stishovite-like CO$_{2}$ phase VI, formed by compressing CO$_{2}$-II above 50GPa and 550K. We define the PT stability domain for the new solid, and present Raman and X-Ray diffraction results consistent with a 6-fold average coordination within a P42/mnm structure. Finally, we propose a phase/bonding diagram for carbon dioxide describing the systematic relationship between its molecular and extended phases at high pressures and temperatures. 1] V. Iota, \textit{et al.}, Science \textbf{283}, 1510 (1999). 2] M. Santoro,\textit{ et al}. Nature \textbf{441}, 857 (2006).   

Phase diagram of Nitrogen at high pressures and temperatures

Nitrogen is a typical molecular solid with relatively weak van der Waals intermolecular interactions but strong intramolecular interaction arising from the second highest binding energy of all diatomic molecules. The phase diagram of solid nitrogen is, however, complicated at high pressures, as inter-molecular interaction becomes comparable to the intra-molecular interaction. In this paper, we present an updated phase diagram of the nitrogen in the pressure-temperature region of 100 GPa and 1000 K, based on in-situ Raman and synchrotron x-ray diffraction studies using externally heated membrane diamond anvil cells. While providing an extension of the phase diagram, our results indicate a ``steeper'' slope of the $\delta $/$\varepsilon $ phase boundary than previously determined$^{1}$. We also studied the stability of the $\varepsilon $ phase at high pressures and temperatures. Our new experimental results improve the understanding of the Nitrogen phase diagram. 1. Gregoryanz et al, Phys. Rev. B 66, 224108 (2002)   

Theoretical precursors to polymeric nitrogen

We predict the existence of new structures of nitrogen based on new observations in analog systems from first-principles density-functional calculations. A series of structures was examined. A structure with orthorhombic symmetry is stable relative to the $\epsilon$ and {\em cubic gauche} phases in LDA, whereas GGA shows the $\epsilon$ and the new orthorhombic structure are energetically competitive. This structure is dynamically stable at least from ambient pressure to 90 GPa and thus may be observed as a stable or metastable polynitrogen phase prior to the transition to the atomic phases of nitrogen.   

Session A24: Focus Session: Particle Dynamics & Organization: Polymer Mediated, Polymer Particles & Anisotropic Particles

Self-Assembly of Amphiphilic Colloids

A rich physics appears when spherical particles in aqueous suspension possess patches of different surface chemical composition. We have explored the assembly of two types of micron-sized spherical particles: those with opposite electric charge on both hemispheres (``bipolar'') and those hydrophobic on one hemisphere and hydrophilic on the other (``amphiphilic''). Bipolar particles form clusters, not strings, because the particle diameter exceeds the electrostatic screening length. The cluster shapes are analyzed by combined epifluorescence microscopy and Monte Carlo computer simulations with excellent agreement, indicating that the particles assemble in aqueous suspension to form equilibrated aggregates. Translational and rotational diffusion are resolved at the single-particle level, with surprising conclusions. Work performed with Erik Luijten, Liang Hong, Angelo Cacciuto, Shan Jiang, Stephen Anthony, Minsu Kim, and Sung Chul Bae.   

Dynamics of polymer microgel nanoparticles and polymer chains.

Microgel nanoparticles were synthesized in aqueous solutions of neutral polymer hydroxypropylcellulose (HPC) through self-association of amphiphilic HPC molecules and subsequent cross linking at room temperature. We present a Dynamic Light Scattering study of transport properties of HPC polymer chains and HPC microgels made out of the same starting polymer solution. The spectra of both systems are highly non-exponential requiring a spectral time moment analysis. Our findings indicate the existence of at least two modes of relaxation in both systems. The comparison of the mean relaxation rates and diffusion coefficients of the different modes in two systems under good solvent conditions will be reported. Temperature induced volume phase transition of the polymer nanoparticles and its sensitivity to salt, polymer, and cross-linker concentration will be reported.   

Icosahedral packing of polymer-tethered nanospheres and stabilization of the gyroid phase

We present results of molecular simulations that predict the phases formed by the self-assembly of model nanospheres functionalized with a single polymer ``tether,'' including double gyroid, perforated lamella and crystalline bilayer phases. We show that microphase separation of the immiscible tethers and nanospheres causes confinement of the nanoparticles, which promotes local icosahedral packing that stabilizes the gyroid and perforated lamella phases. We present a new metric for determining the local arrangement of particles based on spherical harmonic ``fingerprints,'' which we use to quantify the extent of icosahedral ordering.   

Bicontinuous Morphologies in Block Copolymer-Nanoparticle Composites

We present strong segregation approximation based analytical calculations and complementary computer simulation results on the ordering and structural characteristics of block copolymer-nanoparticle mixtures. We consider specifically the case of a symmetric block copolymer organized in a lamella phase, which is mixed with both selective and nonselective nanoparticles. We present results within the strong segregation approximation quantifying the density distribution of nanoparticles and the influence of the nanoparticles upon the lamella thickness and their elastic constants. The case of nonselective nanoparticles is treated in detail to account more accurately for both size effects as well as finite concentrations of nanoparticles. The latter results suggest the possibility of layer instabilities and morphological transitions to bicontinuous phases, resulting from the surfactant-like role of nonselective particles. Qualitative features of our model predictions are in agreement with our computer simulation results and recent experimental results.   

Control of Nanoparticle Distribution with Directed Assembly of Block Copolymer Films

Model CdSe nanoparticles, functionalized with tetradecyl phosphonic acid, were synthesized so as to preferentially segregate into the polystyrene domains of polystyrene-\textit{block}-poly(methylmethacrylate) (PS-$b$-PMMA). Nanocomposites, composed with ternary blends (PS-$b$-PMMA/PS/PMMA) and CdSe, could be directed to assemble into defect-free and registered periodic and non-regular structures on chemically patterned substrates. CdSe nanoparticle arrays, replicating the block copolymer patterns, were obtained by removing the polymer using oxygen plasma. The location and distribution of nanoparticles in the PS domains controls depending on the blend composition, molecular weights of homopolymers and the commensurability between the chemical surface pattern and the bulk lamellar period of the composite and the experimental results are compared to prediction of single chain mean field (SCMF) theory extended to model nanocomposites.   

Controlling Nanoparticle Location and Morphology in Polymer Blend and Copolymer Films.

Polymer blends and block copolymers containing nanoparticles (NP) have potential as optoelectronic devices, chemical sensors and nanoreactors. Because structure governs device performance, self-regulating, stable structures ranging from the micro to nanoscale are highly desirable. This presentation shows how silica nanoparticles (NP) modified with polymer brushes partition in polymer blends. If NP partition into only one phase, phase separation slows down, whereas NP that jam the interface produce a bi-continuous metastable structure. As film thickness increases, jamming occurs at lower NP concentration. In symmetric block copolymer films, the addition of NP also slows down phase evolution and can even produce a metastable perpendicular morphology containing surface segregated NP. However, the mechanism differs from the polymer blend case and the resulting length scale is in the nanometer range. These studies demonstrate the interplay between NP distribution and phase morphology in both blends and copolymer systems that span the micro to nano length scales.   

Molecular Theory Studies of Polymer/Nanoparticle Blends Near Surfaces

Recent experimental results have shown that nanoparticles added to supported thin polymer films can inhibit dewetting by migrating to the substrate. To better understand this phenomenon, we use a classical density functional theory developed by Tripathi and Chapman. The effects of nanoparticle radius and density are examined. Preliminary results for hard-particle hard-chain systems indicate that regular layered structures emerge when a critical density is reached and the particles displace the polymers near the substrate. The effects of particle and polymer attractions and substrate potentials are currently being studied. We also compare our results to molecular simulations.   

Particle Dynamics in Polymer/Metal Nanocomposite Thin Films on Nanometer Length Scales

X-ray photon correlation spectroscopy was used in conjunction with resonance-enhanced grazing-incidence small-angle x-ray scattering to probe the particle dynamics and kinetics in gold/polystyrene nanocomposite thin films. Such enhanced coherent scattering enables, for the first time, to measure the particle dynamics at wavevectors up to 1 \textit{nm}$^{-1}$ (or a few nm spatially), well in the regime where entanglement, confinement and particle interaction dominate the dynamics and kinetics. The dynamics at such length scales has been difficult, if not impossible to study, by any other probes. Measurements of the intermediate structure factor f(q,t) indicate a mechanism of particle motion very different from Brownian diffusion (governed by Stokes-Einstein equation). The measured dynamics is explained in terms of inter-particle and hydrodynamic interactions.   

Investigation of Gold Nanoparticle Diffusion in Polymer Thin Films using X-ray Standing Waves

Nanoparticle marker motion can be used to infer the ordering kinetics and nanoparticle dynamics in polymer/metal nanocomposite thin films. In current experiments, by using x-ray standing waves generated by total external reflection from the substrates, we elucidated the diffusion properties of thermally evaporated gold nanoparticles at homopolymer and diblock copolymer thin films. Different to recent results with gold particle monolayer embedded in a sandwich structure of polymer thin films, with a sub-nm spatial resolution we demonstrate that the monolayer at the surface does not diffuse into the polymer thin films even at a temperature well above the polymer glass transition temperature.   

The Effect of Nanoparticle Shape on Polymer-Nanocomposite Rheology and Tensile Strength

We investigate how nanoparticle shape influences the melt shear viscosity $\eta$ and the tensile strength $\tau$, with a focus on fullerene, carbon nanotube, and clay sheet nanocomposites. We simulate model nanoparticle dispersions of icosahedral, tube or rod-like, and sheet-like nanoparticles, all at a volume fraction $\approx 0.05$. Our results indicate an order of magnitude increase in the viscosity $\eta$ relative to the pure melt. This finding can not be explained by continuum hydrodynamics and we provide evidence that the $\eta$ increase has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod-like nanoparticles and least for the sheet-like nanoparticles. Curiously, the enhancements of $\eta$ and $\tau$ exhibit {\it opposite trends} with increasing chain length $N$ and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in $\tau$ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite.   

Stabilization of nanorods in polymer melts by end-adsorbed chains

Adsorbed or grafted polymers are often used to provide steric stabilization of colloidal particles. When the particle size approaches the nanoscale, the curvature of the particles becomes relevant, and rules of thumb based on the behavior of polymers attached to flat surfaces may no longer apply. To investigate this effect for the case of cylindrical symmetry, I use a classical density functional theory applied to a coarse-grained model to study the polymer-mediated interactions between two nanorods. The rods are immersed in a polymer melt consisting of two kinds of chains: 1) a small fraction of chains of length N with ends that are attracted to the rods so that they form a polymer brush on the rods; and 2) a matrix of chains of length P which have no interactions with the rods. Calculations of the density profiles and potential of mean force reveal the effects of curvature compared to similar calculations for chains adsorbed to flat planar surfaces.   

Dispersion and Percolation Transitions of Nanorods in Polymer Solutions

We present effective pair-interaction potentials and resulting phase behavior, percolation transitions of nanorods dispersed in solutions of polymers. We use polymer self consistent field theory in conjunction with Derjaguin approximation to compute the polymer mediated orientation-dependent pair interaction potential between cylindrical nanorods. A modified Flory theory and a simple analytical model are used to delineate different equilibrium phases and the onset of percolation for nanorods in polymer solutions. Our results suggest that the topology of the phase diagram of mixture of polymer and rods is highly dependent on the anisotropy of the rods, relative sizes of the rods and polymers, concentration of the polymer and the strength of adsorption. For the case of non-adsorbing polymers, the polymer depletion-induced attractive interactions result in a large two phase region which widens with an increase in the polymer concentration. Addition of adsorbing polymers is observed to lead to a richer phase behavior where at high polymer concentrations, the polymer-induced repulsive interactions result in steric stabilization of the particles and lead to an isotropic-nematic transition which closely resembles the behavior for hard rod suspensions. As a model mimicking nanotube-polymer mixtures, we also discuss the influence of strong rod-rod van der Waals interactions on the stability characteristics.   

Self-assembly of anisotropic nanoparticles at oil/water interfaces

Self-assemblies of both bio- and synthetic nanorods with different aspect ratios have been studied at the oil/water interfaces. Tobacco mosaic virus (TMV) shows different geometries at the perfluorodecalin/water interface as the concentration changes in the bulk. With low concentration of TMV in the aqueous phase, TMV prefers lying randomly parallel to the interface to mediate as large interfacial tension per particle as possible. At high concentration, TMV prefers standing up at the interfaces, not only mediating the interfacial tension but also neutralizing the strong electrostatic interaction between each other. The similar phenomenon has also been observed with alkyl-chain-covered Cadmium Selenide nanorods at the toluene/water interface during solvent evaporation. These assemblies can be manipulated by controlling the interfacial tensions between different liquids; the surface properties, the aspect ratio and concentration of nanoparticles; and the ionic strength in solution.   

Session A25: Focus Session: Mechanical Properties, Fracture & Adhesion

Mechanics of polymer interfaces

Although size-dependent effects of constraint and deformation volumes on elastoplastic mechanical behavior of metallic and ceramic structures are increasingly well-studied, relatively little is known about how the deformation of polymers depends on microstructural and physical length scales. In particular, it is not yet clear how the structural and mechanical properties of amorphous (glassy) polymers differ at free surfaces, at rigid interfaces, and within the bulk. Such understanding is important in that free surface and interface properties dominate the mechanical behavior of (bio)polymeric thin film and nanocomposite applications. Recent experiments have demonstrated as much as a 50{\%} depression in the glass transition temperature $T_{g}$ within $\sim $100 nm of the free surface in amorphous polystyrene (PS) and poly(methyl methacrylate) (PMMA) thin films [1-3]. This indicates possible differences in the amorphous topology and/or macromolecular mobility that induce a mechanical response quite different from that indicated via bulk or $\mu $m-scale testing, even at room temperature, within 100 nm of the free surface. Here, we employ spherical nanoindentation experiments and analytical models to determine the indentation elastic moduli $E_{i}$ of three well-characterized, amorphous polymer surfaces (PS, PMMA, and polycarbonate or PC) for maximum contact depths ranging from 5 nm to 250 nm. Over this range, we observe a 200{\%} increase in $E_{i }$with respect to the bulk $E_{i}$. We demonstrate that this apparent stiffening of the polymeric surfaces cannot be attributed to experimental artifacts such as surface roughness, assumptions of indenter contact area, or loading rates. Further, we consider this effect as a function of monomer structure for a given molecular weight, molecular weight for a given monomer structure, processing routes (injection and compression molded, and spin coating), and physical environment (temperature and humidity). We propose a model for the physical basis of and length scale of this surface stiffening with respect to the structural length scales of these macromolecules, and discuss the implications of this effect in terms of mechanical performance for synthetic and biological polymeric nanocomposites   

A novel approach to friction measurements using dewetted polymer droplets

Friction is still quite difficult to accurately measure. The current state-of-the-art in friction measurement is the surface forces apparatus (SFA) or lateral force microscopy (LFM). While both are very useful tools, they suffer from a complicated distribution of pressure between substrate and slider. Here we present an experiment that overcomes that obstacle and also bridges the gap between point (LFM) and large area (SFA) contact. In these experiments we measure directly the constitutive law, which is not hindered by surface curvature effects because the dewetted polymer droplet acts as a slider with a perfectly flat interface. In the case of friction between a polystyrene droplet and an ultra-thin layer of poly(dimethyl siloxane), we obtain a power law dependence of friction on slider speed. Interestingly, the exponent of the power law is related to the normal force applied in a simple way.   

Capillary wrinkling of thin floating films

We study the wrinkling instability induced in freely-floating polystyrene films, tens of nanometers in thickness, by the interfacial tension of tiny drops of water placed on their surface. The wrinkling pattern is characterized by the number, N, and length, L, of the wrinkles. The dependence of N on the elastic properties of the sheet and on the capillary force exerted by the drop provides a detailed experimental test of recent theoretical predictions on wavelength selection in the wrinkling instability. A scaling relation is developed for the length of the wrinkles. These scaling relations for the number and length of the wrinkles demonstrate the basis for a metrology of the elasticity and thickness of extremely thin films that relies on no more than a dish of fluid and a low-magnification microscope.   

Nanometer voids prevent crack growth in polymer thin films

Macroscopic voids initiate cracks and cause catastrophic failure in brittle materials. The effect of micrometer voids in the mechanical properties of polymeric materials was studied in 1980's and 90's with the expectation that such small voids may initiate crazing, the toughening mechanism in polymer solids, similar to dispersed rubber particles widely used in industry. However, the micrometer voids showed only limited resistance against crack growth, and it was concluded that much smaller voids are necessary for the drastic change in mechanical properties. We have recently succeeded the nondestructive introduction of nanometer voids (30--70 nm) in polymeric materials using block copolymer template and carbon dioxide (CO$_2$) by partitioning CO$_2$ in CO$_2$-philic nanodomains of block copolymers. The reduction of Young's modulus with such nanometer voids was minimal (2 to 1 GPa) due to the (short-range) ordered spherical voids. While the unprocessed copolymer films failed in brittle manner at around 2 \% of tensile strain, the processed copolymer films with nanometer voids did not break up to at least 60 \%. A microscopic observation under strain of the crack tip revealed that the nanometer voids were deformed under strain and directly converted into the networked fibrils near the crack tip similar to crazing and thus prevented the crack growth.   

Aging with Applied Strain of a Black-Filled Natural Rubber Vulcanizate: Intrinsic Flaw Sizes

Black-filled natural rubber, with an inefficient sulfur cure, was aged at 90$^{\circ}$C and 110$^{\circ}$C under nitrogen, with and without applied strain. Samples aged under strain became ``double networks'' and retained a residual extension ratio. Intrinsic flaws are distributed randomly throughout the rubber, and influence its breaking strength. Intrinsic flaw sizes of single networks aged under nitrogen purge were larger than those of the unaged networks, except for the most severe aging. The increase is attributed to annealing of the network; however, as aging becomes more severe, this is offset by: 1) decreased ability of the rubber to dissipate energy, and 2) increased oxidation damage to the network. For samples strained to $\lambda_{i}$ = 2.0 for 48 hours at room temperature, the intrinsic flaw size increased by a factor of 1.7. Perhaps aging under strain promotes healing of network defects. For double networks, perpendicular specimens generally had intrinsic flaw sizes similar to single networks. Parallel specimens generally had smaller intrinsic flaw sizes than single networks, similarly aged. The limited extensibility of the oriented chains dominates the effects of microvoid healing and annealing.   

Physical Aging And Non-Exponentiality In A Crosslinked Coating Subjected To Degradative Weathering.

Polymeric coatings provide protection and aesthetics for many materials and equipment, and, in service, they must fulfill their roles for extended periods in a predictable manner. Molecular relaxation in a polymeric coating that is degrading during weathering is affected both by the ambient conditions and concurrent chemical degradation by ultraviolet radiation or other aggressive species. Purely physical aging was contrasted with the effect of concurrent chemical degradation by measuring non-exponentiality which showed some differences according to whether it was determined from `enthalpy recovery' or stress relaxation measurements. Less directly determined parameters, such as `non-linearity' and the size of `co-operatively relaxing regions', also changed. Changes in fictive temperature at each level of degradation demonstrated that physical aging was in competition with the effect of chemical degradation in the crosslinked network. Relaxation times measured in this coating extended longer than cycle periods typical of accelerated weathering tests, suggesting that frequency effects might be important when resolving differences in outcome between natural and laboratory, accelerated weathering cycles.   

The Elastic Properties of Polymer Nanofibers: Influence of Confinement on Conformation State of Macromolecules and Supermolecular Structures

This research deals with open problems concerning polymer materials with reduced size and dimension such as thin and ultra thin films, nanofibers, and nanotubes. Such materials exhibit exceptional mechanical properties compared to those of their macroscopic counterparts. In particular, abrupt increase in Young modulus of polymer nanofibers has been observed when their diameters became small enough. Such features are poorly understood, and lack of explanation of the observed phenomena, based on mechanical (macroscopic) concepts, requires detailed microscopic examination of systems in question. We hypothesize that the supermolecular structure is the dominant role in the deformation process of polymer nanofibers, more precisely, confinement of this supermolecular structures which is caused by shrinking of the transversal size of above objects. In this work we report on results of our studies in conformational statistics of polymer macromolecules under conditions of confinement, and supermolecular structure formation; and on experimental studies of the mechanical and structural properties of electrospun nanofibers.   

Predicting Structure-Property Relationship in Segmented Polyurethanes

We develop new theoretical framework to study the relationship between composition and mechanical properties in segmented polyurethanes (PU) and poly(urethane-ureas) (PUU). In particular, we analyze polymer mechanical properties (quasi-static Young's modulus, E, and temperature-dependent storage shear modulus, G') as function of the hard and soft segment chemistry, hard segment weight fraction, soft segment molecular weight, and temperature. It has been known for some time [1] that in many segmented PU and PUU polymers, the hard-soft microphase separation causes the formation of a ``percolated hard phase''. We propose a new formalism that enables one to predict the onset of the hard phase percolation as function of temperature, soft segment molecular weight, and chemical structures of hard and soft segments. Based on this formalism, we can build micromechanical models to estimate mechanical properties of segmented polyurethanes as function of temperature. We used this theoretical framework to simulate storage moduli of several model compounds, and found very reasonable qualitative agreement with experimental data. [1] See, e.g., A. J. Ryan et al., \textit{Macromolecules,} \textbf{24}, 2883 (1991); \textit{Polymer} \textbf{32}, 1426 (1991).   

Compliance Effects of a Modern Rheometer

Instrument compliance effects caused by both the transducer and entire instrument itself can induce large errors on shear measurements of viscoelastic properties of materials [1,2]. This effect can also lead to an error in estimating the relaxation time and shape parameter in the Kohlrausch-Williams-Watts (KWW) function [3]. We present examples of instrument compliance effects on the measurement of the material properties of small molecular glass formers and a commercially available polydimethysiloxane (PDMS) rubber using a TA Instruments ARES Rheometer. The 2KFRT (Force Rebalanced Transducer) was replaced with a strain gage transducer (Honeywell-Sensotec). Stress relaxation and dynamic frequency sweep experiments were performed. We also present a technique to correct for compliance effects in stress relaxation experiments and dynamic frequency sweep experiments. Recommendations are made for both experimental and instrument design to avoid and/or minimize compliance effects. [1] M Gottlieb and C.W. Macosko, Rheol. Acta 1982 90-94. [2] M.E. Mackay and P.J. Halley, J. Rheol. 1991 1609-14. [3] R. Kohlrausch, Poggendorf's Ann. Phys. 91, 179 (1854).; G. Williams and D. C. Watts, Trans. Faraday Soc. 66, 80 (1970).   

Entanglements of End Grafted Polymer Brushes in a Polymeric Matrix

The entanglement of a polymer brush immersed in a melt of mobile polymer chains is studied by molecular dynamics simulations. A primitive path analysis (PPA) is carried out to identify the brush/brush, brush/melt and melt/melt entanglements as a function of distance from the substrate. The PPA characterizes the microscopic state of conformations of the polymer chain and is ideally suited to identify chain/chain entanglements. We use a new thin-chain PPA technique to eliminate spurious non-entangled inter chain contacts arising from excluded volume. As the grafting density of the brush increases we find that the entanglements of the brush with the melt decrease as the system crosses over from the wet to dry brush regime. Results are compared to brush/brush entanglements in an implicit solvent of varying solvent quality. Sandia is a multiprogram laboratory operated by Sandia Corp., a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.   

High Strength Development at Incompatible Semicrystalline Polymer-Polymer Interfaces

For incompatible A/B interfaces, the strength G$_{1c}$ is related to the equilibrium width w (normalized to the tube diameter) of the interface by G$_{1c}$/G* = (w-1), where G* is the virgin strength [R.P. Wool, C.R, Chimie, 9 (2006) 25]. However, the interface strength is quite weak due to very limited interdiffusion. The mechanism of high strength development of a series of thermoplastic polyurethane elastomers (TPU) bonding with ethylene vinyl alcohol copolymers (EVOH) was investigated. During cool down of the A/B interface in the co-extruded melt, there exits a unique process window---the $\alpha -\beta $ window-which promotes considerable strength development. We used the differences in melting points and the volume contraction during asymmetric crystallization to generate influxes ($\Sigma $ nano-nails/unit area), where an influx occurs by the fluid being pulled into the crystallizing side. TPU samples with higher degree of crystallization typically exhibited higher peel strengths, due to the formation of both inter- and intra- spherulitic influxes of nano-dimension across the interface. The peel energy now behaves as G$_{1c} \quad \sim $ $\Sigma $L$^{2}$, where L is the length of the influx and L$>>$w. Annealing between the $\alpha $ and $\beta \quad {\rm t}$ relaxation temperatures of the EVOH generated additional influxes which provided significant connectivity and peel strength.   

Elastic breakup in extensional flow of entangled melts.

In contrast to shear deformation, extensional flow behavior is more difficult to study because (a) the experimental system is always of finite dimensions and (b) the total strain in any given test is only finite. Despite uncertainties, there has been great deal of research carried out to explore various aspects of nonlinear behavior of entangled polymers. We applied our recently developed new theory [1] for flow of entangled polymers to predict the uniaxial stretching behavior of entangled melts. Specifically, we show that cohesive breakdown would take place, under the same conditions independent of molecular weight, during and after extension when the elastic force due to stretching overcomes a combination of the entanglement force and inter-chain frictional interactions. [1] \textit{Phys. Rev. Lett. }\textbf{97}, 187801 (2006); full manuscript to be submitted to \textit{J. Chem. Phys.}.   

Session A26: Focus Session: Protein Folding: Theory and Simulations I

Exploring The Folding Energy Landscape--Triumphs and Tribulations

The folding process has become one of the best understood transformations of condensed matter,owing to the minimal frustration principle and the collective nature of the key bottlenecks in the folding process. I will discuss the limits of models based on topology alone and also highlight the effects of residual frustration and co-factors in some puzzling examples that challenge the funnel paradigm.   

Simulating protein folding and aggregation on the 10 second timescale

Understanding how proteins self-assemble or ``fold'' is a fundamental problem in biophysics. Moreover, the ability to understand and quantitatively predict folding kinetics would have many implications, especially in the area of diseases related to protein misfolding, such as Alzheimer's Disease. However, there are many challenges to simulating folding, most notably the great computational challenges of simulating protein folding with models with sufficient accuracy to make quantitative predictions of experiments. In my talk, I will discuss our recent work to combine distributed computing with a new theoretical technique (Markov State Models) in order to simulate folding on long timescales as well as the direct and quantitative experimental tests of these methods. I will conclude with the application of these methods to the study of the Abeta peptide, whose aggregation has been directly implicated as the toxic element in Alzheimer's Disease.   

Understanding ensemble protein folding at atomic detail.

Here we present a new all-atom model and development of simple potential functions (inspired by discoveries of general principles of protein folding) that allow to fold small proteins from sequence to near native structure at an atomic level of detail. Availability of numerous successful all-atom folding trajectories and their novel graph theoretical analysis, makes it possible to gain a detailed atomic level understanding of folding pathways/intermediates/transition states for engrailed homeodomain - a small alpha-helical protein that has been recently studied experimentally.   

Investigating the Disordered States of Two Proteins Using Intramolecular Contact Formation

Using the quenching of the triplet state of tryptophan by cysteine, we investigate the unfolded states of two structurally similar but sequentially non-homologous proteins, the IgG binding domain of proteins L and G, under a range of denaturing conditions. These proteins show remarkably similar dynamics of intramolecular diffusion marked by a decrease in contact formation at denaturant conditions that favor folding. A reaction limited rate and the diffusion limited rate are obtained by measuring the viscosity dependence of the intramolecular contact rate. To further investigate the polymer dynamics of the unfolded state under folding conditions, we modeled the proteins as a worm-like chain with excluded volume using Szabo, Schulten and Schulten (SSS) theory to estimate the effective persistence length and intramolecular diffusion constant at various concentrations of GdnHCl. The results reveal an unfolded state under folding conditions that is significantly more compact and less diffusive than the fully denatured state.   

Thermodynamics of the Beta-hairpin to Coil Transition using a Distance Constraint Model

The configuration partition function is calculated exactly [1] for a distance constraint protein model that describes the beta-hairpin to coil transition. The model employs a Gaussian backbone chain of N atoms in which bonds may form to crosslink pairs of atoms in close proximity along the chain, represented by fluctuating distance constraints. Each distinct pattern of cross-linking bonds defines a constant energy over all atomic geometries that are consistent with the constraint topology. This geometrical degeneracy factor is directly calculated from configuration space integrals for each accessible constraint topology. All constraint topologies consistent with no pair of bonds that link two backbone atoms are themselves crossed are enumerated, leading to an analytical closed form expression for the configuration partition function. The phase diagram for the beta-hairpin to coil transition as a function of chain length has been studied. \newline \newline [1] O.K.Vorov, D.J.Jacobs, D.R.Livesay, subm. to Phys.Rev.Lett., 2006, in preparation.   

Lattice Model Investigations of Protein Aggregation

Protein aggregation is known to be important in a variety of diseases. We have expanded a well-known 3-dimensional protein folding computer lattice model with explicit side-chains in order to investigate the thermodynamics and statistical mechanics of protein aggregation between two chains. The modeling of a two-chain system presents technical and physics issues in addition to those found when modeling only a single chain. We report on preliminary results of the simulations.   

Effective potentials for Folding Proteins

A coarse-grained off-lattice model that is not biased in any way to the native state is proposed to fold proteins. To predict the native structure in a reasonable time, the model has included the essential effects of water in an effective potential. Two new ingredients, the dipole-dipole interaction and the local hydrophobic interaction, are introduced and are shown to be as crucial as the hydrogen bonding. The model allows successful folding of the wild-type sequence of protein G and may have provided important hints to the study of protein folding.   

Forced Unfolding of the Coiled-Coils of Fibrinogen by Single-Molecule AFM

A blood clot needs to have the right degree of stiffness and plasticity for hemostasis, but the origin of these mechanical properties is unknown. Here we report the first measurements using single molecule atomic force microscopy (AFM) to study the forced unfolding of fibrinogen to begin addressing this problem. To generate longer reproducible curves than are possible using monomer, factor XIIIa cross-linked, single chain fibrinogen oligomers were used. When extended under force, these oligomers showed sawtooth shaped force-extension patterns characteristic of unfolding proteins with a peak-to-peak separation of approximately 26 nm, consistent with the independent unfolding of the coiled-coils. These results were then reproduced using a Monte Carlo simulation with parameters in the same range as those previously used for unfolding globular domains. In particular, we found that the refolding time was negligible on experimental time and force scales in contrast to previous work on simpler coiled-coils. We suggest that this difference may be due to fibrinogen's structurally and topologically more complex coiled-coils and that an interaction between the alpha C and central domains may be involved. These results suggest a new functional property of fibrinogen and that the coiled-coil is more than a passive structural element of this molecule.   

Session A27: Focus Session: Computational Nanoscience I-Methods and Applications

A Hybrid Density Functional Study of SiC Nanotubes

As a continuation of our previous work on SiC nanoclusters,$^{\ast }$ we report here first principles calculations on the electronic and geometric structures of armchair and zigzag silicon carbide nanotubes from (3,3) to (11,11) and (3,0) to (11,0) respectively. The finite cluster approach with dangling bonds terminated with hydrogen has been used. The theoretical formalism used is the hybrid density functional theory incorporating Hartree-Fock exchange with density functional theory exchange-correlation. In particular, we have used the B3LYP hybrid functional and the Los Alamos pseudopotential LANL2DZ$^{ }$as implemented in the Gaussian 03 suite of programs. For silicon, the 1s, 2s, and 2p electrons have been represented by core potentials and the remaining electrons as valence states. For carbon and hydrogen, all electron basis sets have been used. A detailed comparison of the structures and stabilities of the nanotubes has been performed. The dependence of the electronic band gaps on the respective tube diameters and energy density of states have also been investigated. Results will be compared with other published data in the literature where possible. $^{\ast }$ A. K. Ray and M. N. Huda, J. Comp. Th. Nanosci. \textbf{3}, 315 (2006).   

A Hybrid Density Functional Study of Si Nanotubes

First principles calculations have been used to study the electronic and geometric structures of zigzag and chiral silicon nanotubes. The finite cluster approach with dangling bonds terminated with hydrogen has been used. The theoretical formalism used is hybrid density functional theory incorporating Hartree-Fock (HF) exchange with density functional theory (DFT) exchange-correlation. In particular, we have used the B3LYP hybrid functional and the Los Alamos pseudopotential LANL2DZ as implemented in the Gaussian 03 suite of programs. For silicon, the 1s, 2s, and 2p electrons have been represented by core potentials and the remaining electrons as valence states. A detailed comparison of the structures and stabilities of the nanotubes has been performed and the dependence of the electronic band gaps on the respective tube diameters has been investigated. We will also compare our results with previously published data on Si armchair nanotubes published by our group$^{\ast }$ and with other results published in the literature. $^{\ast }$P. Pradhan and A. K. Ray, J. Comp. Th. Nanosci. \textbf{3}, 128 (2006).   

Tetra, a modeling system for the generation of the atomic configurations of branched wurtzite/zincblende nanostructures

The first step in simulating properties of nanostructures is generation of accurate atomic configurations. For complex objects such as the multiply branched heterostructures synthesized by Alivisatos et al.$^{1}$, this is nontrivial. We report here on our code, ``tetra,'' that accomplishes this task. Borrowing from techniques of computer graphics, we represent the complex structure as a tree, each node of which is a shape with fixed crystal structure, and use concatenation of 4 by 4 homogeneous transformation matrices to arrange these fixed building blocks into the final object. A simple text based input ``language'' describes the connectivity and dimensions of the structure. The ultimate purpose of this code is use within a package that will explore and optimize electronic properties of such structures with respect to their geometry$^{2}$. We will present examples of both structures and subsequent semi-empirical pseudopotential-based$^{3}$ electronic structure calculations. [1] A. P. Alivisatos, et al., \textit{Nature,} \textbf{430}, 190 (2004). [2] J. Li and L. W. Wang, \textit{NanoLetters}, \textbf{3}, 10, 1357-1363 (2003). [3] L. W. Wang and A. Zunger, \textit{Phys. Rev. B} \textbf{51}, 17398 (1995).   

Global optimization approaches for finding the atomic structure of surfaces and nanowires

In the cluster structure community, global optimization methods are common tools for seeking the structure of molecular and atomic clusters. The large number of local minima of the potential energy surface (PES) of these clusters, and the fact that these local minima proliferate exponentially with the number of atoms in the cluster simply demands the use of fast stochastic methods to find the optimum atomic configuration. Therefore, most of the development work has come from (and mostly stayed within) the cluster structure community. Partly due to wide availability and landmark successes of scanning tunneling microscopy (STM) and other high resolution microscopy techniques, finding the structure of periodically reconstructed semiconductor surfaces was not generally posed as a problem of stochastic optimization until recently [1], when we have shown that high-index semiconductor surfaces can have a rather large number of local minima with such low surface energies that the identification of the global minimum becomes problematic. We have therefore set out to develop global optimization methods for systems other than clusters, focusing on periodic systems in one- and two- dimensions as such systems currently occupy a central place in the field of nanoscience. In this talk, we review some of our recent work on global optimization methods (the parallel-tempering Monte Carlo method [1] and the genetic algorithm [2]) and show examples/results from two main problem categories: (a) the two-dimensional problem of determining the atomic configuration of clean semiconductor surfaces [1,2], and (b) finding the structure of freestanding nanowires [3]. While focused on mainly on atomic structure, our account will show examples of how these development efforts contributed to elucidating several physical problems and we will attempt to make a case for widespread use of these methods for structural problems in one and two dimenstions. \newline [1]C.V. Ciobanu and C. Predescu, Reconstruction of silicon surfaces: a stochastic optimization problem, Phys. Rev. B 70, 085321 (2004). \newline [2]F.C. Chuang, C.V. Ciobanu, V.B. Shenoy, C.Z. Wang and K.M. Ho, Finding the reconstructions of semiconductor surfaces via a genetic algorithm, Surf. Sci. 573, L375 (2004). \newline [3]T.L. Chan, C.V. Ciobanu, F.C. Chuang, N. Lu, C.Z. Wang and K.M. Ho, Magic structures of H-passivated [110] silicon nanowires, Nano Letters 6, 277 (2006).   

Strained InAs/GaAs quantum structures: non-parabolic simulating model.

A single sub-band model for InAs/GaAs quantum dot (quantum ring), taking into account the strain and piezoelectric potentials, is applied to study the electron spectral properties of QD(QR). The finite confinement band-gap potential is estimated by the band gap difference of the InAs quantum object and the GaAs substrate. An additional potential Vs(Vs=const for QD, and Vs=0 for a substrate) is included in the model to simulate the total effect of the strain and piezoelectricity. The non-parabolic approximation is defined by dependence of electron effective mass on the confinement energy according to the Kane formula. The 3D confined energy problem is solved numerically by the finite element method. The adequacy of our model is illustrated by comparing electron energy spectra with \textit{ab initio} calculations [1]. The experimental data by A. Lorke, et al.(PRL \textbf{84} 2223 (2000)) for few electrons tunneling into InAs/GaAs QD(QR) are well reproduced within the present model. The non-parabolic effect, which is quite noticeable in our calculations, is also discussed. [1] C. Pryor, PR B \textbf{57} 7190 (1998); O. Stier, M. Grundmann, and D. Bimberg, PR B \textbf{59} 5688 (1999); J.I. Climente, J. Planelles, F. Rajadell, J. Phys.: Condens. Matter \textbf{17} 1573 (2005).   

Size reduction in layered semiconducting compounds

In the last decade numerous experiments have shown dramatic changes in the optical properties of bulk semiconductors as their size is decreased to nanoscale dimensions. Most investigations have focused on 3D compounds such as II-VI and group IV. A few experiments have also been conducted for layered semiconductors, such as transition-metal dichalcogenides, indicating changes in photoluminescence properties apparently comparable to those found in 3D systems. We present extensive electronic structure calculations of the structural and electronic properties of $\mbox{MoS}_2$ nanostructures showing no appreciable quantum confinement effects in single sheet nanoparticles, whose electronic structure is dominated by the surface and in particular edge states near the Fermi level. On the other hand, a strong dependence of the electronic structure is observed as a function of layer stacking and distance. We suggest that the observed photoluminescence variation as a function of size does not pertain to size reduction in single sheets but rather to the number of planes composing the nanoparticle. We also suggest a way to engineer metallic nanowires taking advantage of edge states in nanosheet composites.   

The design of a nanocontainer for high pressure storage of hydrogen

Molecule hydrogen is known to have a weak van der Waals potential, which makes it difficult to raise its storage efficiency for physisorption based methods. In this report, we explore the other side of such a weak potential, the well-known compressibility of hydrogen. A (20,0) single wall carbon nanotube based nanocontainer is designed, in which a C$_{60}$ ``peapod'' at the cap section of the nanotube serves as a molecular valve. Diffusion barriers through such a valve is examined by molecular dynamics simulations under various conditions. It is demonstrated that H$_2$ can first be filled into the container upon compression at low temperature, and then be locked inside it after the release of external pressure. The internal pressure that can be achieved in this design is in the GPa range at room temperature, which is much higher than the typical pressure of a few hundred bar currently employed for hydrogen storage. At 2.5 GPa, the storage weight ratio approaches a promising 7.7$\%$.   

Surface Green functions in molecular transport junctions: The generalization to interacting electrons in the leads

The expression for current in transport junctions is generalized to interacting electrons in the leads. We derive a formula for the current where in the expression for line-width matrices the lead density of states is replaced by the surface spectral density matrix for arbitrary {\em e-e} interactions in the leads and in the bridge, respectively. This expression is only valid for small lead-bridge interactions. A novel computational method for a surface Green function matrix is introduced to find the surface spectral density ($\sim$ the trace of the imaginary part of the surface Green function matrix). The proposed non-recursive approach results in the solution of the second order matrix equation for the spectral density matrix (the density of states for noninteracting electrons). The single and double principle layer models are studied for {\em aluminum} surfaces. We find that the peak in the spectral function is rather narrow ($\sim 2\;eV$). and can cause a peak in the $\Gamma$ matrices resulting in a peak in the current-voltage characteristics. Beside the {\em aluminum} surface with {\em fcc}-structures, we study a {\em hexagonal} structure as well. Such surfaces exhibit a gap and two bands in the spectral density. The gap and the band widths depend on the parameters of the lead Hamiltonian. We show that the narrow gap and the narrow bands can result in large negative resistances in the conduction.   

Adiabatic quantum pumping in an Aharonov-Bohm loop and in a Si-like nanowire: interference in real space and in k-space

We study interference effects in the current generated by adiabatic quantum pumping in two extended chain models. The first model contains an Aharonov-Bohm loop within a tight-binding chain of sites. It exhibits interference between the two arms of the loop. We investigate the effect of magnetic field reversal on the pumped current. Our second model is a tight-binding chain of sites with next-nearest-neighbor hopping terms. The resulting Si-like indirect band structure can have 4 degenerate Fermi wave vectors $\pm k_{1F}$ and $\pm k_{2F}$ rather than the usual 2 Fermi wave vectors $\pm k_{F}$. It exhibits signatures of interference between these degenerate conduction band states.   

Hypervelocity impact on carbon nanotube reinforced a-SiC composite targets: An atomistic simulation study

Atomistic simulation studies, employing the Tersoff many-body reactive potential, have been performed to investigate the hypersonic velocity impact protection properties of carbon nanotube (CNT) reinforced a-SiC composites, for a diamond spherical projectile velocities ranging from 1 km/s to 20 km/s. The scaling relations and analytical forms are derived to describe the penetration depth as a function of the velocity and radius of the projectile. A theoretical framework has been developed to describe the penetration depth behavior in the case of impact of hard projectile on hard target material. The atomistic simulation results are found to compare well with the obtained analytical forms. The effects of diamond nanoparticle impact on the a-SiC composites, with CNTs aligned parallel and perpendicular to the impact direction, caused by impact induced shock absorption and damage creation, will be described in this presentation.   

Session A28: Focus Session: Carbon Nanotube Optics I

Magnetic Brightening of Dark Excitons in Carbon Nanotubes

To gain insight into the internal energy structure and radiative properties of excitons in single-walled carbon nanotubes (SWNTs), we have studied photoluminescence (PL) from individualized HiPco and CoMoCAT samples as a function of magnetic field ($B$) and temperature ($T$). The PL intensity increased, or ``brightened,'' with $B$ applied along the tube axis and the amount of brightening increased with decreasing $T$. These results are consistent with the existence of a dark state below the first bright state~[1]. In the presence of time reversal symmetry, exchange-interaction-induced mixing between excitons in two equivalent valleys (the K and K' valleys) is expected to result in a set of exciton states, only one of which is optically active. This predicted bright state, however, is not the lowest in energy. Excitons would be trapped in the dark, lowest-energy state without a radiative recombination path. When a tube-threading $B$ is applied, addition of an Aharonov-Bohm phase modifies the circumferential boundary conditions on the wave functions and lifts time reversal symmetry~[2,3]. This symmetry breaking splits the K and K' valley transitions, lessening the intervalley mixing and causing the recovery of the unmixed direct K and K' excitons, which are both optically active. We have calculated PL spectra through $B$-dependent effective masses, populations of finite-$k$ states, and acoustic phonon scattering, which quantitatively agree with the observations. These results demonstrate the existence of dark excitons, their influence on the PL quantum yield, and their elimination through symmetry manipulation by a $B$. This work was performed in collaboration with J.~Shaver, S.~Zaric, O.~Portugall, V.~Krstic, G.~L.~J.~A.~Rikken, X.~Wei, S.~A.~Crooker, Y.~Miyauchi, S.~Maruyama, and V.~Perebeinos and supported by the Robert A.~Welch Foundation, the NSF, and EuroMagNET. \newline \newline [1]~V.~Perebeinos {\it et al}., Phys.~Rev.~Lett.~{\bf 92}, 257402 (2004); H.~Zhao and S.~Mazumdar, Phys.~Rev.~Lett.~{\bf 93}, 157402 (2004); V.~Perebeinos {\it et al}., Nano Lett.~{\bf 5}, 2495 (2005); C.~D.~Spataru {\it et al}., Phys.~Rev.~Lett.~{\bf 95}, 247402 (2005). \newline [2]~T.~Ando, J.~Phys.~Soc.~Jpn.~{\bf 75}, 024707 (2006). \newline [3]~S.~Zaric {\it et al}., Science {\bf 304}, 1129 (2004); Phys.~Rev.~Lett.~{\bf 96}, 016406 (2006).   

Magnetic field effects on the excitonic absorption spectra of semiconducting single-walled carbon nanotubes

We have investigated the magnetic field effects on the electronic structure and absorption spectra of semiconducting single-walled carbon nanotubes (S-SWCNTs) within a Coulomb correlated $\pi$-electron model. \footnote{H. Zhao and S. Mazumdar, Phys. Rev. Lett. {\bf 93}, 157402(2004).} \footnote{Z. Wang, H. Zhao, and S. Mazumdar, Phys. Rev. B {\bf 74}, 195406 (2006).} We consider magnetic field parallel to the nanotube axis, which introduces the Aharonov-Bohm phase in the wavefunction. Recent experiments claim to have observed the energy shift and splitting due to the magnetic fields \footnote{S. Zaric {\it et al.,} Phys. Rev. Lett. {\bf 96}, 016406 (2006).} Some of our theoretical results are substantively different from existing results. Comparison with recent experiments are made.   

Activating Dark Excitons on Carbon Nanotubes with Electric Fields

The valley degeneracy of the singlet excitons on a semiconducting carbon nanotube is lifted by Coulomb backscattering which produces two intervalley superposition states: a bright optically allowed singlet exciton, and a dark (dipole forbidden) singlet exciton at lower energy. We study theoretically the perturbations to this spectrum due to a longitudinal static electric field. We find the electric field transfers oscillator strength from the bright to the dark singlet states and activates the lower energy state in the fluorescence spectrum for modest values of the field strength. Modelling the K and K' point excitons as a two state system, we find that the field induces a complex phase in the intervalley scattering amplitude, which in turn renders the dark state optically active. We study the dependence of this effect on the chiral angle of the tube and further analyze other field configurations that can coherently manipulate the intervalley superposition states produced in this system.   

Aromatic trends in single-walled carbon nanotubes: diamagnetic anisotropy for arbitrary chiralities

The chirality dependence of single-walled carbon nanotube (SWNT) properties often leads to ``fan-out'' diagrams whose departure from the large diameter scaling limit is of fundamental interest. ~Here we present the first experimental indication of fan-out behavior for orbital magnetic anisotropy ($\Delta $\textit{$\chi $}), which has long been an important probe of electronic structure in aromatic molecules. ~We will discuss the experimental approach (polarized resonant photoluminescence) that made this background-free measurement possible, and explain how these results can be used to predict $\Delta $\textit{$\chi $} for \textit{arbitrary} SWNT chiralities. ~Taking into account general symmetry considerations, \textit{ab initio} calculations, large-diameter tight-binding theory, and our experimental data, we obtain a chiral expansion for $\Delta $\textit{$\chi $} using a single fitting parameter. ~The results show (2n+m) family trends whose asymmetry between ``mod 1'' and ``mod 2'' semiconducting families is reminiscent of those seen in other SWNT optical, phonon, and exciton properties. ~Finally, we discuss the (n,m) dependence of zone-folding tight binding calculations when applied to realistic tube sizes.   

Electron-electron interaction effects on cross-polarized optical absorption in semiconducting single-walled carbon nanotubes (S-SWCNTs)

Within the tight binding theory of S-SWCNTs optical transitions polarized transverse to the nanotube axis, E$_{12}$ and E$_{21}$, are degenerate, and occur at (E$_{11}$ + E$_{22}$)/2, where E$_{11}$ and E$_{22}$ are the optical transitions polarized along the nanotube axis. Electron-electron interactions split the degeneracy of the transverse transitions, giving new eigenstates that are a redshifted optically forbidden odd superposition and a blueshifted (by several tenths of 1 eV) optically allowed even superposition of the one-electron excitations \footnote{H. Zhao and S. Mazumdar, Phys. Rev. Lett. {\bf 93}, 157402 (2004)}. Recent experiments \footnote{Y. Miyauchi, M. Oba and S. Maruyama, Phys. Rev. B, accepted (2006)} have confirmed our qualitative prediction. Here we report quantitative calculations of the longitudinal versus transverse optical absorptions in the four S-SWCNTs studied by Miyauchi {\it et al.}, within a $\pi$-electron Hamiltonian with long range Coulomb interactions \footnote{Z. Wang, H. Zhao and S. Mazumdar, Phys. Rev. B {\bf 74}, 195406 (2006)}. We make detailed comparisons between experiments and theory. We also comment on the role of electron hoppings beyond nearest neighbor and the binding energy of the transverse exciton.   

Dielectric response of aligned semiconducting single-wall nanotubes

We report measurements of the full intrinsic optical anisotropy of isolated single-wall carbon nanotubes (SWNTs). By combining absorption spectroscopy with transmission ellipsometry and polarization-dependent resonant Raman scattering, we obtain the real and imaginary parts of the intrinsic SWNT permittivity from aligned semiconducting carbon nanotubes dispersed in stretched polymer films. Our results are in agreement with theoretical predictions, highlighting the limited polarizability of excitons in a quasi-1D system. We discuss the dependence of the measured optical response on nanotube length.   

Electronic Structure Effects in Single Wall Carbon Nanotubes Dielectric Response.

The electronic structure of various single wall carbon nanotubes is considered within the $sp^3$ tight-binding model. Parameters for this model are taken from the Slater-Koster model. The $sp^3$ approach is applied in order to take into account the hybridization of the carbon $\sigma -\pi $ orbitals due to curvature of the cylindrical surface of the nanotubes. The curvature dependence of the hopping integrals is also taken into account. Only nearest neighbor interaction is used. The obtained electronic states and energies are then used to calculate the dielectric response of the carbon nanotubes within random phase approximation methods. The real and imaginary parts of the dielectric response function are calculated and the curvature and geometry effects of the different nanotubes are discussed.   

Bilayer Graphene: An Electrically Tunable Semiconductor

Using \textit{ab initio} density functional theory calculations, we verify [1,2] that the energy band structure of bilayer graphene can be tuned by applying an external electric field. As the strength of the external electric field increases, the electronic spectrum of bilayer graphene changes from a that of a zero-gap semiconductor to that of a gapped semiconductor. From the \textit{ab initio} calculations the external field dependence of the screened interlayer potential difference and tunneling amplitudes are extracted by fitting to a tight-binding model. We discuss the role of interlayer correlations in determining the size of the gap and the accuracy of local density approximation. [1] Edward McCann and Vladimir I. Fal'ko, Phys. Rev. Lett. {\bf 96}, 086805 (2006). [2] Taisuke Ohta, Aaron Bostwick,, Thomas Seyller, Karsten Horn, and Eli Rotenberg, Science {\bf 313}, 951 (2006).   

Magneto-optical conductivity in Graphene: signatures of the Dirac quasiparticles

Landau level quantization in graphene reflects the Dirac nature of its quasiparticles and has been found to exhibit an unusual integer quantum Hall effect. In particular the lowest Landau level can be thought as shared equally by electrons and holes and this leads to characteristic behavior of the diagonal and Hall magneto-optical conductivity as a function of frequency $\Omega$ for various values of the chemical potential $\mu$. We show that the evolution of the pattern of absorption lines as $\mu$ is varied encodes the information about the presence of the anomalous lowest Landau level. The first absorption line related to the lowest level always appears with full intensity or is entirely missing, while all other lines disappear in two steps. We demonstrate that if a gap develops, the main absorption line splits into two provided that the chemical potential is greater than or equal to the gap.\\ \noindent References: V.P.~Gusynin, S.G.~Sharapov and J.P.~Carbotte, cond-mat/0607727.   

Excitations from Filled Landau Levels in Graphene

We consider particle-hole excitations of graphene over an integer quantum hall state. We first analyze the two-body problemof a single Dirac electron and hole in a magnetic field interactingvia Coulomb forces. We then turn to the many-body problem, where particle-hole symmetry and the existence of two valleys lead to a number of effects peculiar to graphene. The appearance of different branches in the exciton spectrum is sensitive to the filling factor. The coupling together of a large number of low-lying excitations leads to strong many- body corrections, which could be observed in inelastic light scattering or optical absorption.   

Magnetoplasmon excitations in graphene.

Graphene is a monolayer of graphite with a band structure composed of two cones located at two inequivalent corners of the Brillouin zone at which conduction and valence bands merge. In contrast with conventional two dimensional electron gas, the dispersion relation obeys a Dirac law with an energy linear as a function of momentum which leads to a specific square root dependence of the Landau levels under an applied magnetic field. The magneto-optical transitions are either of cyclotron type or valence to conduction type. We derive in this frame the magnteplasmon picture, for filling factor lower than 2, which should be used to interpret the magneto-optical experiments in this compound.   

Infrared absorption in graphene

We present evidence for the cyclotron resonance transition between the lowest lying Landau levels near the Dirac point in a single layer of graphene, in magnetic fields up to 18T. At constant field, we modulated the back gate voltage on large area graphene samples to determine the infrared absorption from 400 to 3000 cm$^{-1}$ using a FTIR spectrometer. All data were taken at 4.2K with simultaneous measurement of the graphene carrier densities and mobilities. We find transmission minima having widths of $\approx$500 cm$^{-1}$, whose shift in energy is consistent with a square root dependence on the magnetic field as expected for two dimensional Dirac fermions. From this field dependence, the Fermi velocity is estimated at 1.1$\times$10$^6$m/s, in good agreement with literature values.   

Session A29: Focus Session: Colloids I

How confinement modifies the colloidal glass transition

We study concentrated colloidal suspensions, a model system which has a glass transition. These are suspensions of small solid particles in a liquid, and exhibit glassy behavior when the particle concentration is high; the particles are roughly analogous to individual molecules in a traditional glass. We view the motion of these colloidal particles in three dimensions by using an optical confocal microscope. This allows us to directly study the microscopic behavior responsible for the macroscopic viscosity divergence of glasses. In particular, we study how confinement changes the particle dynamics. We confine a colloidal suspension between two parallel walls, and find that in thin sample chambers the particle motion is greatly slowed. This suggests that confinement causes the onset of the glass transition to happen ``sooner,'' at particle concentrations which are not normally glassy.   

Periodic Stresses and Shear Thickening in an Attractive Colloidal Gel

We report on the observation of periodic stresses in a colloidal gel at rest and under minute shear deformation. Dilute suspensions of carbon black colloidal particles in hydrocarbon oil with an attractive Van der Waals interaction are found to shear thicken in two distinct regimes. The first, low shear rate regime is ascribed to network elongation and the high shear regime to hydrodynamic clustering, akin to that observed in concentrated hard sphere systems. Due to the attractive interaction between particles, the shear thickened state persists long after cessation of flow and in the high shear rate regime gives rise to high modulus, compacted networks. These gels display residual stresses and exhibit a peculiar time dependent aging in which the normal force exerted by the stationary gel as well as the shear modulus display low frequency long lived oscillations. Simple tensile deformation of the gel results in comparatively higher frequency periodic normal forces. We propose a simple mechanism to account for the observed data.   

Plastic restructuring in compressed colloidal glasses

We report the observation of localized plastic restructuring in compressed colloidal glasses. By placing a expanding bulk hydrogel in contact with the colloidal glass, we can drive the system above the glass transition volume fraction, $\phi=0.58 \to 0.64$. We measure the local strain tensor using three dimensional confocal microscopy and particle tracking techniques. The increase in volume fraction exhibits a smooth exponential increase. However, local irreversible transformations exhibit strong fluctuations that are correlated to the local free volume. We will elucidate the mechanisms for these localized relaxation events, and make comparisons to recent models of sheared amorphous solids.   

Ideal Glass Transitions, Barrier Hopping and Dynamic Heterogeniety in Suspensions of Nonspherical Colloids

The slow translational dynamics and nongaussian fluctuation effects of glassy isotropic fluids composed of nonspherical objects is studied based on a nonlinear stochastic Langevin equation of motion that includes activated barrier hopping. Suspensions of homonuclear diatomic and linear triatomic shaped colloids of variable bond length have been studied. The ideal glass transition boundary (crossover to activated dynamics) is predicted to be a nonmonotonic function of particle aspect ratio and surprisingly occurs at a nearly unique value of the dimensionless compressibility. The magnitude and volume fraction dependences of the entropic barrier, localization length and shear moduli for different aspect ratio systems collapse well onto master curves based on a reduced volume fraction variable that quantifies the distance from the ideal glass transition. Calculations for long polyatomic rods have also been performed. The ideal glass boundary decreases with aspect ratio slower than the nematic phase transition boundary. Solution of the nonlinear Langevin equation via Brownian trajectory simulation have also been performed. Results for the mean square displacement, decoupling of relaxation and diffusion, nongaussian parameter and other measures of dynamic heterogeneity have been determined for different colloidal shapes.   

Experimental Measurement of Freezing Kinetics in Two-Dimensional Colloidal Crystals

We study the freezing kinetics of two-dimensional colloidal crystals formed by a short-range attractive potential. We use aqueous suspensions of micron-sized latex spheres mixed with surfactant micelles, which create a depletion attraction among the spheres. The depletion attraction between the spheres and the coverslip enables us to create a two-dimensional system. Upon uniformly heating or cooling the sample, the micelles grow or shrink and the depletion attraction changes in magnitude. Optical microscopy is used to track the motions of thousands of colloidal spheres in the process of freezing or melting . By varying the density (area fractions of 17-34{\%}) and the amount of supercooling, we can measure the dynamics of nucleation and growth of crystallites. A two-stage nucleation process can be seen in samples with density of 30{\%} in which a meta-stable liquid droplet is first formed; then the crystallite is nucleated from within. At higher and lower densities the crystals nucleate in the typical fashion with large 6-fold orientational symmetry at small cluster size. We will present results on the evolution of the orientational order of crystallites and their degree of crystallinity as a function of both time and cluster size. We will also compare and contrast these density dependent freezing results to earlier work done on the melting process. This work is supported by the NSF-DMR 0605839.   

Particle dynamics near the re-entrant glass transition

Colloidal suspensions are a model system for studying the glass transition. At the volume fraction $\phi $g $\approx $ 0.58 a hard sphere colloidal glass is formed. The formation of a hard sphere glass is attributed to the caging effect, in which the particles form cages around each other that restrict their movement. Introducing an attractive depletion force between the particles causes the hard sphere glass to melt and the system becomes a liquid. Through further increase of the attractive force an attractive glass is formed. Our system is a suspension of nearly hard-sphere colloidal particles and nonadsorbing linear polymer which induces a depletion attraction between the particles. Using microscopy techniques, we study how the dynamics of the particles change as the attractive potential is increased and attractive glass is approached. In particular, we examine the mean square displacement and frequency of particle jumps over a range of attraction strengths.   

Translation-rotation coupling in dense colloidal suspensions

Single-particle tracking has been used to contrast translational and rotational diffusion in colloidal suspensions. Not enough is known from prior study about the rotation of colloids, owing perhaps to the paucity of suitable measurements techniques, but this is now remedied by using Modulated Optical Nanoparticles(MOONs), which are fabricated by capping one hemisphere with a thin layer of reflective metal. Density of the suspensions is varied and both translational and rotational mean squared displacement are quantified.   

Single liposome tracking in dense suspensions of stabilized liposomes

Methods developed to stabilize phospholipid vesicles against fusion, up to volume fraction around 80{\%}, enable one to perform single-particle tracking on these soft, flexible, hollow objects. Stabilization is accomplished by studding the outer leaflet with charged nm-sized particles. Image analysis of time trajectories, obtained using epifluorescence imaging, was performed at sub-pixel resolution. This talk will emphasize aspects of curiously heterogeneous dynamics and also quantification of ``cage'' size in this system. Taken together, this system of charged, polydisperse, flexible objects displays rich dynamics that contrasts acutely with known behavior for hard-sphere dense particle systems.   

Yield stress of stearically stabilized colloids

The bulk property, yield stress has been modeled by Larson in the past for spherical colloidal particles with dependence on volume fraction of solids particle diameter and interaction potential (sum of van der Waals potential and electrostatic potential. In our organic pigment dispersions polymer stabilized followed Herschel-Bulkley equation with yield stress which was non-linearly dependent on pigment surface area measured by BET. Stability of dispersions changed with time in terms of particle size and yield stress as well as on the type of deformation, shear applied to the dispersion. The results of yield stress are compared with models in terms of interaction potential, particle size and zeta potential..   

Janus Colloids Assemble into Cluster Shapes

We explore the assembly of two types of micron-sized, spherical Janus particles: those with opposite electric charge on both hemispheres (``bipolar'') and those hydrophobic on one hemisphere and hydrophilic on the other (``amphiphilic''). Bipolar particles form clusters, not strings, as the particle diameter exceeds the electrostatic screening length. The cluster shapes are analyzed by combined epifluorescence microscopy and Monte Carlo computer simulations with excellent agreement, indicating that the particles assemble in aqueous suspension to form equilibrated aggregates. The simulations show that charge asymmetry of individual bipolar particles is preserved in the clusters. The assembly of amphiphilic particles presents analogies to the self-assembly of molecular surfactants, forming monolayers at the air-water interface and micelles in the aqueous suspension. By tuning the salt concentration, different phases of micelle can be imaged in real space. Computer simulations confirm the geometries of these micelles and reveal possible formation mechanisms.   

Wetting layer dynamics in colloid polymer mixtures by evanescent wave dynamic light scattering

Evanescent wave obtained at the total internal reflection can be used as the incident beam of a dynamic light scattering experiment where its short penetration depth allow to selectively probe fluctuations close to a hard wall. Colloid concentration fluctuation in gas-liquid phase separated colloid-polymer mixtures obtained with PMMA hard spheres (R=120nm) and polystyrene polymer in index match cis/trans decalin were investigated in the vicinity of a vertical hard wall with in particular the dense colloidal layer wetting the hard wall in the top (gas) phase. There, the q-dependent collective dynamics reveal a liquid like behaviour similar to the one observed in the bottom phase dynamics, both marginally slower than the dynamics measured in the bottom (liquid) phase bulk and very different from the dilute like dynamics observed in the bulk top phase. Results are discussed in terms of hydrodynamic interactions.   

Gravitational collapse of depletion gels

We study how colloidal gels collapse under the presence of a gravitational stress. We do so macroscopically, monitoring the time dependence of the creaming or sedimentation front, and microscopically, using confocal microscopy. Our system consists of fluorescently labeled spheres that are index matched to the surrounding solvent. Temperature allows fine control of the density mismatch, further enabling fine tuning of the gravitational stress. Addition of non-adsorbing polymer induces an attraction whose range and strength can also be tuned. We will present results pertaining macroscopic studies for different particle volume fractions and interaction energies and preliminary microscopic results aiming to locally describe the structure collapse.   

Depletion Interaction: Effect of Depletant's Non-ideality

Depletion interaction is one of the central issues of colloidal stability; it arises between colloidal bodies suspended in a solution of non-adsorbing polymers, micelles, spheres, rods etc. Recently depletion of ideal non-ionic monodisperse polymers, monodisperse hard spheres and rods was extensively studied using various theoretical methods [1]. These cases enable a detailed theoretical analysis and serve as a model for other more complicated systems. However, in many experimental cases the depletants deviate from the requirements of the theories, for example, one has to deal with polydisperse, charged or (partly) adsorbing depletants. Another problem can arise when it is not possible to use the Derjaguin approximation to compute the depletion potential (e.g. the size of depletant is comparable with the size of colloids). All these effects can lead to the crucial deviations from the idealizing theories. We experimentally studied depletion interaction induced by non-ideal depletants between a charged colloidal sphere and a charged solid wall using Total Internal Reflection Microscopy (TIRM). Here we discuss the influence on the depletion potential due to the polymer size polydispersity (dextran), polymer's adsorption (polyethylene oxide (PEO)) and the colloid/ depletant's size ratio (fd-viruses). .1. Tuinier, R. et al., \textit{Adv. Colloid Interface Sci }\textbf{2003,} 103, 1.   

Direct observation of dynamical heterogeneity near the colloidal gel transition

We use confocal microscopy to probe the microscopic dynamics near the colloidal gel transition where the dynamics shows spatial heterogeneity. We are able to separate fast and slow particles independently from self part of van Hove density-density correlation function. The distinct part of van Hove correlation function shows clearly a signature of dynamical heterogeneity and the behavior is dominated by the fast particles. We further observe intermittent dynamics for these particles: the motion is not continuous. This provides the first microscopic picture of intermittent dynamics in colloidal gels.   

Session A30: Self-Assembly of Particles, Droplets, and Amphiphilic Molecules

Solution Phase Behavior of Gold Nanoparticles in Colloidal Solution

Gold nanoparticles in colloidal solution can aggregate to form gold nanocrystal superlattices. To explore and understand the solution phase behavior of nanoparticles, the gold nanoparticles ligated with dodecanthiol in a mixture of 4-tert-butyltoluene and butanone were studied by UV-vis spectroscopy, static light scattering and dynamic light scattering. The results showed that there is a reversible dissolution-aggregation process. The phase diagram was obtained by measuring the size of the nanoparticles with dynamic light scattering and the scattered light intensity. The UV-vis spectroscopy also proved the existence of a phase transition.   

Self Assembly of Colloidal Particles at Small N

We confine the dilute colloidal suspension inside emulsion droplets and study the structures of the aggregated clusters at small particle number ($N\approx10$) in order to understand the governing rules of equilibrium self-assembly. The aggregation process is controlled by the short-range weak depletion attraction between particles, and the structural and dynamic properties of self-assembled colloidal clusters are monitored via optical microscopy. We compare the experimental results with the theory and simulations, which probe how the number of local minima increases with number of particles. Our system may be a good model system for understanding generic features of glass and gel transitions.   

Self-Organization of Bouncing Oil Drops: Two-Dimensional Lattices and Spinning Clusters

Multiple oil drops bouncing on the surface of a vertically vibrating bath of the same oil exhibit self-organization behavior in two dimensions. S.~Proti\`ere et al. [J.~Phys.: Condens.\ Matter \textbf{17}, S3529 (2005)] recently reported that such drops arrange themselves in triangular lattices, with a lattice spacing dependent on the driving frequency of the bath. We describe here the morphology and dynamic behavior of stable assemblies of large bouncing oil drops, for which we find that not only the spacing but the lattice structure itself changes with frequency, with variants of both square and hexagonal structures being observed. Large ``rafts'' of drops form soft triangular lattices with faceted boundaries. Small clusters of drops are unstable to coherent, collective spinning under certain driving conditions, manifesting spontaneous rotational symmetry breaking.   

Self-assembly of helical tubules using a single-tailed surfactant.

Hollow micro or nanotubules are an unusual type of self-assembled structure that can be formed in aqueous solution. Such structures could be useful in a variety of applications such as in controlled drug delivery and in electroactive composites. However, these structures are typically formed only by some unusual lipids (i.e., two-tailed amphiphiles) or certain peptides. Here we present a very simple and economical process to make stable tubules by using a single-tailed diacetylenic surfactant in conjunction with an alcohol. The formation of tubules as a function of solution composition and temperature are systematically investigated in this study. The tubules are visualized by optical microscopy, while their detailed structure is seen under TEM. We find that the tubules have helical markings, which is remarkable considering that the precursor molecules are achiral. Our results provide further evidence that molecular chirality is not essential to forming tubules; presumably, tubules can form from achiral molecules by a chiral symmetry-breaking process.   

Aggregation Properties and Liquid Crystal Phase of a Dye Based on Naphthalenetetracarboxylic Acid

R003 is a dye produced for thin film optical components by Optiva, Inc.$^1$ made from the sulfonation of the dibenzimidazole derivative of naphthalenetetracarboxylic acid. Its molecular structure is very different from the aggregating food dye previously investigated in our laboratory$^2$ and R003 forms a liquid crystal phase at significantly lower concentrations. We have performed polarizing microscopy, absorption spectroscopy, and x-ray diffraction experiments in order to determine the phase diagram and aggregate structure. In addition, we have included both translational and orientational entropy in the theoretical analysis of the aggregation process, and have used a more realistic lineshape in analyzing the absorption data. Our results indicate that the ``bond energy'' for molecules in an aggregate is even larger than for the previously studied dye and that the aggregate structure has a cross-sectional area equal to two or three molecular areas rather than one.\\ $^1$Lazarev, P., N. Ovchinnikova, M. Paukshto, SID Int. Symp. Digest of Tech. Papers, San Jose, California, June XXXII, 571 (2001).\\ $^2$V. R. Horowitz, L. A. Janowitz, A. L. Modic, P. A. Heiney, and P. J. Collings, Phys. Rev. E 72, 041710 (2005).   

Effects of Multivalent Salts and Polyamines on Lyotropic Chromonic Liquid Crystals

Multivalent salts and polyamines cause significant structural and phase changes in lyotropic chromonic liquid crystals (LCLCs) such as water solutions of sunset yellow (also known as Edicol), disodium chromoglycate, and blue 27. Using polarizing microscopy, rheoscopy, retardance mapping, and preliminary small-angle neutron scattering data, we demonstrate that multivalent additives cause significant shifts of phase boundaries in the temperature-concentration coordinates, formation of aggregate bundles, as well as induce phase separation of a homogeneous nematic phase into hexagonal columnar and isotropic phases. The multivalent phenomena are discussed within the framework of the strong coupling model of polyelectrolyte interactions and hydration effects.   

Nanoparticle organization in surfactant mesophases

Dispersing colloidal particles in surfactant liquid crystalline phases leads to the formation of materials with ordered microstructures. The influence of the liquid crystalline medium leads to organization of the colloidal particles, and the driving force for self-assembly scales with the size of the colloids. Micron-sized colloids organize into linear arrays in liquid crystals, while nanoparticles can be confined in surfactant liquid crystal structures. We investigate the dispersion of silica nanoparticles with sizes of 7, 11 and 23nm in hexagonal mesophases of aqueous solutions of nonionic surfactants. The surfactant mesophase is preserved after dispersion of these particles, and the particles organize to form lamellar structures. We will discuss the implications of our results for the synthesis of novel materials.   

Self-assembly of ionic detergents: a simulation study of sodium dodecyl sulfate micellization

Detergents, amphiphilic molecules used to separate and dissolve molecular aggregates and also as cleaning agents, consist of a polar head group and one or more hydrophobic tails. Above a critical concentration, they self-aggregate in an aqueous solution to form micelles. While industrially extremely important, surprisingly little is known about molecular details of the self-assembly of detergents. Here we extend our previous work of modeling and model construction of charged soft-matter systems [1] by a description of an anionic detergent, sodium dodecyl sulfate (SDS) [2]. We present the results of large-scale Molecular Dynamics simulations of the formation dynamics and structure of SDS micelles. We demonstrate that temperature affects micelle morphologies through the packing and discuss the effect of SDS concentration on the micellization. \newline [1] M. Patra et al., Biophys. J. 84, 3636 (2003); A. A. Gurtovenko et al., J. Phys. Chem. B 109, 21126 (2005); A. A. Gurtovenko et al., Biophys. J. 86, 3461 (2004). \newline [2] The SDS parameters are available at www.softsimu.org.   

Evidence for condensed lipid/cholesterol complexes in lipid membranes.

Certain binary mixtures of phospholipids and cholesterol exhibit phase diagrams with two immiscibility regions with a sharp cusp in between. The cusp has been suggested to represent the stoichiometry of phospholipid/cholesterol complexes, and cholesterol is thought to exist in two states: a bound, low activity state, and an unbound, high activity state. To better understand the interaction between phospholipids and cholesterol, we have studied the effect of a possible displacing agent, hexadecanol, on the behavior of the binary mixture. Our cholesterol desorption assays indicate that hexadecanol can displace cholesterol from its association with phospholipids, thereby activating it. Phospholipid/cholesterol/hexadecanol systems in which a fraction of cholesterol is replaced by the alcohol have phase diagrams that mimic those of binary systems with the same apparent molar stoichiometry. X-ray data show a broad Bragg peak in these binary systems, indicating that order in these complexes extend over only several molecular dimensions.   

Concentration-curvature coupling in endocytosis,

The wrapping of symmetric particles by lipid bilayers depends on the membrane bending rigidity and the adhesion between the membrane and the particle. We consider the additional effects of a membrane composed of a binary lipid mixture. The different lipid components induce different spontaneous curvatures, which mediates the wrapping process through an induced phase separation near the particle-membrane contact region. We find that mixtures always enhance the wrapping. Asymptotic results are also found for the membrane shape in the limit of strong and weak spontaneous curvature-lipid concentration coupling.   

Entropy-driven ordering in soft matter

In this talk, we discuss the entropic effects on the structural organization on the basis of the following three examples of our recent works: 1) phase behavior in thin film of confined colloid-polymer mixtures, 2) the organization in inclusion-membrane complexes, and 3) lateral organization in supported membrane on a geometrically patterned substrate. The result will be helpful for understanding the physical mechanism of structural organization and controlling novel structures of soft materials under the guidence of entropy driven ordering.   

Soft quasicrystals - Why are they stable?

In the last two years we have witnessed the exciting experimental discovery of soft matter with nontrivial quasiperiodic long-range order---a new form of matter termed a \emph{soft quasicrystal}. Two groups have independently discovered such order in soft matter: The first in a system of dendrimer liquid crystals [1]; and the second in a system of ABC star-shaped polymers [2]. These newly discovered soft quasicrystals not only provide exciting platforms for the fundamental study of both quasicrystals and of soft matter, but also hold the promise for new applications based on self-assembled nanomaterials with unique physical properties that take advantage of the quasiperiodicity, such as complete and isotropic photonic band-gap materials [3]. Here we provide a concise review of the emerging field of soft quasicrystals [4], and invoke an old theory [5] suggesting that the existence of two natural length-scales, along with 3-body interactions, may constitute the underlying source of their stability.\par\noindent [1] Zeng \emph{et al.}, Nature {\bfseries 428} (2004) 157.\par\noindent [2] Takano \emph{et al.}, J.\ Polym.\ Sci.\ Polym.\ Phys.{\bfseries 43} (2005) 2427.\par\noindent [3] Zoorob \emph{et al.}, Nature {\bfseries 404} (2000) 740.\par\noindent [4] Lifshitz \& Diamant, preprint (cond-mat/0611115).\par\noindent [5] Lifshitz \& Petrich, Phys.\ Rev.\ Lett.\ {\bfseries 79} (1997) 1261.   

Directing self-assembly by tailoring pair potentials of soft shoulder systems

Monodisperse spheres interacting via `hard core/soft shoulder' (HCSS) pair potentials (e.g., hard spheres with an additional repulsive step interaction) exhibit extremely rich phase behavior, including a diverse array of two- and three-dimensional liquid crystal phases and a wide variety of complex crystal structures [M. A. Glaser et al., cond-mat/0609570], including relatively open crystal structures such as the 2D honeycomb lattice [E. A. Jagla, J. Chem. Phys. 110, 451 (1999)]. The complex phase behavior of this class of systems derives from competition between an underlying `soft shoulder' clustering instability [W. Klein et al., Physica A 205, 738 (1994)] and excluded volume constraints. We show that it is possible to derive soft shoulder potentials to promote self-assembly of specific target structures using only geometrical information. We have applied this approach to the self-assembly of a stable 3D diamond lattice in systems of particles with isotropic pair interactions, demonstrating that anisotropic, directional bonding is not a necessary requirement for formation of the diamond lattice. This approach, which exploits soft shoulder clustering behavior, is a powerful tool for the directed design of a variety of unusual and complex self-assembled systems. Work supported by NSF MRSEC Grant DMR-0213918 and GAANN Fellowship P200A030179.   

Session A31: Cold Fusion I

Cold Fusion -- An 18 Year Retrospective Short Description

18 years after the APS voted to refute the reality of Cold Fusion in Baltimore, it is appropriate to consider what has changed. Who was right? We will review the current state of knowledge from the perspective of what we know now compared to what we knew then\footnote{Hagelstein, M.C.H. McKubre, et al, Proc ICCF11, pp 23-59 (2006). http://www.lenrcanr.org/acrobat/Hagelsteinnewphysica}. Discussion will be made of various avenues of research that we have followed from the original Fleischmann Pons proposal: some failed, some unresolved and some successful.   

Production of High Energy Particles Using the Pd/D Co-Deposition Process

Using the Pd/D co-deposition technique\footnote{S. Szpak et al, J. Electroanal. Chem., v 580, 284(2005).}, we have obtained evidence (i.e., heat generation, hot spots, mini-explosions, radiation, and tritium production) suggestive that nuclear reactions can and do occur within the Pd lattice. It was found that these reactions are enhanced in the presence of either an external electric or magnetic field. SEM analysis of the cathodes shows morphological features suggestive of localized melting of the palladium. EDX analysis of these features show the presence of new elements which result form transmutation\footnote{S. Szpak et al, Naturwissenschaften, v 92, 394-397(2005).}. To verify that these new elements are indeed nuclear in origin, experiments have been conducted using CR-39 detectors, a commonly used etch-track detector for recording the emission of high energy particles such as alphas and protons. When the co-deposition reaction was conducted in either an external electric or magnetic field, numerous tracks due to high energy particles were clearly observed on the CR-39 detector in those areas where the cathode is in direct contact with the detector.   

Accuracy of Cold Fusion Calorimetry

The cold fusion controversy centers on the precision and accuracy of the calorimetric systems used to measure excess enthalpy generation. For open, isoperibolic calorimetric systems, there is no true steady state during D2O+LiOD electrolysis. Exact calorimetric measurements, therefore, require modeling by a differential equation that accounts for all heat flow pathways into and out of the calorimetric systems. The improper use and misunderstanding of this differential equation is a major source of confusion concerning cold fusion calorimetric measurements. The use of a platinum cathode as a control showed that excess power due to the controversial recombination effect was measurable at 1.1 plus or minus 0.1 mW. Theoretical calculations using Henry's Law and Fick's Law of Diffusion yield approximately 1 mW for this effect due to oxygen reduction at the cathode. Palladium-boron alloy materials prepared at the Naval Research Laboratory have shown a remarkable ability to produce excess power effects in the range of 100 to 400 mW. The excess power increased to over 9000 mW during the final boil-off phase in one experiment.   

Resonant Interaction, Approximate Symmetry, and Electromagnetic Interaction (EMI) in Low Energy Nuclear Reactions (LENR)

Only recently (talk by P.A. Mosier-Boss et al, in this session) has it become possible to trigger high energy particle emission and Excess Heat, on demand, in LENR involving PdD. Also, most nuclear physicists are bothered by the fact that the dominant reaction appears to be related to the least common deuteron(d) fusion reaction,d+d $\rightarrow \alpha$+$\gamma$. A clear consensus about the underlying effect has also been illusive. One reason for this involves confusion about the approximate (SU2) symmetry: The fact that all d-d fusion reactions conserve isospin has been widely assumed to mean the dynamics is driven by the strong force interaction (SFI), NOT EMI. Thus, most nuclear physicists assume: 1. EMI is static; 2. Dominant reactions have smallest changes in incident kinetic energy (T); and (because of 2), d+d $\rightarrow \alpha$+$\gamma$ is suppressed. But this assumes a stronger form of SU2 symmetry than is present; d+d $\rightarrow \alpha$+$\gamma$ reactions are suppressed not because of large changes in T but because the interaction potential involves EMI, is dynamic (not static), the SFI is static, and because the two incident deuterons must have approximate Bose Exchange symmetry and vanishing spin. A generalization of this idea involves a resonant form of reaction, similar to the de-excitation of an atom. These and related (broken gauge) symmetry EMI effects on LENR are discussed.   

1.6 MHz Sonofusion Model and Measurement

Years of data collected by First Gate, involving various sonofusion systems, gains some support from recent extrapolations of hot fusion research. Consider the 10$^4$ k/sec of the high density low energy jet plasma of deuterons that originates from the collapse of the transient cavitation bubble (TCB), in D$_2$O that implants a target foil. And compare it to the jet plasma of Tokamak type plasmas with all their stability problems. Also consider the relevance of the imploding wire technology where the magnetohydrodynamic pressures exceed the crystal forces that bind atoms in wire conductors and inertial confinement fusion (ICF). Applying this developed technology to the TCB jet plasmas of sonofusion makes the transition between hot and ``cold'' fusion more attractive. Our measurements show there is no long range radiation (gammas or neutrons) and $^4$He is the fusion product. These problems are addressed via coherence in the implanted high density transient deuteron Bosons (and proton Fermions) clusters in the heat producing target.   

Selective Resonant Tunneling through Coulomb Barrier by Confined Particles in Lattice

In 1993, Kasagi discovered the anomalous yield of 3 deuteron fusion reaction while searching the branching ratio of d+d fusion at low energy. In 1995-1997, Takahashi carefully studied this anomalous yield of 3 deuteron fusion reaction again. Distinct from the early Kasagi's study, Takahashi studied another 3 deuteron fusion channel: i.e. d+d+d$\rightarrow$ t (4.75MeV) + 3He (4.75MeV). Because only 2 nuclear products were emitted from this reaction channel, triton and helium-3 were clearly identified by their energy. From this information,Takahashi estimated the life-time of the 2 deuteron (2-d) resonance. It was in the order of 10$^5$ seconds. In this paper, selective resonant tunneling model was applied to calculate the life-time of this 2-d resonance inside the deuterated titanium. A square-well is assumed for the nuclear well, and a Coulomb repulsive potential is assumed for the long range interaction between two deuterons. The Coulomb potential is down shifted to include the electron- metal-screening. The lattice confined deuteron may bounce back and forth inside the lattice well. This may be called as the resonance which will greatly enhance the fusion reaction rate inside the nuclear well. An imaginary part of nuclear potential is introduced to describe this fusion rate.The calculated 2-d resonance lifetime, 10$^5$ seconds, agrees with Kasagi's and Takahashi's experimental data.   

Low Energy Nuclear Reactions: 2007 Update

This paper presents an overview of low energy nuclear reactions, a subset of the field of condensed matter nuclear science. Condensed matter nuclear science studies nuclear effects in and/or on condensed matter, including low energy nuclear reactions, an entirely new branch of science that gained widespread attention and notoriety beginning in 1989 with the announcement of a previously unrecognized source of energy by Martin Fleischmann and Stanley Pons that came to be known as cold fusion. Two branches of LENR are recognized. The first includes a set of reactions like those observed by Fleischmann and Pons that use palladium and deuterium and yield excess heat and helium-4. Numerous mechanisms have been proposed to explain these reactions, however there is no consensus for, or general acceptance of, any of the theories. The claim of fusion is still considered speculative and, as such, is not an ideal term for this work. The other branch is a wide assortment of nuclear reactions that may occur with either hydrogen or deuterium. Anomalous nuclear transmutations are reported that involve light as well as heavy elements. The significant questions that face this field of research are: 1) Are LENRs a genuine nuclear reaction? 2) If so, is there a release of excess energy? 3) If there is, is the energy release cost-effective?   

Physics in a Many-Centered Environment

Physics in a many-center environment was born as the electron physics of metals. Electrons moving from the electrolyte of a battery to anode metal become quasi-particles with a many-centers geometry\footnote{ T.A. Chubb, Infinite Energy, Issue 70, in press (2006)}$^,$\footnote{ T.A. Chubb, ``Many-Centers Nuclei,'' submitted to Infinite Energy} The Ion Band State Theory of cold fusion assumes that a fraction of the deuterons in PdD$_x$ reconfigure to a many-centers geometry\footnote{T.A. Chubb and S.R. Chubb, Fusion Technol.,20, 93 (1991)}. Many-center geometry seems to apply to deuteron populations in nano-metal crystals as studied by Arata and Zhang, to Bloch-sensitive nuclei created in Iwamura's permeation studies, to the metastable nuclei forming alpha shower flakes as discovered by Oriani and Fisher and reproducibly produced by P. Mosier-Boss.   

Heat Produced During Electrolysis with a Tubular Pd Cathode

An explosion occurred during electrolysis of heavy water with a tubular Pd cathode\footnote{ X.-W. Zhang, W.-S. Zhang, D.-L. Wang et al, Proc. ICCF3, Nagoya, Japan, Oct 21 to 25, 1992, p. 381.} A Pd tube from the same batch was used as the cathode during electrolysis in a Seebeck envelope calorimeter which is capable of accurate heat measurements. Data was obtained first from a three cm length of the tube on one end, and then from a three cm length on the opposite end. There were no explosions, but both ends of the tube produced continuous excess thermal power (356 mW +/- 11 mW maximum). In addition there were 39 heat bursts (1.1 W maximum) from the first end during 201 hours of electrolysis and 58 heat bursts (1 W maximum) during 443 hours of electrolysis from the opposite end of the tube. The period of the heat bursts ranged from a few minutes to 3.3 hours. \\ \\ Data on the topography and microchemical composition of the tube surface before and after electrolysis will also be presented.   

Session A32: Focus Session: Rotating Quantum Gases

Rotation of fermions in a two dimensional lattice with a harmonic trap

Rotation of fermions in a lattice is studied using a Hubbard model. It is found that the fermions are still contained in the trap even when the rotation frequency is larger than the trapping frequency. This is very different from the behavior in continuum. Bragg scattering and coupling between angular and radial motion are believed to make this stability possible. In this regime, density depletion at the center of the trap can be developed for spin polarized fermions.   

Using custom potentials to access quantum Hall states in rotating Bose gases

The exact ground states of zero-temperature rotating Bose gases confined in quasi-two-dimensional harmonic traps are studied numerically, for small numbers of alkali atoms. As the rotation frequency increases, the interacting Bose gas undergoes a series of transitions from one quantum Hall state to another. We have investigated the possibility of facilitating access to specific quantum Hall states through the addition of customized potentials to the existing trapping potential. For the right choice of potential, we show that creation of predetermined quantum Hall states in rotating Bose gases should be possible using current experimental setups. (Research supported by NSERC, iCORE and CFI)   

Quantized vortex states of strongly interacting bosons in a rotating optical lattice

The analogy between ultracold atoms in optical lattices and electrons in crystal lattices is a manifestly rich one. If the optical lattice is rotating rapidly, many of the features associated with electrons in strong magnetic fields emerge. Even high correlated effects and quantum states like those underlying the fractional quantum Hall effect can potentially be realized. We examine small square two-dimensional systems with low filling via exact diagonalization of a modified Bose-Hubbard Hamiltonian. In this talk I will present some results showing the effects of the quantization of circulation, the appearance of vortices, and some of the novel features of quantum phase transitions in these systems.   

Quantum Hall physics in rotating Bose-Einstein condensates

A few years ago it was realized theoretically that there is a close analogy between the physics of rapidly rotating atomic Bose condensates (BEC) and the quantum Hall effect (i.e. a two-dimensional electron gas in a strong magnetic field). Due to an extremely rapid development in experimental techniques over the past few years, experiments on BEC are now very close to reaching the quantum Hall regime. In this talk I will review the theoretical connection between these two seemingly very different physical systems, and show how intuition and techniques from quantum Hall physics can be applied to study the properties of rotating Bose condensates.   

Vortices in two-component weakly interacting Bose-Einstein condensates

Weakly interacting Bose-Einstein condensates that are set rotating, are studied by numerical diagonalization of the many-body Hamiltonian. In particular, we investigate the structure of the lowest-energy states as a function of angular momentum, when pseudospin is introduced. Coreless vortices and vortex lattices in the exact soutions are compared to the results earlier obtained within the Goss-Pitaevskii mean field approach (see for example, Kasamatsu, Tsubota and Ueda, Phys Rev Lett 93, 250406 (2004) and Phys Rev A 91, 150406 (2005)).   

Persistent flow in a Bose-Einstein condensate

We will describe experiments on the study of quantized ~flow of Bose-condensed atoms in a multiply-connected trap. This torus-shaped trap is formed by the combination of an elliptically shaped, magnetic trap with a blue detuned laser beam in the middle to exclude atoms from the center of the magnetic trap. The rotation was initiated by transferring the orbital angular momentum from Laguerre-Gaussian photons to the atoms. We have observed that the rotational flow of atoms persists for several seconds, even when the condensate fraction is less than 10{\%}. We have also observed flow with high angular momentum and its splitting into singly charged vortices when the trap in no longer multiply-connected.   

Vortex-Lattice Phases in the Strongly-Interacting Limit of the Bose-Hubbard Model

We observe a structural phase transition in the vortex lattice described by the rotating Bose-Hubbard model as the system approaches the insulating phase. A weak optical lattice potential pins vortices to the potential maxima (S. Tung, et. al. arXiv:cond-mat/0607697). However, using Gutzwiller mean-field theory in the strongly-interacting limit of the rotating Bose-Hubbard model, we find an interaction driven phase transition from the potential maximum centered vortex lattice to a potential minimum centered configuration. In addition, even closer to the insulating phase, our results suggest a recurrence of the maximum-centered phase.   

Lifshitz-like transition and enhancement of correlations in a rotating bosonic ring lattice.

We study the effects of rotation on one-dimensional ultra-cold bosons confined to a ring lattice. For commensurate systems, at a critical value of the rotation frequency, an infinitesimal interatomic interaction energy opens a gap in the excitation spectrum, fragments the ground state into a macroscopic superposition of two states with different circulation and generates a sudden change in the topology of the momentum distribution. These features are reminiscent of the topological changes in the Fermi surface that occurs in the Lifshitz transition in fermionic systems. The entangled nature of the ground state induces a strong enhancement of quantum correlations and decreases the threshold for the Mott insulator transition. In contrast to the commensurate case, the incommensurate lattice is rather insensitive to rotation. Our studies demonstrate the utility of noise correlations as a tool for identifying new physics in strongly correlated systems.   

Vortices of Lattice Bosons Acquire Spin and Fermi Statistics

Lattice bosons a respond differently to a magnetic field, or a rotation, than continuum bosons, e.g. their Hall conductivity is not a linear function of their density. Such effects are mostly pronounced for hard-core bosons at half filling. For a periodic lattice on a torus threaded by fluxes, we can explicitly construct a conserved SU(2) `vortex spin' algebra. For odd total vorticity, even-fold spectral degeneracies are discovered on every lattice site. In particular, {\em the single vortex has spin half}. The vortex effective mass and spin-orbit coupling are extracted by diagonalizing the Hamiltonian on a 4x4 lattice. For two vortices, numerical `vortex-spin' correlations and orbital symmetries are consistent with Fermi and not Bose statistics. We discuss implications of the our results on the `vortex metal' phase at large magnetic fields.   

Spin Hall effects for cold atoms in a light induced gauge potential

We propose an experimental scheme to observe spin Hall effects with cold atoms in a light induced gauge potential. Under an appropriate configuration, the cold atoms moving in a spatially varying laser field experience an effective spin-dependent gauge potential. Through numerical simulation, we demonstrate that such a gauge field leads to observable spin Hall currents under realistic conditions. We also discuss the quantum spin Hall state in an optical lattice.   

Rapidly rotating strongly-correlated few bosons

A small number, $N \leq 11$, of bosons in a rapidly rotating harmonic trap, interacting via a contact potential or a Coulomb repulsion, is studied via an exact diagonalization in the lowest Landau level. For both low and high fractional fillings, the bosons localize and form rotating boson molecules (RBMs) consisting of concentric polygonal rings. As a function of the rotational frequency and regardless of the type of repulsive interaction, the ground-state angular momenta grow in specific steps that coincide with the number of localized bosons on each concentric ring. Comparison of the conditional probability distributions (CPDs) for both interactions suggests that the degree of crystalline correlations appears to depend more on the fractional filling $\nu$ than on the range of the interaction. The RBMs behave as nonrigid rotors, i.e., the concentric rings rotate independently of each other. At filling fractions $\nu < 1/2$, we observe well developed crystallinity in the CPDs (two-point correlation functions). For larger filling fractions $\nu > 1/2$, observation of similar molecular patterns requires consideration of even higher-order correlation functions.   

Symmetry breaking and symmetry restoration for bosonic gases in rotating traps: Rotating boson molecules and Gross-Pitaevskii vortex structures.

We recently introduced a new variational wave function for strongly repelling bosons in two-dimensional rotating traps.\footnote{Phys. Rev. Lett. {\bf 97}, 090401 (2006); {\bf 93}, 230405 (2004)} The approach consists of constructing a single permanent out of displaced Gaussian orbitals that break the rotational symmetry and of subsequent symmetry restoration via projection techniques, thus taking into account correlations beyond the mean field. In our approach, the bosons are localized and form rotating boson molecules (RBMs). The projected wave functions of the RBMs do not violate the circular symmetry; nevertheless, they exhibit crystalline patterns in their intrinsic frame of reference. Gross-Pitaevskii (GP) vortex solutions are also known to break the circular symmetry. Here, we apply projection techniques to restore the broken-symmetry GP solutions. We find that the spectral decomposition of the GP vortex solutions are drastically different from that of the RBMs. The RBM spectra, however, are in agreement with exact diagonalization results in the lowest Landau level.   

Statistics of vortex trapping in cyclically coupled Bose-Josephson junctions

We investigate the problem of vortex trapping in cyclically coupled Bose-Josephson junctions. Starting with $N$ independent BECs we allow the system to reach a stable circulation by adding a dissipative term in our semi-classical equations of motions. We then ask, ${\it inter \, alia}$ the question: ``Starting with an initial normal distribution of total phases with variance $ \sim \sqrt{N} $ and allowing for phase slips, what is the probability to trap a stable vortex with winding number $2 \pi m$''? We find that the final distribution of winding numbers is narrower than the initial distribution of total phases, indicating an increased probability for no-vortex configurations. The role of dissipation has been studied in determining the final probability distibution. It is also possible to get a non-zero circulation starting with zero total phase around the loop. The final width of the distribution scales as $ \sim d \times N^{\alpha } $, where $ \alpha = 0.47 $ and $ d<1 $ (indicating a shrinking of the final distribution), the actual value of $ d $ depending on the strength of dissipation.   

Session A33: Focus Session: Quantum-Limited Measurements

Quantum-Limited and Ultra-Precision Measurements

I will provide a brief overview of the current state of the field of experimental quantum-limited measurements. In particular I will focus on the role of entanglement in metrology and quantum parameter estimation for achieving fundamental uncertainty limits established by quantum mechanics. In addition to summarizing the state of the art as this pertains to experimental implementations, I will conclude by discussing a current proposal to improve existing quantum metrological techniques by exploiting multi-body quantum interactions.   

Assessing the Quality of Quantum Sensors

A general sensor can be modeled in the following way: a well-characterized physical system is prepared in some initial state, the system then interacts with a classical field through a well-understood mechanism, and then a measurement is made on the original system. From this procedure it is possible to infer the characteristics of the classical field. A number of proposals have been made to develop \textit{quantum sensors}, whose physical systems (which are prepared, interact with the classical field, and are then measured) are quantum mechanical in nature. In this talk I introduce this general description of quantum sensors and demonstrate how the unitary (interacting) dynamics and probabilistic measurements afforded by quantum mechanics can be used to infer the value of a classical field using a Bayesian statistical analysis. I also discuss the use of the mathematical measure of mutual information to compare different sensors.   

Using a qubit to measure photon number statistics of a driven, thermal oscillator

We demonstrate theoretically how photon number statistics of a driven, damped oscillator at finite temperature can be extracted by measuring the dephasing spectrum of a two-level system dispersively coupled to the oscillator; previous results only dealt with the purely thermal or zero-temperature driven cases [1][2]. We also consider the fidelity of this scheme-- to what extent does the measurement reflect the initial number statistics of the mode? Finally, we make a connection to the theory of full counting statistics in mesoscopic physics. Our results have relevance both to experiments in circuit cavity QED, as well as with quantum nano-electromechanical systems. \newline \newline [1] M.I. Dykman and M.A. Krivoglaz, Sov. Phys. Solid State 29, 210, (1987). \newline [2] J. Gambetta et al, Phys. Rev. A 74, 042318 (2006).   

Evidence of Dispersive Coupling between a Nanomechanical Resonator and a Cooper-Pair Box

Many proposals have been put forth to prepare and observe quantum nano-electromechanical systems (quantum NEMS or QEMS) via coupling to a Cooper-pair box (CPB). A natural first step in the realization of these proposals is to study the dispersive interaction between a NEMS and CPB. In the dispersive limit, the coupling between the NEMS and CPB is a second-order effect that should result in a CPB-state-dependent renormalization of the nanoresonator's frequency. For typical parameters, the relative magnitude of the frequency shift should be a few ppm, resolvable with current NEMS detection capabilities. In fact, using a capacitive nanomechanical transduction scheme, we have been able to observe a red-shift of approximately 150 Hz in the frequency of a 61 MHz silicon nitride nanoresonator while tuning the ground state of a nearby CPB through a charge-degeneracy point. In my talk, I will present our most recent data and discuss the implications for the development of QEMS.   

Laser cooling of a microcantilever using a medium-finesse optical cavity.

We report on a Fabry-Perot optical cavity formed between a 30 $\mu $m-wide metal-coated microcantilever and a commercial concave dielectric mirror. A finesse of 55 is achieved with the mirrors 75 mm apart in a near-hemispherical geometry. This finesse was limited by loss in the metal coating of the cantilever; diffraction loss from the microcantilever was negligible. The cantilever was passively laser cooled from 300 K to 50 K when the cavity was detuned.   

Noise Temperature and Thermodynamic Temperature of a Sample-on-Cantilever System Below 1K

Micromechanical systems such as cantilevers are frequently used to detect ultra-small forces and displacements. In a sample-on-cantilever geometry, operation at low temperature requires cooling the thermodynamic temperature of the sample T$_{S}$ and the noise temperature of the cantilever T$_{N}$. This can be challenging because for high-Q cantilevers, these temperatures are only weakly coupled. In addition, for insulating cantilevers monitored by a reflected laser beam, these temperatures may also be weakly coupled to the refrigerator temperature. We have made quantitative measurements of T$_{N}$ and T$_{S}$ for a sample-on-cantilever set-up as a function of incident laser power and refrigerator temperature below 1 Kelvin. We infer T$_{S}$ from measurements of the critical magnetic field of a superconducting sample mounted on the cantilever. T$_{N}$ is inferred from the cantilever's Brownian motion. We find that for this system both T$_{S}$ and T$_{N}$ remain quite close to the refrigerator temperature.   

Intrinsic Noise Properties of Atomic Point Contact Displacement Detectors

By coupling an atomic point contact (APC) to a nanomechanical beam, we measure the noise properties of an APC, an object which is the basis of scanning tunneling microscopy and is used to create electrical contact to single molecules. Using a microwave technique, we detect the resonant motion of the nanomechanical beam at frequencies up to 200 MHz. This measurement is sensitive enough to observe the random thermal motion of the nanomechanical beam at 250 mK. We use this thermal motion to evaluate the noise properties of the APC, demonstrating a displacement imprecision limited by the shot-noise in the number of electrons that tunnel across the APC and observing the force due to measurement backaction. Together, the imprecision and backaction yield a total uncertainty in the beam's displacement that is 42 times the standard quantum limit. In addition, we detect the beam's response to piezoelectric, electric, and magnetic forces, and use feedback to ``squash'' the shot-noise.   

Heisenberg limited Sagnac interferometry

When two electromagnetic waves counter-propagate along a circular path in rotation they experience different travel times to complete the path. This induces a phase shift between the two counter-propagating waves proportional to the angular velocity of the rotation. It was studied and used in optics only with lasers until recently when single photons were used. However, it turns out that the results of interference are no different than with classical sources. Thus a natural question would be --what is the nature of interference if we replace the single photon source by entangled photon pair source. This is what we examine in detail. We find that the sensitivity of Sagnac interferometer could be considerably improved by using entangled photons produced by a down-converter. We present analytic results for the sensitivity of the interferometer. In particular, two-photon and four-photon entanglements increase the sensitivity by a factor of 2 and 4 respectively.   

Generalized Limits for Single-Parameter Quantum Estimation

We develop generalized bounds for quantum single-parameter estimation problems for which the coupling to the parameter is described by intrinsic multi-system interactions. For a Hamiltonian with $k$-system parameter-sensitive terms, the quantum limit scales as $1/N^k$ where $N$ is the number of systems. These quantum limits remain valid when the Hamiltonian is augmented by any parameter-independent interaction among the systems and when adaptive measurements via parameter-independent coupling to ancillas are allowed.   

Quantum projection noise limited spectroscopy with ions in a Penning-Malmberg trap. ---Progress toward spin squeezed states.

We describe plans and summarize initial progress towards making spin squeezed states with up to $\sim$100 $^{9}$Be$^{+}$ ions in a Penning-Malmberg trap. We use the ground-state electron spin-flip transition, which in the 4.5 T magnetic field of the trap has a transition frequency of 124 GHz, as the ion qubit. With a 30 mW Gunn diode oscillator we have observed Rabi flopping rates as high as $\sim$7 kHz. We will summarize experimental progress on realizing projection noise limited spectroscopy on this transition, which is a prerequisite for demonstrating spin squeezing. For entangling the ions we plan to use a generalization of the few ion qubit phase gate developed at NIST \footnote{D. Leibfried, et al., Nature {\bf 438}, 639 (2005).} to generate an $\exp{(i\chi {J_{z}}^2 t)}$ interaction between all of the ion qubits. This interaction can be implemented on a single plane of ions \footnote{T.B. Mitchell, et al., Science {\bf 282}, 1290 (1998).} with a motional sideband, stimulated Raman transition.   

Session A38: Focus Session: Acoustic and Optical Instrumentation

Vibration Potential Imaging: Results for the Forward Problem

A colloid is a suspension of charged particles in a liquid, with each particle surrounded by a counter charge. When ultrasound propagates through a colloid where the particles have either a higher or lower density than that of the surrounding fluid, the amplitude and phase of the particle motion, owing to the difference in inertia between the particle and the volume of fluid it displaces, differs from that of the fluid so that the particle and the fluid execute different motions. Since the counter charge is carried by the fluid, the oscillatory motion of the fluid relative to the particle distorts the normally spherical counter charge distribution in the fluid creating an oscillating dipole at the site of each particle. The addition of the polarization created at the sites of the particles over a macroscopic length results in a voltage that can be recorded by a pair of electrodes placed in the solution. The ultrasonic vibration potential can be used as a method of imaging where contrast in the image is governed by the presence of colloidal or ionic regions within the body under consideration. We describe the use of a frequency domain method of imaging where the current in a pair of electrodes is recorded as a function of the frequency of a plane ultrasonic wave. The method is applied to imaging a variety of objects including a thin layer, a thick layer, pairs of layers, layers with differing colloidal concentrations and spheres. The experimental results show agreement with the theory of vibration potential imaging that gives the recorded signal as proportional to the integral of the concentration of colloid over the pressure gradient in the ultrasonic wave.   

Picosecond Ultrasonic Measurement of Liquids

We study acoustic waves launched using a 400 fs blue pulse (407.5 nm) from a Ti:sapphire laser, focused on a SiO$_{2}$/GaAs interface (r $\sim $ 25 $\mu $m, fluence \underline {$<$}15 $\mu $J/cm$^{2})$. Because of the asymmetry of the (114) GaAs, thermoelastic and piezoelastic processes generate quasishear and quasilongitudinal acoustic pulses that propagate in both materials. Pulse echoes in the thin (0.2 $\mu $m) SiO$_{2}$ layer cause a variation in optical reflectivity at the interface. In thicker layers, including the GaAs substrate and liquid layers on top of the SiO$_{2}$ surface, variations in the bulk optical reflectivity caused by the pulses can also be detected if the layer is transparent to the probe wavelength (407 or 815 nm). We look at the pulse propagation in water, ethylene glycol and glycerine. We measure a longitudinal sound velocity for glycerine of 2800 m/s, 32{\%} larger than low frequency values, giving evidence of considerable elastic stiffening. Our pulses have central frequencies $\sim $50 GHz. A more modest 4.6{\%} increase in the longitudinal sound velocity for water (1552 m/s) is also observed. In spite of this notable stiffening, no shear waves were observed in any of the liquids studied, indicating that propagation is still within the hydrodynamic regime.   

Electromagnetic stimulation of the ultrasonic signal for nondestructive detection of the ferromagnetic inclusions and flaws

It was recently shown that thermal or optical stimulation can be used to increase sensitivity of the conventional nondestructive ultrasonic detection of the small crack, flaws and inclusions in a ferromagnetic thin-walled parts. We proposed another method based on electromagnetic modulation of the ultrasonic scattered signal from the inclusions or defects. The electromagnetically induced high density current pulse produces stresses which alter the ultrasonic waves scanning the part with the defect and modulate ultrasonic signal. The excited electromagnetic field can produces crack-opening due to Lorentz forces that increase the ultrasonic reflection. The Joule heating associated with the high density current, and consequent thermal stresses may cause both crack-closure, as well as crack-opening, depending on various factors. Experimental data is presented here for the case of a small cracks near small holes in thin-walled structures. The measurements were taken at 2-10 MHz with a Lamb wave wedge transducer. It is shown that electromagnetic transient modulation of the ultrasonic echo pulse tone-burst suggest that this method could be used to enhance detection of small cracks and ferromagnetic inclusions in thin walled metallic structures.   

Resonant Ultrasound Spectroscopy Characterization of Annealing and Grain Growth in Copper

Resonant Ultrasound Spectroscopy (RUS) is used for determining the bulk elastic properties of a solid material with known dimensions, density and shape from its characteristic vibration frequencies. RUS characterization of polycrystalline materials is based on the assumptions of material uniformity, and the existence of isotropic polycrystal-averaged moduli. The elastic properties of a polycrystalline material depend on the material's microstructure, which can be changed by heat treatment. In this present work, RUS has been applied to heat treated polycrystalline copper specimens; measurements of the resonance frequencies as a function of heat treatment were obtained and used to derive elastic constants. The elastic constants are correlated to the average grain size in the sample, determined by a visual measurement. We find that when the grain size reaches 10{\%} of the sample dimension, elastic constant fit errors suggest that the sample is losing uniformity. We also discuss a number of measurement results that depend on details of the sample mounting and transducer placement.   

Vibrational Modes of MEMS based Directional Sound Sensor

A directional sound sensor was fabricated using micro-electromechanical system (MEMS) technology based on the operational principle of Ormia ochracea fly's hearing organism [1]. The fly uses coupled bars hinged at the center to achieve the directional sound sensing by monitoring the difference in vibration amplitude between them. The MEMS design employed in this work consisted of a 1x2 square millimeter polysilicon membrane hinged at the center. The membrane was positioned about 2 micrometers above the substrate by using a sacrificial silicon dioxide layer. The membrane has two primary vibrational modes (rocking and bending) which were analysis by finite element analysis and found to be at 2.5 kHz and 8 kHz. The incident sound wave causes the two sides of the membrane to oscillates with slightly different amplitudes due to the arrival time difference. In this abstract, the vibrational modes of the system measured using electrical and sound sources will be presented. The experimental data were found to be in good agreement with the modeling. [1] R.N. Miles, et. al.: ``Mechanically coupled ears for directional hearing in the parasitoid fly Ormia ochracea,'' J. Acoust. Soc. Am., \textbf{98}, 3059, (1995).   

Development of a new ABS Acoustic Bubble Spectrometer$^{\mbox{{\textregistered}}\copyright }$ system

D\textsc{ynaflow} has developed an acoustic based device, the ABS Acoustic Bubble Spectrometer$^{\mbox{{\textregistered}}\copyright }$, that measures bubble size distributions and void fractions in liquids based on the measurement of sound propagation through the liquid. In the original system, a pair of hydrophones is used to transmit and receive short monochromatic bursts of sound at different frequencies through the liquid. These signals are processed and analyzed to obtain the frequency dependent attenuation and phase velocities of the acoustic waves. Subsequently, the bubble size distribution is obtained following solution of an inverse problem. In the new system, we have utilized multiple hydrophone pairs that have different frequency response ranges to cover a wider range of bubble size measurement. A transmission signal amplifier is integrated into the system to improve the signal noise ratio. We have also implemented an adaptive control scheme that automatically adjusts the transmitting signal strength and acquisition resolution to optimize the measurement process and used a rectangular and a sine acoustic wave pattern to improve accuracy of signal analysis.   

Numerical modeling of the impact of the propagation of a finite wave in a bubbly media on the Acoustic Bubble Spectrometer ABS$^{\copyright \mbox{{\textregistered}}}$.

The propagation of acoustic waves in bubbly media has been extensively studied over the years. Several methods have been developed for the inversion of the propagation characteristics in order to compute the size and number of bubbles present in the field. At the core of these inversion methods are the assumptions that bubbles are homogeneously dispersed and behave in a steady-state monochromatic linear fashion. However, instruments designed for the detection and measurements of bubbles (such as Dynaflow's Acoustic Bubble Spectrometer ABS$^{\copyright \mbox{{\textregistered}}})$ are limited to the use of finite duration and amplitude signals. Consequently, the transient characteristics of the bubble field can provide a significant impact on the received signal. We will present some recent work in the numerical modeling of transient and finite amplitude effects and their impact on the received signals and inversion procedure.   

Resolving dynamics of acoustic phonons by surface plasmons

In this work, we employ surface plasmons as a sensitive probe technique to detect acoustic phonons in metal films following impulsive optical excitation. Surface plasmons are shown to have an enhanced sensitivity in detecting acoustic phonons in metals. Our study shows that the surface plasmon technique is a promising tool to detect small optical or mechanical property changes in metals at a miniature scale, suitable for a variety of applications, such as sensors and MEMS.   

Long Range Surface Plasmon Fluorescence Spectroscopy

Surface plasmon modes, excited at the two sides of a thin metal layer surrounded by two (nearly) identical dielectric media interact via the overlap of their electromagnetic fields. This overlap results in two new-coupled modes, a short and a long-range surface plasmon (LRSP). We demonstrate that combining the LRSP optics with fluorescence spectroscopy can result in a huge enhancement of the fluorescence signal due to the enhanced optical field of the LRSP at the metal dielectric interface, and to its increased evanescent depth into the analyte. This was demonstrated for the detection of the fluorescence intensity of chromophore labeled protein bound to the surface sensor. Beside that, some fundamentals were studied leading to some interesting difference between SPFS and LRSPFS.   

Evanescent field response to patterned features on a planar waveguide measured with a buried detector array.

The evanescent field of an appropriately designed waveguide can be very sensitive to the local refractive indices of the cladding layers surrounding the core. In this study, a planar waveguide has been fabricated on a chip that contains buried p-Si photo-detectors, located about 1 micron from the waveguide core and arrayed down the length of the waveguide. Local changes in the index of the upper cladding, such as the formation of an adlayer, result in signal changes at the detector. The buried detector format provides significant opportunities for localized detection of chemical or biological analytes in complex milieu through monitoring of the evanescent field. To test the responses to refractive index changes in the upper cladding, small photoresist features were fabricated on the surface of the waveguide. This material was selected because it is easily patterned, its thickness can be tightly controlled, and its refractive index is similar to that of biological molecules. The results of the experiments measuring evanescent field intensity as well as detector fabrication details will be presented; these results are compared with parallel numerical modeling studies.   

AlGaN based Tunable Hyperspectral Detector: Growth and Device Structure Optimization

We report on fabrication and growth optimization of an AlGaN/GaN based tunable hyperspectral detector. III-Nitride based detectors possess the potential to detect a large portion, from UV to IR, of the electromagnetic spectrum. Control over the detection wavelength with applied bias across an AlInGaN heterostructure can provide a compact tunable hyperspectral detector eliminating use of filters and gratings which make current tunable detectors bulky. Challenges involved in the development of the device include controlled deposition and characterization of thin layers of Al$_{x}$Ga$_{1-x}$N with Al composition varying from 0{\%} to 100{\%} and back to 0{\%}. Performance of such detector is greatly affected by the thickness and quality of the thin heteroepitaxially grown layers which control the dark current and operating voltage of the device. We will present the effect of growth conditions and heterostructure parameters such as composition and thickness on the device performance.   

Dielectric Effects in Electro-optic Field Sensors

The use of electro-optic (EO) crystals for electromagnetic field detection is an attractive alternative to conventional techniques, due to their compactness, large intrinsic bandwidth, and ability to measure field amplitude and phase with minimum field perturbation. In our LiNbO$_{3}$ sensors, anomalously large detection sensitivities were observed, which were found to be due to dielectric relaxation effects within the crystals. In this presentation, we demonstrate these effects, their impact on the EO sensor responsivity, and discuss implications for improving future EO field sensors.   

Session A39: Focus Session: Phase Transitions and Domains in Ferroelectric Nanostructures I

Hybrid semiconductor-ferroelectric and metal-ferroelectric nanostructures

The reduction of scale and dimensionality of ferroelectric materials enables study and application of important size-dependent differences in the mechanism for ferroelectric stability. These scale and dimensionality reductions also facilitate new opportunities for integrating ferroics with other material systems for multi-functional nano-scaled devices. First, we review our recent progress in understanding ferroelectric stability and the finite size-dependent evolution of the ferroelectric phase transition temperature in single-component nanostructures and its implications. We present results of a versatile synthetic approach we have developed to produce multi-component nanostructures, with examples of semiconductor-ferroelectric and metal-ferroelectric hybrid nanostructures. We discuss characterizations of their component structure and composition, and we also present the results of measurements of the properties of these hybrid nanostructures as individually and electrically addressable device elements.   

The Hunt for a Snark: Spatially Resolved Imaging of Nucleation Centers in Ferroelectrics

Ferroelectric polarization switching in non-volatile memory and high density data storage devices is governed by a number of nucleation centers that are necessary to account for experimentally observed low values of coercive fields. Despite 50 years of extensive research addressing the role of conductivity, surface dead layers, charge injection, and other factors, the microstructural origins of the Landauer paradox (switching fields correspond to implausibly large nucleation activation energies) are still a mystery. Here, Switching Spectroscopy Piezoresponse Force Microscopy (SS-PFM) is developed as a quantitative tool for real-space mapping of imprint, coercive bias, remanent and saturation responses, work of switching, and nucleation biases in ferroelectrics. Several examples of switching behavior in low dimensional ferroelectrics are presented, including (a) pinning at grain boundaries in polycrystalline PZT, (b) non-uniform work of switching in ferroelectric nanodots and (c) switching in the vicinity of topographic defects. The ``abnormal'' hysteresis loops were observed in the vicinity of topographic defects in multiferroic thin films and PZT ceramics and attributed to the interaction of nascent domain with the strain field of the defect. The mapping of the spatial and energy distribution of Landauer switching centers is demonstrated.   

Probing Ferroelectricity in Barium Titanate Nanorods by Optical Spectroscopy

Finite-size effects in ferroelectric materials have attracted interest for both fundamental reasons and applications. In particular, previous studies have examined the role of film thickness and grain size on the ferroelectric properties of the well-known BaTiO$_{3}$ system. In this work we examine chemically synthesized nanorods of BaTiO$_{3 }$to probe ferroelectricity in well-controlled samples. The ferroelectric response in nanorods of 30-100 nm diameter and micron length was measured using optical second-harmonic generation (SHG) and Raman spectroscopy. SHG serves as a non-contact method of identifying the ferroelectric-paraelectric phase transition since the process is allowed only for the non-centrosymmetric ferroelectric phase; Raman spectroscopy provides a complementary method of probing structure relevant for the phase transition. Both the SHG and Raman signals show evidence of the expected ferroelectric to paraelectric phase transition at temperature above the bulk transition temperature. Results obtained both for ensemble samples and for many individual nanorods will be presented and compared.   

Ferroelectric domain structures near the morphotorpic phase boundary in the piezoelectric material Pb(Zr$_{1-x}$Ti$_{x})$O$_{3}$

In the simple perovskite oxide Pb(Zr$_{1-x}$Ti$_{x})$O$_{3}$, an\textbf{ }excellent piezoelectric response was obtained in the vicinity of a morphotropic phase boundary (MPB) between the ferroelectric monoclinic (F$_{M})$ and rhombohedral (F$_{R})$ phases. To understand the origin of the excellent response, we have investigated the detailed features of ferroelectric domain structures near the MPB in PZT by transmission electron microscopy. In the F$_{M}$ side of the MPB, as a result, there were two types of domain structures at room temperature. On the other hand, a usual domain structure having the 109\r{ } and 180\r{ } boundaries existed at room temperature in the F$_{R}$ side. The notable feature is that each domain in the F$_{M}$ and F$_{R}$ domain structures near MPB can be identified as an aggregation of nanometer-sized domains with an average size of about 10 nm. Based on this feature, we propose a new concept of an aggregation-type domain structure for ferroelectric domain structures near the MPB.   

Ferroelectric Phase transition in (1-x)Pb(Fe$_{2/3}$W$_{1/3})$O$_{3}$-xPbTiO$_{3}$ solid solutions thin films

We have deposited thin films of (1-x)Pb(Fe$_{2/3}$W$_{1/3})$O$_{3}$-xPbTiO$_{3}$ (PFWT) on Pt/Si substrates. The metamorphic phase diagram of PFWT solid solution indicates that it changes from natural relaxor to an ordered ferroelectric state above x = 0.33 of lead titanate concentration. The microstructure and surface morphology were investigated using SEM and AFM techniques that indicated surface roughness of 10-15 nm with particle size of $\sim $ 30-50 nm. The dielectric relaxation studies in these films were carried out measured in the temperature range of 100K-650K and the frequency range of 100Hz-1MHz. The ferroelectric phase transition was found at 575K for all frequencies. The Relaxation indication coefficient ($\gamma \sim $1.30) was estimated from a linear fit of the modified Curie-Weiss law and results suggested a long range ordering. The temperature dependant micro Raman studies revealed a ferroelectric phase transition from tetragonal to cubic phase above 575K. The polarization hysteresis curve at room temperature illustrated a ferroelectric nature of the material having ramanat polarization (P$_{r})$ to be 3$\mu $C/cm$^{2}$ and the saturation polarization (P$_{s})$ 30$\mu $C/cm$^{2}$.   

Near-field second-harmonic imaging of ferroelectric domain structure of YMnO$_3$

Ferroelectrics have attracted much recent interest for applications in, e.g., data storage devices. The ferroelectric domain formation and order in a single crystal is the result of a subtle interplay between electric field and the elastic and domain wall energies to minimize the total free energy of the system. This makes the prediction of domain size and shape a priori difficult. Due to its symmetry selectivity optical second-harmonic generation (SHG) is sensitive with respect to the ferroelectric order in a system. For spatially resolved imaging we combine it with tip-enhanced near-field optical microscopy providing resolution down to 10 nm. Unpoled single-crystalline multiferroic YMnO$_{3}$ with the order parameter along the hexagonal z-axis and in the surface plane was probed. With the incident laser field polarized parallel to the tip axis we selectively access the nonlinear tensor component $\chi_{zxx}$ of the sample. The imaging contrast arises from the local interference between the induced SH-polarization in the sample and the SH reference field of the tip apex itself. The domains are found to be anisotropically elongated along the hexagonal axis with dimensions of several 100 nm.   

Nanoscale 180 Degree Stripe Domains in PbTiO$_{3}$ Films

Nanoscale 180 degree stripe domains have been found to be the equilibrium structure of ultrathin ferroelectric films on insulating substrates [Fong, D. D. \textit{et al.}, \textit{Science }\textbf{304}, 1650 (2004)]. Here we report a study of the morphology of these stripe domains in PbTiO$_{3}$ films using room-temperature AFM imaging and high-temperature synchrotron x-ray scattering. The stripes can be aligned with surface steps, or with the underlying crystal lattice, depending upon film thickness and temperature. These equilibrium domains provide a new class of electrically active, controllable ``soft'' patterns in a hard material that are promising for self-assembly of oppositely charged adsorbates on sub-lithographic length scales.   

Local decomposition of solid solutions at the ferroelectric-antiferroelectric interphase boundaries and formation of nanostructures in the process of phase transformation

Local decomposition of (PbLa)(ZrTi)O$_{3}$ near the interphase boundaries separating domains of coexisting FE and AFE phases was investigated. We studied the local decomposition kinetics in the process of aging of samples quenched to room temperature from the paraelectric phase. Mechanisms defining the kinetics of the attainment of the equilibrium state of coexisting FE and AFE domains (with sizes of 20 to 30 \textit{nm}) are analyzed. There are two main mechanisms determining the establishing of the equilibrium inhomogeneous chemical composition. The slower mechanism is the diffusion of the oxygen vacancies the nonequilibrium concentration of which was created during the annealing at T $>$ T$_{c}$. The faster process is due to the cation diffusion caused by the local mechanical stresses at the interphase boundaries. The sizes of segregates formed at the interphase boundaries are from 8 to 15 \textit{nm}.   

Quasi-amorphous pyro- and piezo- electric SrTiO3.

Recent publications about quasi-amorphous BaTiO3 materials have demonstrated that non-crystalline ionic solids can exhibit pyro- and piezo- electricity. This posed a question whether the quasi-amorphous state is unique to BaTiO3 or other compounds can form non-crystalline polar phases. We report that pulling through a temperature gradient converts amorphous thin ($<$100 nm) films of SrTiO3 into a pyro- and piezoelectric phase, which is nevertheless non-crystalline according to XRD and SEM. Thus SrTiO3 may form a quasi-amorphous phase. This implies that: (1) the quasi-amorphous state is not unique to BaTiO3 but other compounds may form similar phases; (2) polarity of a compound in a quasi-amorphous phase is not related directly to the polarity of this compound in a crystalline form. In this view, one may expect that other quasi-amorphous phases will be found. Owing to the simplicity of their preparation, quasi-amorphous materials are very promising for future pyroelectric and piezoelectric devices that can be integrated with modern semiconductor technology.   

Electroactive Properties of Potentially Ferroelectric Cyanopolymer Systems

Piezoelectric, pyroelectric, and potentially ferroelectric behavior have been observed in newly synthesized cyanopolymer systems. These systems are chemical analogs to the well known ferroelectric polymer poly(vinylidene fluoride), PVDF. Various chemical groups have been used to replace the electronegative fluorine and electropositive hydrogen atoms found in PVDF. This substitution maintains the polar nature of the all-trans conformation while increasing the amphiphilic nature of the said polymers. The increased amphiphilic nature of the polymers allows for the employment of the Langmuir-Blodgett technique in the fabrication of ultra-thin (less than 10 nm) polymer films. These cyanopolymers include poly(methyl vinylidene cyanide) and several of its copolymers. Piezoelectricity and pyroelectricity have been clearly observed in several of these systems. In addition, evidence for polarization reversal suggests that some members of this family of polymers may be ferroelectric in nature. Piezoelectric, pyroelectric, and ferroelectric properties make these cyanopolymers a promising new class of materials for use in electromechanical transducers, nonvolatile memories, and infrared imaging.   

Session A40: Semiconductors: Growth of Nitrides

Optimized growth of lattice-matched InAlN/GaN heterostructures by molecular beam epitaxy

A fundamental problem in the epitaxial growth of hexagonal group III/Nitride heterostructures along their c-axis is the in-plane lattice-mismatch between the binary compounds GaN, AlN and InN. This mismatch is responsible for stress and strain formation and leads in its extreme to cracking, deteriorating the optical and electrical properties of the samples. The ternary compound In$_ {x}$Al$_{1-x}$N with x$\sim$0.17 is expected to have an identical in-plane lattice constant as GaN. Here we report on the MBE growth of lattice-matched In$_{x}$Al$_ {1-x}$N on thick GaN templates. Optimizing the growth conditions and systematically investigating the influence of the flux ratio between Aluminum, Indium and Nitrogen leads to high quality layers, as assessed by x-ray diffraction. The extracted full widths at half maximum of the InAlN peak in $\omega$-2$\theta$ and rocking curve scans are 190arcsec and 300arcsec respectively and the lattice-match is confirmed by reciprocal lattice mapping. Sharp, intense high-order satellite peaks as well as the occurrence of interface interferences in the x-ray diffraction spectra confirm the high crystalline quality and abrupt interfaces of short period GaN/InAlN superlattices. These simple heterostructures are preludes to more complex structures like distributed Bragg reflectors and micro cavities.   

AlN, InN, and their alloys' growth issues in Plasma Source MBE.

A systematic investigation of the growth of AlN, InN,and InAlN by Plasma Source MBE (PSMBE) was performed. The growth conditions were optimized based on RHEED analysis during growth and dissociation RGA experiments. For the PSMBE technique, the most important growth parameters are the flux levels (as determined by RF power and Ar/N ratio), and growth temperature. We present experimental work on AlN, InN, and InAlN grown on an AlN buffer layer deposited on sapphire (c), (r), and (a) plane substrates. The films are epitaxial with no phase segregation as shown by x-ray diffraction analysis. In-situ RHEED analysis was used to determine RHEED intensity oscillations, strain profiles, and coherence length profiles simultaneously. The results indicate a 2D-3D type's growth mode. Characterization of the (Al, In)-Nitrides film were performed by post growth techniques such as XRD, XPS, AFM, Optical (micro-Raman, photoluminescence, and UV-VIS- NIR-IR spectroscopy), and Electrical (Hall measurements). The results of the in-situ end ex-situ characterization of (Al, In)-Nitrides films by are presented in this work and confirmed high structural and optical qualities of (Al, In) - Nitride films.   

Preferential growth of zinc-blende and wurtzite GaN as effected by the conditions of MBE

Homoepitaxial growth of GaN on its (0001) or (111) may result in both wurtzite and zinc-blende phases. We have conducted a detailed study to identify the dependence on various conditions. The experiments show that at low substrate temperatures but high gallium fluxes, the meta-stable zinc-blende phase will be strongly favored, while at high temperatures and/or low gallium fluxes, thermal equilibrium wurtzite phase will dominate. There is no significant dependence of crystallographic structure on deposition rate observed. In the STM study of initial stage nucleation on wurtzite film, 2D islands of both phases have been identified and statistical relative stabilities of the two phases are obtained at different temperatures. The relative stabilities show a significant asymmetry at low versus high temperature, which indicates that preferential nucleation at the initial stage would determine the film's crystallographic structure.   

Non-polar GaN structures on $\gamma $-LiAlO$_{2}$ grown by plasma-assisted molecular beam epitaxy

A-plane lithium aluminate (LAO) in $\gamma $-phase crystal structure, $\gamma $-LiAlO$_{2}$ (100), was used as the substrate which was grown by Czochralski pulling method. With a lattice mismatch of [0001]GaN$\vert \vert $[010]LAO $\sim $ 0.3{\%} and [11\underline {2}0]GaN$\vert \vert $[001]LAO $\sim $1.7{\%}, $\gamma $-LiAlO$_{2}$ (100) has a much smaller lattice mismatch with the GaN (1\underline {1}00) than the conventional substrates. M-plane GaN epilayer was successfully grown by plasma-assisted molecular beam epitaxy. X-ray diffraction theta/two-theta scan shows a diffraction peak due to m-plane GaN. Raman scattering confirms Raman modes from the GaN (1\underline {1}00) structure. Cathodoluminescence yields a peak at 363 nm at room temperature. Nanostructures were explored also. Comparisons to structures grown on the c-plane will be presented.   

Effect of nitridation on the molecular beam epitaxy growth of GaN on ZrB$_{2}$(0001)/Si(111)

ZrB$_{2}$ is a conductive, reflective, and lattice-matched buffer layer for GaN growth on Si. Here we report the effect of nitridation on the epitaxial growth of GaN on ZrB$_{2}$(0001) films prepared \textit{ex situ} and \textit{in situ}, which was studied using an ultrahigh vacuum molecular beam epitaxy - scanning probe microscopy (MBE-SPM) system. The growth of GaN was carried out by rf-plasma assisted MBE, and epitaxy of wurtzite GaN with N-polarity was observed on both \textit{ex-situ} and \textit{in-situ} prepared ZrB$_{2}$ films. The nitridation of ZrB$_{2}$ films were conducted by exposing them to active nitrogen, and well-ordered hexagonal boron nitride (h-BN) formation was observed when the annealing temperature was above 900$^{o}$C. The partially formed BN layer affected neither the epitaxy nor the polarity of GaN, but when the surface was fully covered with well-ordered h-BN, GaN growth did not occur. The high GaN nucleation selectivity observed between clean and h-BN covered ZrB$_{2}$ suggests the possibility of applying epitaxial lateral overgrowth method, which is known to be difficult in elemental source GaN MBE growth. Ref. Z. T. Wang \textit{et al.,} J. Appl. Phys. 100, 033506 (2006).   

Critical parameters for growth of optimized GaN and InGaN/GaN MQW structures on freestanding HVPE GaN substrates by MOCVD

With the continued improvement and availability of freestanding Nitride substrates, such as those grown by HVPE, these substrates are becoming more commonly used for growth and device applications. However, even with a reduced dislocation density as compared to heteroepitaxially grown GaN layers on sapphire or SiC, devices fabricated on these substrates are often less efficient. One reason for this is that generally growth is carried out using optimized conditions for growth on non-native substrates. In this work optimization of the growth conditions was carried out for GaN layers and InGaN/GaN MQW structures on freestanding HVPE GaN substrates. It was found that the optimized conditions for growth on these substrates are different as compared to growth on GaN on sapphire templates. The results of the optimization and the differences in the growth will be presented along with insight into the differences seen experimentally.   

Electroluminescence from Er doped III-nitride light emitters synthesized by metal organic chemical vapor deposition

It has been well recognized that GaN is a very attractive host for Er due to the low degree of thermal quenching of radiative intra-4f Er$^{3+}$ transitions and the large Er doping concentrations that can be achieved. These properties, in conjunction with the 1.54 $\mu $m transition of Er$^{3+}$, make Er doped GaN structures promising for light emitters and amplifiers operating at the telecommunication wavelength. Recently, our group has reported on the optical properties of Er doped GaN epilayers synthesized by metal organic chemical vapor deposition (MOCVD) using photoluminescence (PL). We now report on the electroluminescence (EL) of Er doped III-nitride light emitters synthesized by MOCVD. These structures were characterized with x-ray diffraction, atomic force microscopy, scanning electron microscopy, PL, EL, and Hall measurements. EL spectra of these emitters exhibit emission at 537 and 558 nm (intra-4f Er$^{3+ }$transitions from the $^{2}$H$_{11/2 }$and $^{4}$S$_{3/2}$ to the $^{4}$I$_{15/2}$, respectively), and at 1.0 and 1.54 $\mu $m (transitions from the $^{4}$I$_{11/2}$ and $^{4}$I$_{13/2}$ to the $^{4}$I$_{15/2}$, respectively). The effects of growth conditions such as temperature, V/III ratio, and growth rate will be discussed. EL from emitters of different Er concentrations as well as potential applications of these Er doped III-nitride light emitters will also be discussed.   

Effects of polarity on material's quality of Al-rich AlGaN alloys

AlGaN alloys have the capability of tuning the direct band gap in a large energy range, from about 3.4 to 6.1 eV, which makes them very useful for ultraviolet (UV) and deep UV (DUV) optoelectronic device applications. Although recent progresses have led to the realization of several operational DUV devices such as light emitting diodes operating at wavelengths $<$ 300 nm, high performance DUV optoelectronic devices working at $\lambda \quad \le $ 280 nm still suffer from many serious problems such as stability and reliability. One of the important growth parameters that affects the properties of III-nitrides is the growth polarity. In this work, Al-rich Al$_{x}$Ga$_{1-x}$N alloys (x$\sim $0.8) with different polarities were grown on sapphire substrates by metal organic chemical vapor deposition (MOCVD). Various characterizations techniques were used to study the structural, electrical, and optical properties of these alloys. It was found that the material quality is significantly influenced by the growth polarity. Samples with Al-polarity have a much higher crystalline quality and better surface morphology than those of N-polarity. Additionally, photoluminescence spectra of Al-polarity samples exhibit only the band edge transition, while those of N-polarity also comprise a deep level impurity transition.   

Growth of Mg-doped InN by Metal Organic Chemical Vapor Deposition

InN with an energy gap of $\sim $ 0.7 eV, has recently attracted extensive attention due to its potential applications in semiconductor devices such as light emitting diodes, lasers, and high efficiency solar cells. However the ability to grow both p-type and n-type InN is essential to realize these devices. All as grown unintentionally doped InN are n-type. The tendency of native defects in InN to form donors manifests itself severely at surfaces where high levels of electron accumulation are observed. The highly n-type conductive layer at the surface of InN films creates difficulties in the demonstration of p-type InN. Nevertheless it is important to investigate the optical and structural properties of Mg-doped InN. We report here on the growth of Mg-doped InN epilayers by metal organic chemical vapor deposition. Photoluminescence (PL) was employed to study the effects of different growth conditions of Mg-doped InN. PL studies revealed that in addition to emission peak at $\sim $ 0.82 eV in undoped InN layers, Mg-doped InN layers exhibit an emission peak at $\sim $ 0.75 eV. The peak at $\sim $ 0.75eV for Mg-doped InN could be related to defects generated by Mg doping in InN. Various other measurements such as Hall effect measurement, X-ray diffraction and atomic force microscopy were carried out to provide further understanding.   

Cantilever Epitaxy of AlN using Hydride Vapor Phase Epitaxy

AlN is an important material for AlGaN-based electronic and optoelectronic devices such as UV Light Emitting Diodes and High Electron Mobility Transistors. We have grown AlN films with reduced Threading Dislocation (TD) densities using Cantilever Epitaxy with the Hydride Vapor Phase Epitaxy growth method. Prior to growth, 6H-SiC substrates were processed using standard lithography and ICP etching to form periodic ridge/trench patterns. Ridges were oriented in the $\left\langle {1\bar {1}00} \right\rangle _{SiC} $ direction, and trenches were etched up to 12.6 $\mu $m deep. AlN was grown laterally from 2-4 $\mu $m wide ridges over 3-6 $\mu $m wide trenches and coalesced. Plan-view TEM analysis showed that TD densities in the wing regions were less than 8.3 x 10$^{6}$ cm$^{-2}$ as compared to 3.9 x 10$^{9}$ in the seed regions. The TDs are predominantly edge-type with \textbf{b} =$\frac{1}{3}\left\langle {11\overline 2 0} \right\rangle $. Most of these TDs originate from the AlN-SiC interfaces on the tops of the ridges and propagate vertically. A small number of inclined dislocations propagate into the wing region.   

Growth and structural properties of hexagonal BN thin films on graphitized 6H-SiC substrates

Hexagonal boron nitride (h-BN) is a promising material system for optical device applications in the ultraviolet spectral region because of its wide bandgap and large exciton binding energies of 5.97 eV and 149 meV, respectively. An exploration of a suitable substrate is a central challenge for high-quality h-BN thin film growth. We report here the successful growth of h-BN thin films by metalorganic vapor phase epitaxy (MOVPE) on graphitized 6H-SiC substrates. Annealing 6H-SiC substrates in ultrahigh vacuum prior to MOVPE growth provides graphitized 6H-SiC substrates whose surfaces are covered with graphite having several monolayers thickness. X-ray diffraction reveals that the BN thin films are pure single-phase (0001) h-BN with the c-axis normal to the 6H-SiC (0001) surface and that the c-axis lattice constant of the h-BN thin films is identical to that of bulk h-BN samples. This work is partly supported by a Grant-in-Aid for Scientific Research (A) {\#}18206004 from the Japan Society for the Promotion of Science.   

Photoluminescence studies of impurity transitions involving nitrogen vacancies in Mg-doped AlGaN alloys

Although tremendous progress has been made in the development of AlGaN alloys and their applications in deep UV devices, achieving p-type conductivity in Al-rich AlGaN alloys is still highly challenging because of the large activation energy of the magnesium (Mg) acceptors and strong compensation effects due to the presence of intrinsic defects. We report on the growth by metalorganic chemical vapor deposition and photoluminescence studies of Mg-doped Al$_{x}$Ga$_{1-x}$N alloys. A group of deep level impurity transitions was observed in Mg-doped Al$_{x}$Ga$_{1-x}$N alloys which was identified to have the same origin as the previously reported blue line at 2.8 eV in Mg-doped GaN and was assigned to the recombination of electrons bound to the nitrogen vacancy with three positive charges (V$_{N}^{3+})$ and neutral Mg acceptors. Based on the measured activation energies of the Mg acceptors in AlGaN and the observed impurity emission peaks, the V$_{N}^{3+}$ energy levels in Al$_{x}$Ga$_{1-x}$N have been deduced for the entire alloy range. The presence of high density of V$_{N}^{3+}$ deep donors translates to the reduced p-type conductivity in AlGaN alloys due to their ability for capturing free holes. With the identification of the emission peaks associated with V$_{N}^{3+}$ hole compensating centers, we were able to improve the p-type conductivity of Al-rich AlGaN by monitoring and suppressing the intensity of the V$_{N}^{3+}$ related emissions.   

Defect Ordering in InN

Energetic particle irradiation followed by thermal annealing has been used to create InN films with both high electron concentration and high mobility. The mobility values are larger than have been reported for as-grown, undoped InN films with comparable electron concentrations ($>$ 10$^{19}$ cm$^{-3})$. The high mobility can be explained by a thermally-induced ordering of the native point defects produced by the irradiation. An analysis of the concentration dependence of the electron mobility shows that the defects are triply charged, and therefore the strong Coulomb interaction energy between them is minimized by the formation of a donor superlattice. Here we present evidence for this ordering, including experimental results and theoretical modeling.   

Redirecting of misfit dislocations from AlN/Si interface into the substrate

In order to increase lifetime of CW lasers based on the III-nitrides, a low defect density in GaN/AlN based materials is required. For the first time it was shown that misfit dislocations formed at the AlN/Si interface can interact with dislocation loops formed around He bubbles created by He implantation into Si, and dislocations can move into the Si substrate instead of into the epi-layer. The optimal implantation dose and the distance of the He bubbles from the surface were determined. The growth temperature of AlN was used as the annealing temperature. Understanding of physical basis of strain relaxation at the AlN/Si interface can lead to the development of techniques leading to annihilation of threading dislocations in the GaN/AlN layers grown on foreign substrates.   

Rare-earth nitride films; Ion assisted growth.

We have recently reported a study of Gd nitride films grown by evaporating Gd in the presence of low-pressure N$_{2}$ gas. That work demonstrated that the material is a semiconductor in both the ambient-temperature paramagnetic and low-temperature ferromagnetic phases, with a conductivity determined by nitrogen vacancies. The present paper will report growth in a reactive environment that reduces the density of those vacancies. Films were grown by evaporating a number of rare earths by ion-assisted deposition (IAD), exploring films grown in ions with energies from 0 to 1000 eV. All of these IAD films show reduced crystallite size, expanded lattice constant, depressed magnetic ordering temperature and increased resistivity as compared to N$_{2}$-grown films. The optical band gap is largely unchanged by IAD.   

Session A41: Semiconductors: Thermodynamics and Transport

Heat Capacity and Isotopic Masses of Semiconductors

The heat capacity of semiconductors has been investigated both theoretically and experimentally since the early 20$^{th}$ century. Its dependence on the isotopic masses of its constituents, however, has only received attention during the past few years [1]. The quantity usually investigated vs. temperature$ T $is D( $T$ )= d ln $C_{v} T^{-3}$ / d ln $M. $For monatomic diamond, Si, and Ge, D($T)$ exhibits a peak at a temperature 0.1 times that of TA phonons at the X-point of the BZ. In binary tetrahedral semiconductors (GaN, ZnO) D($T)$ differs for the heavier and lighter mass, peaking at 0.15 times the TA temperature of the former and at 0.25 times the TO temperature of the latter. The ratio 0.15 can also can also be estimated with a one-oscillator Einstein model. Here we present similar measurements for a binary compound with rock salt structure: PbS (galena). The phonon density of states (DOS) of this material is shown to peak at 80K for the Pb-like phonons. For the S-like phonons a broad band between 150 and 350K is found, in \textit{ab initio} calculations, to dominate the DOS. The corresponding D($T)$ peaks in both cases at 0.14 times the temperature of the corresponding phonons ( 80K and 240K, respectively). The D($T)$ will be compared with \textit{ab initio} calculations, performed with the ABINIT code. [1] J.Serrano, Phys. Rev. B 73, 094303 (2006) and references therein.   

Magnetic and electrical transport properties of Fe$_{1-x}$Cr$_{x}$Sb$_{2}$

We have investigated magnetic, thermodynamic and electrical transport properties of Fe$_{1-}$xCr$_{x}$Sb$_{2}$ (0$\le $x$\le $1) single crystals. Ground state of the system evolves from nonmagnetic semiconductor for x = 0 to antiferromagnetic semiconductor for x = 1. In contrast to Co substitution, Cr doping in FeSb$_{2}$ does not result in metallic state and magnetoresistance is negligible. Magnetic phase diagram and conduction mechanism will be discussed.   

High Temperature thermoelectric properties of Ba$_{x}$Yb$_{y}$Co$_{4}$Sb$_{12}$ composites

In materials where the mean free path of charge carriers is smaller than that of phonons, enhancing boundary scattering in the matrix may improve the thermoelectric figure of merit$^{1}$. We have applied this idea to n-type skutterudites that have large effective mass and consequently small carrier mean free path. We prepared double-filled Ba$_{x}$Yb$_{y}$Co$_{4}$Sb$_{12}$ skutterudite composites with a wide range of the filling fractions $x$ and $y$. The experimental filling fraction limits are in a good agreement with the values predicted theoretically. In cases where we intentionally exceeded the filling limit, the excess filler atoms form fine oxide particles that are distributed mainly on the grain boundaries. While the composites maintain good electrical transport properties due to weak charge carrier scattering from the oxide particles, the lattice thermal conductivity is reduced significantly. The highest ZT in these composite skutterudites reaches 1.3 at 800K.   

Reciprocal capacitance transients?

When the reverse bias across a semiconductor diode is changed, charge carriers move to accommodate the appropriate depletion thickness, producing a simultaneous change in the device capacitance. Transient capacitance measurements can reveal inhibited carrier motion due to trapping, where the depth of the trap can be evaluated using the temperature-dependent escape rate. However, when we employ this technique on a GaAs$_{0.72}$P$_{0.28}$ n+/p diode (which is a candidate for incorporation in multi-junction solar cells), we observe a highly non-exponential response under a broad range of experimental conditions. Double exponential functions give good fits, but lead to non-physical results. The deduced rates depend on the observation time window and fast and slow rates, which presumably correspond to deep and shallow levels, have identical activation energies. Meanwhile, we have discovered a universal linear relationship between the inverse of the capacitance and time. An Arrhenius plot of the slope of the reciprocal of the transient yields an activation energy of approximately 0.4 eV, independent of the observation window and other experimental conditions. The reciprocal behavior leads us to hypothesize that hopping, rather than escape into high-mobility bands, may govern the transport of trapped holes in this system.   

First principles calculation of bulk semiconductor mobilities for radiation detection application

The development of high energy resolution, room temperature semiconductor radiation detectors requires the development of materials with both an increased carrier mobility-lifetime product ($\mu\tau$) and a band gap in the 1.6-2.5 eV range. An adequate $\mu\tau$ is required for efficient collection of generated carriers from large devices, maximizing S/N ratio and resolution. We use density functional theory to study the microscopic mechanisms of mobility degradation from point defects and to calculate the intrinsic limits of mobility for a given bulk material. Scattering rates obtained from the Born approximation allow us to calculate the contributions of different point defects on mobility degradation, within Boltzmann transport theory. Both native defects and impurities were considered. Formation energies for the various defects were calculated to determine their equilibrium concentrations. Combined with calculations of the defect chemical potentials, we make predictions on the feasibility of improving mobility by thermal annealing to remove the most detrimental defects. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.   

Two-contact and four-contact magnetoresistance in InSb / Au hybrid structures.

We present magnetoresistance measurements on hybrid InSb-Au structures in two-contact and four-contact configurations. Large geometrical magnetoresistances in InSb-Au structures are enabled by the high electron mobility, and hence large Hall angle, in InSb and by the difference in conductivity between semiconductors and metals. InSb / metal hybrid magnetoresistors have attracted attention for applications in data storage and sensing, where a two-contact geometry is appealing. Our geometries consist of mm-sized thin-film InSb bar mesas paralleled by Au shunts, fabricated by lithographic techniques. The four-contact magnetoresistances are experimentally observed to be substantially higher (up to 8000 perc. at a magnetic field of 1 T, at 6 K and at an InSb mobility 40,000 cm2/Vs) than the two-contact magnetoresistances (average 80 perc.) over the temperature range studied. The two-contact magnetoresistances further stay short of the Corbino limit. Effects of the hybrid structure are evident however: for two-contact magnetoresistances at 1 T, an absence of Au shunts in otherwise equivalent geometries leads to magnetoresistances of about 15 perc., one-sided shunts result in about 70 perc., and two-sided shunts in about 140 perc. (NSF DMR-0618235).   

Nonadiabatic electron heat pump

We investigate a mechanism for extracting heat from metallic conductors based on the energy-selective transmission of electrons through a spatially asymmetric resonant structure subject to ac driving. This quantum refrigerator can operate at zero net electronic current as it replaces hot by cold electrons through two energetically symmetric inelastic channels. We present numerical results for a specific heterostructure and discuss general trends. We also explore the conditions under which the cooling rate may approach the ultimate limit given by the quantum of cooling power.   

Scanned-gate and Kelvin-probe microscopy to investigate surface-acoustic-wave-driven transport through a depleted GaAs channel

Electron transport driven by a surface acoustic wave (SAW) through a depleted GaAs channel is the basis for a proposed device capable of quantum information transfer or processing. Device fabrication benefits from a detailed understanding of the capture process at the channel entrance and the dynamics in the channel. We report two experiments to obtain spatial information uniquely provided by low-temperature scanning-probe microscopy. Scanned-gate microscopy, which generates images of SAW-induced current, shows features near the channel entrance that evolve from spots to crescents. Comparison with simulations confirms that the SAW current increases when the maximum potential gradient along the channel is reduced. Kelvin-probe microscopy is adapted to make images of SAW-induced charge, revealing a build-up of negative charge at the channel entrance when no SAW current flows, and a broken line of negative charge, and occasionally positive charge or dipole behavior, with a SAW current.   

Can we use scanned probe microscopy to measure local carrier mobility?

A local measurement of charge carrier mobility in pi conjugate systems would provide much new insight into charge injection, trapping and transport. We have demonstrated recently that low-spring-constant cantilevers can be used to observe minute electric field fluctuations arising from thermal dielectric fluctuations in polymers [S. Kuehn et al., PRL, \textbf{96, }156103 (2006); S. Kuehn et al., JPCB 110, 14525 (2006)]. Here we show how ultra-sensitive cantilevers can also be used to measure the local charge diffusion constant via the effect of the associated electric field fluctuations on cantilever frequency and ringdown time. Analytical scaling laws and numerical simulations of the electric field power spectrum resulting from the thermal motion of holes in a N,N'-diphenyl-N-N'-bis(3-methylphenyl)-(1,1'-biphenyl)-4,4'-diamine (TPD) / polystyrene field effect transistor suggest that the local hole diffusion constant can be inferred from measurements of cantilever frequency and ringdown time as a function of tip height and charge density. We suggest a route to directly testing the Einstein relation by comparing the locally measured charge diffusion constant to the bulk field effect transistor mobility.   

Charge Transfer Statistics in Quantum Point Contact

We present the results of the experimental study of the Charge Transfer Statistics for a Quantum Point Contact up to the third cumulant. QPC creates a variable transmission probability barrier, and therefore allows to check the CTS predictions [1] beyond the Poissonian limit. It has been recently understood that the intrinsic CTS is strongly affected by the measurement circuit, see [2] and references therein. We calculated the effect of the measurement circuit for a simple and realistic model of a capacitively shunted resistive load. We found the experimental results to be consistent with the calculations. We believe the results to be the first measurements of the third cumulant in a system different from the low transmission tunneling junction. \newline \newline [1] L.\,S. Levitov, G.\,B. Lesovik, JETP Lett. {\bf 58}, 230 (1993). \newline [2] B.~Reulet, J. Senzier and D. E. Prober, Phys. Rev. Let. {\bf 91}, 196601 (2003).   

Thermopower of a Quantum Dot in a Coherent Region

Thermoelectric power can provide useful information on electron transmission processes. Recently, thermoelectric power of quantum dots made in two-dimensional electron gases and carbon nanotubes has been measured by several groups, and compared with the theory based on sequential-tunneling and co-tunneling. It, however, remains an unsolved problem to study how electron coherency during transmission affects the thermoelectric power. In this presentation, thermoelectric power due to coherent electron transmission through a quantum dot is theoretically discussed. In addition to the known features related to resonant peaks, we show that a novel significant structure appears between the peaks. This structure arises from the so-called transmission zero, which is characteristic of coherent transmission through several quantum levels. It has also been shown that these structures are sensitively suppressed by weak phase-breaking, and that the calculated thermoelectric power coincides with the co-tunneling theory for sufficiently large phase-breaking. It has been proposed that, due to sensitivity to phase breaking, thermoelectric power can be used to measure electron coherency in a quantum dot. We also present the improved Mott formula, which can reproduce correct results for arbitrary transmission probabilities. (Reference: T. Nakanishi and T. Kato: cond-mat/0611538.)   

Green Kubo calculations of thermal conductivity for skutterudites

The thermal conductivity of skutterudites have been studied experimentally for several years and the results clearly show a strong dependence on whether or not the skutterudite is filled. This result has been explained, and indeed predicted, by the presence of a rattling ion in the filled materials. On the other hand, it has been shown that the potential of the rattling ion is not dramatically anharmonic as expected within a simple rattling ion concept. In this work we will discuss the thermal conductivity of a realistic model of the skutterudites through a Green-Kubo calculation using molecular dynamics. We represent the interatomic potentials as Taylor series in displacements from equilibrium with up to quartic anharmonic terms. In this initial study we explore different central force parameters from empirical models and first principles calculations in the literature.   

Lattice thermal conductivity of porous silicon : Molecular dynamics study

Thermoelectric (TE) materials, which are important for power-generation and solid-state refrigeration devices, have received revived interest due to the discovery of a high figure of merit, $ZT$, in materials with reduced dimensions such as BiTe/SbTe superlattices or BiTe nanocomposites. Recently, nanowires and nano-porous materials have also been considered experimentally as good candidates for increasing $ZT$ beyond 3, considered a minimum for practical applications of TE materials. Although such materials are very promising, it is important to understand the underlying principles of how charge and heat transport occur at the nanoscale in order to predict the dependence of $ZT$ on, e.g., structure, surface chemistry, and defects. In this work, we perform theoretical studies of lattice thermal conductivities, $\kappa_{L}$, of nano-porous silicon with a range of configurations. Specifically, $\kappa_{L}$ is calculated using classical molecular dynamics with varying hole diameter, hole-hole distance, and hole passivation chemistry. These results are compared both with bulk calculations as well as the inverted case of nanowires, and $\kappa_{L}$ is discussed in terms of specific phonon scattering at surface boundaries.   

Session A42: Focus Session: Quantum Size Effects in Metallic Thin Films

Quantum size effects in metallic thin films: from thermodynamic stability to superconductivities

In ultra-thin epitaxial metallic film, confinement of electronic states along the vertical direction leads to the formation of quantum well states (QWS). Over the past few years it has been shown that such QWS have profound effects on the thermodynamic stability of thin metal films. It has also been shown that such QWS can modulate local free energy landscape and influence the kinetic processes of mass transport. More recently, evidences that such QWS can also impact collective electronic properties such as superconductivities have also been reported. This talk will focus on direct correlations of all these aspects.   

Non-classical second layer nucleation in Pb/Si(111) and the kinetics of the wetting layer.

By studying the island growth in stepwise deposition experiments with STM we showed two non-classical features i.e. the unusual second layer ring morphology and the crucial role of the wetting layer in the kinetics. The filling of the vacancy island inside the ring is much slower process than the ring formation due to higher radial diffusion barrier towards the island center. In addition Pb is transferred to unstable islands from the continuous spreading of the wetting layer to the island top uncovering the underlying 7x7 reconstruction. Combined Monte Carlo simulations on a novel Potential Energy Surface (PES) constructed with input from first principles calculation can account for most of these unusual non-classical observations.   

Quantum Modulation of Island Nucleation on Top of a Metal Nanomesa

We present a theoretical analysis of selectivity of nucleation location for the two-dimensional island on top of a metal nanomesa. It has been observed experimentally that the nucleation can start either along the periphery of the mesa top or in the middle, depending on the mesa thickness. Such an intriguing nucleation behavior is shown to be originated from the thickness-dependent mesa edge barrier for an adatom to jump off the mesa, induced by the quantum size effect. Based on the experimentally observed nucleation locations, we estimate that the mesa edge barriers for the 5- and 6-layer Pb(111) mesas can differ by $\sim 23\pm 7$ meV.   

In situ x-ray scattering investigation of the Pb/Si(111)7x7 interface

In situ x-ray scattering was used to investigate the structure of Pb deposited on the Si(111)7x7 surface, which exhibits a one- monolayer-thick wetting layer followed by quantum-size-effect nanocrystals at higher coverages. The structure of the wetting layer and its relationship to the nanocrystals is important to understand in order to explain the novel growth kinetics [PRL 96, 106105 (2006)] in this system as well as the charge transfer at the interface. The nanocrystals consume the wetting layer and exhibit a smooth buried interface while displacing the nanocrystal vertically by 0.4 angs. This study examines how the Pb modifies the Si, both in the wetting layer, which exhibits a modified 8x8 structure, and beneath the nanocrystals.   

Strongly-Driven Coarsening of Height-Selected Pb Islands on Si(111)

A rapid coarsening behavior was observed experimentally for Pb islands grown on Si(111) surface. It was found that quantum size effects lead to the breakdown of the classical Gibbs-Thomson analysis for this novel behavior. Here we propose a rate equation model where quantum size effects are incorporated by introducing an appropriate dependence of the chemical potential of Pb islands on their heights as well as on their curvatures. The evolution of the chemical potential of the wetting layer between islands is also incorporated. It is shown that rate equations predict evolution of the island density and height distribution in good agreement with experiments.   

Stability of magic planar Ag clusters

The spontaneous assembly of atoms and molecules in a system has attracted many research interests and created numerous potential applications. Utilizing the periodic pattern found on the Pb quantum islands, which are grown on the Si(111) surface, we have recently discovered that self-organized Ag planar clusters formed on these templates exhibit enhanced stability at some particular sizes [1]. Existence of the magic atom numbers in these clusters is mainly attributed to the electronic confinement effect. Here, we further explore the strength of these magic clusters subject to the temperature rise and oxygen exposure. Detailed calculations based on \textit{ab initio} density functional theory have also been performed. The results help establish the relation between the physical and chemical stability of a magic Ag cluster and its size and shape. Ref:[1] Ya-Ping Chiu, Li-Wei Huang, Ching-Ming Wei, Chia-Seng Chang, and Tien-Tzou Tsong, Phys. Rev. Lett. \textbf{97}, 165504 (2006).   

Self Organization of Pb Islands on Si(111) Caused by Quantum Size Effects

Growth of metallic Pb islands on Si(111) by vacuum deposition was studied in real time using synchrotron x-ray diffraction. The islands coarsen and order, maintaining a nearly uniform inter-island distance but without angular correlation. The resulting inter-island structure is akin to a two-dimensional liquid. Over a wide temperature range, the inter-island ordering is well correlated with the development of ``magic'' island heights caused by energy minimization of the Pb electrons. The results demonstrate quantum confinement effects as a driving force for self organization, as opposed to strain effects that generally govern the formation of semiconductor quantum dot arrays.   

First-principles Study of Pb(111) Nanofilms in the Quantum Regime

We report first-principles calculations to investigate surface free energy, interlayer spacing, surface stress, and surface self-diffusion barrier for Pb(111) films in the thickness range of 1 to 31 monolayers, where the quantum size effect (QSE) dominates. We show that similar to surface free energy, all these properties exhibit an oscillation behavior and a beating pattern as a function of film thickness. We will discuss correlations between these properties in terms of QSE.   

Strength modulation of quantum-well states in Pb islands with periodic distortions

We use scanning tunneling microscopy and spectroscopy to revisit the system of three-atomic- layer Pb islands with two types of patterns grown on Si(111) surface. Our results demonstrate that the pattern on the island surface appears as the superposition of geometric corrugation and local variation of the electronic structure. The former originates from two kinds of interface relaxations, resulting in two types of periodic distortions in the Pb island. The latter is due to the periodic strength modulation of quantum-well states in Pb islands, causing inhomogeneity in the integration of the density of states, and the pattern is bias-dependent. This strength modulation of the quantum-well states can be correlated to the electronic screening effect induced by the lattice distortion in Pb islands.   

Coherent Electronic Fringe Structure in Incommensurate Silver-Silicon Quantum Wells

Atomically uniform Ag films grown on highly doped n-type Si(111) substrates show fine-structured electronic fringes near the Si valence band edge as observed by angle-resolved photoemission. No such fringes are observed for Ag films grown on lightly doped n-type substrates or p-type substrates, although all cases exhibited the usual quantum well states corresponding to electron confinement in the film. The fringes correspond to electronic states extending over the Ag film as a quantum well and reaching into the Si substrate as a quantum slope, with the two parts coherently coupled through an incommensurate interface structure.   

First-principles studies of quantum growth of PbBi alloy films

Quantum growth of Pb$_{0.89}$Bi$_{0.11}$ alloy films freestanding or grown on Si(111) and Ge(111) substrates has been studied using first-principles calculations within density functional theory. Our studies show that the surface energy, work function, and lattice relaxation of the quantum alloy films all oscillate strongly with the film thickness. Similar to the case of pure Pb(111) films, the oscillation pattern is bilayer, interrupted with even-odd crossovers. However, the positions of the crossovers and the beating periodicity can be tuned by the contents of Bi in the alloys, with the beating periodicity given by 13ML, 15ML and 17ML for Pb$_{0.89}$Bi$_{0.11}$, Pb$_{0.86}$Bi$_{0.14}$ and Pb$_{0.75}$Bi$_{0.25, }$respectively. These results are in quantitative agreement with experiment.   

Umklapp-Mediated Quantization of Electronic States in Ag Films on Ge(111)

We employ angle-resolved photoemission to study the electronic structure of atomically uniform films of Ag grown on Ge(111). A new kind of quantum well state is observed near a specific emission direction away from the surface normal. In contrast with the usual quantum well state arising from electron confinement by specular reflections at the surface and interface of the film, the new kind involves retroreflections, or umklapp reflections, at the interface. It requires four reflections, instead of the usual two reflections, to complete a coherent interference path.   

The Phases of Ag on Ge(111): A Low Energy Electron Microscopy Investigation.

The phases of Ag on Ge(111) have been investigated with Low Energy Electron Microscopy (LEEM). We have studied the growth of the well known (4x4) and ($\surd $3x$\surd $3)R30$^{o}$ phases of Ag. LEEM images show the (4x4) phase grows on the surface with a high dependency on surface steps. The ($\surd $3x$\surd $3)R30$^{o}$ phase then grows as the Ag concentration increases with little dependence on the steps. These features are explained by the diffusivity of Ag on the surface. LEEM has also been used to study the phase transitions at the Ag desorption temperature. Video rate data shows an interesting phase transition as small domains of Ag abruptly change from the ($\surd $3x$\surd $3)R30$^{o}$ to the (4x4) phase and then from the (4x4) to a disordered 2D gas phase. Although the disordered phase shows no contrast in the LEEM images we know it exists because as the sample is cooled down the remaining Ag on the surface condenses back into the (4x4) and ($\surd $3x$\surd $3)R30$^{o}$ phases depending on how much Ag has desorbed.   

Session A43: Focus Session: Physics of Thermoelectric Materials and Phenomena I

Searching for new Thermoelectric Materials from Theory

Thermoelectric (TE) materials is a type of energy materials that can be applied to directly convert waste heat into electricity. Research on advanced TE materials has been a world-wide focus in recent years. By employing density functional \textit{ab initio} methods, we are trying to find new compounds with promising TE performance. In this talk, the following topics will be mainly covered. 1) General discussion on the directions of searching for new TE compounds with good performance; 2) Filling fraction limits (FFLs) for filler impurities in CoSb$_{3}$. By combining \textit{ab initio} calculations and thermodynamic consideration, we explained the FFLs, revealed the underlined physical mechanism behind FFLs, and found a simple rule for selecting new filler atoms. A few new filled skutterudites with ultra high filling fractions of impurities were predicted theoretically and synthesized experimentally, and they do show promising thermoelectric performance. 3) Rare-earth-related Half-Heusler compounds are used as model systems to discuss the effect of localized electronic states on thermoelectric performance. By that, we will partially discuss the possibility of going beyond narrow-gap materials for thermoelectrics.   

Atomic Ordering and Gap Formation in Ag-Sb Based Ternary Chalcogenides

Ag-Sb based ternary chalcogenides are important in optical phase change and thermoelectric applications. Although discovered almost 50 years ago and thought to be semiconductors, a fundamental understanding of their electronic structures had been lacking. We report \textit{ab initio} electronic structure studies using density functional theory (DFT) to explain their observed atomic structures, the physics of gap formation and their low-energy properties. Total energy calculations yield theoretical atomic structures which are consistent with experiment. Ag/Sb ordering is found to have a huge impact on the electronic structure near the Fermi energy. It gives pseudogap structure in some ordered structures, and either a pseudogap or a gap in others. For the lowest energy structures, as one goes from Te to Se to S, the (indirect) band gap goes from being negative to positive. Transport properties of AgSbTe$_{2}$ can be understood in terms of a small intrinsic band gap and extremely shallow impurity states. The calculated negative band gap in this compound can be ascribed to the defficiency of DFT.   

First-principles Studies of ErAs and ErAs/GaAs Heterostructures

We present a computational investigation of the materials properties of rare-earth pnictides. ErAs, a semimetal with rock-salt structure, has been demonstrated to grow epitaxially on GaAs substrates with a continuous As sublattice and low strain. Such structures have the potential to provide high-quality thermoelectric materials. Using plane-wave based density-functional methods we have performed a detailed investigation of the effects of $f$ electrons on the electronic and atomic structure, using both norm- conserving pseudopotentials and the projector-augmented-wave method. Our preliminary results indicate that it is possible to obtain an adequate description of the band structure without having to include the $f$ electrons as valence electrons. The resulting reduction in computational complexity allows us to perform explicit simulations of heterostructures. We have also calculated deformation potential constants, to be used in detailed comparisons with experiments where strain affects the band structure.   

Electronic and vibrational properties of the Na$_{16}$Rb$_{8}$Si$_{136}$ and K$_{16}$Rb$_{8}$Si$_{136}$ clathrates

We have studied the electronic and vibrational properties of the Na$_{16}$Rb$_{8}$Si$_{136}$ and K$_{16}$Rb$_{8}$Si$_{136}$ clathrates, using the local density approximation. In qualitative agreement with the rigid-band model, the electronic band structures display no major modifications due to inclusion of the alkali metal guests. However, the electronic densities of states show two sharply peaked structures and a dip near the Fermi level. This feature may help to qualitatively explain the temperature dependent Knight shift observed for the NMR active nuclei in Na$_{16}$Rb$_{8}$Si$_{136}$. Phonon dispersion curves show low frequency, localized ``grattler'' h modes for both clathrates. These modes may efficiently scatter the heat carrying host acoustic phonons, potentially suppressing the lattice thermal conductivity. Based on the harmonic oscillator model and on our calculated rattler frequencies, we predict the isotropic mean square displacement amplitude (U$_{iso})$ of the various guests in these clathrates. Our predicted values of U$_{iso}$ for Na and Rb in Na$_{16}$Rb$_{8}$Si$_{136}$ are found to be in good agreement with experiment.   

Theoretical study of lattice thermal conductivity in Si clathrate materials

Recent experiments have shown that Si and Ge clathrate crystals are promising candidates as high ZT thermoelectric materials because of their glass-like low thermal conductivity. Based on a detailed \textit{ab initio} calculation of equilibrium statistical properties, we conclude that the distinct structural differences in the diamond-structured Si (d-Si) and the type-II Si clathrate (Si$_{136})$ only lead to some minor differences in the equilibrium thermal properties in the two tetrahedrally bonded Si phases. In this talk, we will present our recent calculations of non-equilibrium thermal transport properties of d-Si and Si$_{136}$ crystals, based on the statistical linear response theory. The key step of our calculation of lattice thermal conductivity ($\kappa )$ is to evaluate the fluctuation-correlation relation of bulk heat currents at equilibrium conditions. In the current study, we have adopted the molecular dynamics (MD) simulation techniques, using large atomic supercell models and the Tersoff potential. Our results suggest that the cage-like open framework of clathrate crystals will lead to a factor of 5-8 reduction in thermal conductivity. The MD simulation results are also discussed in the context of the simple kinetic transport model. The ``anomalous'' oscillation feature in the correlation functions of clathrate materials is explained.   

Lattice Thermal Conductivity of Superlattices from an Adiabatic Bond Charge Model

The adiabatic bond charge model (ABCM) has successfully rendered phonon dispersions of a host of bulk semiconductors [1,2] and has also been used to calculate the phonon dispersions in quantum well superlattices [3]. We have developed an ABCM for superlattices and combined it with a symmetry-based representation of the anharmonic interatomic forces to calculate the lattice thermal conductivity of short-period superlattices, using an iterative solution to the Boltzmann-Peierls equation [4]. We compare our ABCM results with those obtained from some commonly used models for the interatomic forces in semiconductors to assess the importance of accurate descriptions of the phonon dispersions in thermal conductivity calculations. [1] W. Weber, Physical Review B 15, 4789 (1977). [2] K. C. Rustagi and W. Weber, Solid State Communications 18, 673 (1976). [3] S. K. Yip and Y. C. Chang, Physical Review B 30 7037 (1984). [4] D. A. Broido, A. Ward, and N. Mingo, Physical Review B 72, 014308 (2005).   

First principles Theory of the Lattice Thermal Conductivity of Si and Ge

The room temperature lattice thermal conductivity of high quality crystalline semiconductors is limited by the scattering between phonons arising from the anharmonicity of the interatomic potential. We have calculated the lattice thermal conductivity of isotopically enriched silicon and germanium, combining a first principles approach to extract the harmonic and anharmonic interatomic force constants [1] with an iterative solution of the full Boltzmann-Peierls equation for phonon transport [2]. Our calculated lattice thermal conductivities for Si and Ge, obtained with no adjustable parameters, show very good agreement with measured values [3,4] and are a marked improvement to results obtained previously using empirical interatomic potentials [2]. [1] G. Deinzer, G. Birner, and D. Strauch, Physical Review B 67, 144304 (2003). [2] D. A. Broido, A. Ward, and N. Mingo, Physical Review B 72, 014308 (2005). [3] M. Asen-Palmer, et al, Physical Review B 56, 9431-9447 (1997). [4] T. Ruf, et al, Solid State Communications 115, 243-247 (2000).   

Three-Phonon Phase Space as an Indicator of the Lattice Thermal Conductivity in Semiconductors

The room temperature lattice thermal conductivity of many semiconductors is limited primarily by three-phonon scattering processes arising from the anharmonicity of the interatomic potential. We employ an adiabatic bond charge model [1,2] for the phonon dispersions to calculate the phase space for three-phonon scattering events of several group IV and III-V semiconductors. We find that the amount of phase space available for this scattering in materials varies inversely with their measured thermal conductivities. Anomalous behavior occurs in III-V materials having large mass differences between cation and anion, which we explain in terms of the severely restricted three-phonon phase space arising from the large gap between acoustic and optic phonon branches. \newline \newline [1] W. Weber, Physical Review B 15, 4789 (1977). \newline [2] K. C. Rustagi and W. Weber, Solid State Communications 18, 673 (1976).   

Monte Carlo Simulation of Thermal Conductivity in Randomly Distributed Nanowire Composites

In this paper, we investigated the thermal conductivity of composites made of two types of randomly stacked nanowires with high contrast ratio of bulk thermal conductivity. Thermal conductivity predictions based on solving the phonon Boltzmann transport equation by using the Monte Carlo method are presented for different contrast ratios of thermal conductivity, sizes of nanowires and the volumetric fractions in the composites. For composites made of nanowires with high contrast ratio thermal conductivity, the thermal conductivity of the nanocomposites increase dramatically when the volumetric fraction of high thermal conductivity nanowire is higher than the geometry percolation threshold, although existing correlations in percolation theory do not fit the results due to the phonon interface scattering. On the other hand, when the the size of nanowires is small and the volumetric fraction of high thermal conductivity nanowire is less than percolation threshold, the thermal conductivity of the nanocomposites decreases with increasing the volumetric fraction of the high thermal conductivity nanowires. The results of this study may help the development of nanoscale thermoelectric materials in which the figure of merit is optimized by choosing appropriate nanowire size, property contrast and composition. RY acknowledges the funding support for this work by DoD/AFOSR MURI grant FA9550-06-1-0326. The simulation was conducted on a 24-node cluster supported by Intel Corporation and managed by Prof. Gang Chen and Mr. Lu Hu at MIT.   

Optimized thermal conductivities of Silicon Germanium nanowires

The measure of the thermoelectric efficiency of a material is given by its ``Figure of merit'' (Z), which is inversely proportional to its thermal conductivity, and directly proportional to its electrical conductivity. Alloys of Si and Ge are promising thermoelectric materials, since they can be engineered so as to have a low thermal conductivity relative to their electrical conductivity. We present molecular dynamics simulations of the thermal conductivities of Si$_{x}$Ge$_{1-x}$ nanowires, and an optimization strategy to obtain maximal values of ZT for these systems. We found that Si-Ge alloy nanowires have a significantly lower thermal conductivity than pure Si or Ge nanowires of the same diameter. Furthermore the alloy ordering is found to significantly effect thermal conductivities, and hence is a key parameter to control and vary in order to optimize thermal conductivities and eventually Z values. Towards this end optimal orderings of Si and Ge for low thermal conductivities have been predicted. This work was performed under the auspices of the U.S. Dept. of Energy at the University of California/Lawrence Livermore National Laboratory under contract no. W-7405-Eng-48.   

First Principles Studies of Thermoelectric Figure of Merit of Si and SiGe Nanowires

We present predictions of the thermoelectric figure of merit (ZT) of Si$_{x}$Ge$_{1-x}$ nanowires based on Density Functional Theory calculations and cluster expansion optimizations. The electrical conductivity, $\sigma $, and Seebeck coefficient, S, were obtained using the Boltzmann transport equation in the relaxation time approximation, and first principles, electronic structure calculations. The thermal conductivity was computed using classical molecular dynamics runs. A range of SiGe nanowires with different Ge concentrations and Ge distributions were investigated. We found that the transport coefficients $\sigma $, S, and thus ZT strongly depend on the wire growth direction, surface structure, and Ge concentration, and Ge distribution. These parameters were varied to obtain a nanostructure with an optimal, high figure of merit above 2 or 3, depending on the electronic doping.   

Calculation of figure of merit for Bi$_2$Te$_3$ nanostructures

Bi$_2$Te$_3$-based materials comprise one class of promising candidates for novel thermoelectric devices, for which low/high thermal/electrical conductivity are desired. We shall present calculations highlighting the effects of reduced dimensionality on the thermoelectric figure of merit ZT for such materials, with particular emphasis on Bi$_2$Te$_3$ / Sb$_2$Te$_3$ superlattices. The calculation consists of two components, a tight-binding electronic calculation for the electrical conductivity and electronic contribution to the thermal conductivity and a Green-Kubo molecular dynamics approach for the lattice contribution to the thermal conductivity.   

Non-equilibrium thermoelectric transport in thin film heterostructures

The Monte Carlo technique is used to calculate thermoelectric transport properties across thin-film heterostructures. We study the size and position dependence of the Seebeck coefficient across a thin film InGaAsP barrier layer sandwiched between two InGaAs contact layers. With decreasing size, the effective Seebeck coefficient is increased. The transition between pure ballistic thermionic transport and fully diffusive thermoelectric transport is described. We characterized the non-equilibrium length of the device and deduce the power dissipated to the lattice.   

Session A44: Focus Session: Nanoscale Transport - Wires, Dots, Point Contacts

Time Resolved Characterization of Tunneling in a Quantum Dot

Measurements are presented of the rates for tunneling on and off a laterally defined GaAs quantum dot as a function of drain source bias, plunger gate voltage, and magnetic field. The measurements are obtained using a quantum point contact as a real-time charge sensor, and utilizing pulsed gate techniques. In zero magnetic field, we find evidence that the tunneling is elastic, and that the observed exponential dependences of the tunneling rates on drain-source bias and plunger gate voltage agree quantitatively with a model that takes into account changes in the electron energy relative to the top of the tunnel barrier. In a magnetic field applied parallel to the two dimensional electron gas, we resolve contributions to the tunneling from the two Zeeman sublevels, and discuss how the magnetic field modifies the tunneling rates. This work has been supported by the ARO (W911NF-05-1-0062), the NSF (DMR-0353209), and in part by the NSEC Program of the NSF (PHY-0117795).   

Charge Transitions in a Quantum Dot Induced by an Adjacent Quantum Point Contact

Quantum point contact (QPC) charge sensors have become an important tool for measuring the occupation of laterally gated quantum dots in AlGaAs/GaAs heterostructures. However, electrical fluctuations across the QPC have been shown to induce changes in the dot occupation. Using real-time charge detection techniques, we observe this effect in the increased rates at which electrons tunnel on and off the dot with increasing bias applied across the adjacent QPC. Applying an in-plane magnetic field splits the orbital states by the Zeeman energy. We present measurements of the probability of being in the excited spin state after a large bias pulse is applied across the QPC. We propose that changes in dot occupation can qualitatively account for an observed enhancement in the probability of being in the excited spin state. This work is supported by the ARO (W911NF-05-1-0062), the NSF (DMR-0353209) and in part by the NSEC Program of the NSF (PHY-0117795).   

Interpretation of Fano lineshape reversal in quantum waveguides

Fano lineshape parameter (q) reversal is a proxy for interaction beyond the usual interference of indistinguishable quantum pathways. Reversal of the Fano parameter has been observed recently in quantum dots (QD). We show that such a profile reversal may come about from the interaction of interlopping over-the-top states (shape resonances) in the ``non-resonant'' channel with the QD bound states, interacting with the continuum channel (Feshbach resonances). Using this mechanism we show that with minimal modifications of the QD parameters, we can affect the presence or absence of interlopping resonances and hence lineshape profile reversal, as a way of coherence engineering.   

Spontaneous Spin Polarization in Quantum Point Contacts

Mesoscopic systems exhibit a range of non-trivial spin-related phenomena in the low density regime, where inter-particle Coulomb interactions become comparable to their kinetic energy. In zero-dimensional systems spontaneous polarization of a few-electron quantum dot leads to a spin blockade, a remarkable effect where mismatch of a single spin blocks macroscopic current flow. In two-dimensional hole gases there is an experimental evidence of a finite spin polarization even in the absence of a magnetic field. In one-dimensional systems – quantum wires and quantum point contacts - a puzzling so-called ``0.7 structure'' has been observed below the first quantization plateau. Experiments suggest that an extra plateau in the conductance vs gate voltage characteristic at $0.7\times 2e^2/h$ is spin related, however, the origin of the phenomenon is not yet understood and is highly debated. We report direct measurements of finite polarization of holes in a quantum point contact (QPC) at conductances $G < 2e^2/h$ [1]. We incorporated QPC into a magnetic focusing device so that polarization can be measured directly using a recently developed spatial spin separation technique [2]. Devices are fabricated from p-type GaAs/AlGaAs heterostructures. A finite polarization is measured in low-density regime, when conductance of a point contact is tuned to $< 2e^2/h$. We found that polarization is stronger in samples with well defined ``0.7 structure''. \newline\newline [1] L.P. Rokhinson, L.N. Pfeiffer and K.W. West,``Spontaneous spin polarization in quantum point contacts,'' Physical Review Letters {\bf 96}, 156602 (2006) \newline [2] L.P. Rokhinson, V. Larkina, Y.B. Lyanda-Geller, L.N. Pfeiffer and K.W. West, ``Spin separation in cyclotron motion,'' Physicsl Review Letters {\bf 93}, 146601 (2004)   

``0.7'' Conductance Anomaly in quantum point contacts

We demonstrate that an anomaly close to 0.7(2e$^{2}$/h) [rather than 0.5(2e$^{2}$/h) as in a Kondo-type model$^{1}$] in the conductance plot of quantum point contacts$^{2}$ arises naturally in a model with a quasi-bound state \textit{at the Fermi level} within an Anderson impurity model framework. The same model yields good agreement with the observed dependence$^{3}$ of conductance with gate voltage, magnetic field, temperature and also with the observed zero bias anomaly. Further implications within this model are explored and contrasted with other proposed explanations of the anomaly$^{1}$. \newline 1. Y. Meir, K. Hirose and N. S. Wingreen, Phys. Rev. Lett. \textbf{89,} 196802 (2002). \newline 2. K. J. Thomas \textit{et al.}, Phys. Rev. Lett. \textbf{77}, 135 (1996). \newline 3. S. M. Cronenwett \textit{et al.}, Phys. Rev. Lett.\textbf{ 88}, 226805 (2002).   

Spin-orbit induced spin-density wave in a quantum wire

We consider an interacting quantum wire in the presence of a magnetic field and spin-orbit interaction. We show that under a subtle interplay of magnetic and spin-orbit terms, new scattering channels open up when the magnetic field and the spin-orbit axes are orthogonal: two electrons with opposite momentum and in the same spin-subband scatter into a different spin-subband while conserving momentum. This scattering process is relevant and results in a spin-density wave (SDW) state. We next analyze charge transport property in a scenario when the SDW state survives the presence of a single weak impurity. We find that the single particle back-scattering off a non-magnetic impurity becomes irrelevant. The sensitivity of the SDW state, and hence the charge transport, to the mutual orientation and magnitude of the magnetic and spin-orbit terms can be used for the experimental verification of this novel field and spin- orbit induced state.   

Suppression of Landau level spin splitting in quantum point contacts

We investigate low temperature transport properties of split-gate devices lithographically patterned on a GaAs/AlGaAs heterostructure containing a 2D electron gas with mobility 2000 m$^{2}$/Vs in a perpendicular magnetic field. By using quantum point contacts (QPCs) with different lithographic widths and varying the voltage applied on the gates for each QPC, we can control the width of the conduction channel continuously from $\sim$3000 to $\sim$100nm. The width of the channel is estimated from the low-field magnetic field dependence of the conductance through the QPC. We find that the spin-splitting of the Landau levels is suppressed in the QPCs compared to the bulk, and we measure the filling factor $\nu$$_{max}$ above which spin splitting can no longer be observed. Surprisingly, we find that $\nu$$_{max}$ is approximately half the number of quantum channels in the QPC for all widths less than ~1200 nm. This work was partially supported by ARO (W911NF-05-1-0062), by the NSEC program of NSF (PHY-0117795), by NSF (DMR-0353209) and by Project Q of Microsoft.   

Effect of a strong spin-charge separation on tunneling into a 1D wire with impurity

We analyze the tunneling of electrons into a 1D nanowire with a large difference in velocities of spin and charge excitations: charges are ``fast,'' spins are ``slow.'' This system is modeled as a Wigner crystal of charges whose spins are ordered as in a antiferromagnetic Heisenberg spin chain. If the wire contains an impurity, electron tunneling in its vicinity causes a novel type of the orthogonality catastrophe. The tunneling electron shifts the charge distribution of a Wigner-crystal, which causes a shake-up processes in the spin sector. The corresponding suppression of the tunneling has a novel temperature dependence, which can be used for an experiemental validation of the spin-charge separation in low-density nanowires.   

Quantum Dots on Silicon Nanowires

Silicon nanowires have single-crystal structure, well-controlled doping, and can be integrated into devices using either directed assembly and dielectrophoresis or electron-beam lithography and lift-off. Such nanowires, with nanometer size in two dimensions, provide advantages for the fabrication of ultra-small silicon quantum dots with potentially long spin coherence times. We present methods for the fabrication of silicon nanowire-based single electron transistors, and we show results of both room temperature and low temperature transport measurements. The metal electrode structure and annealing process have been intensively investigated to obtain the necessary contact properties. Either metal/nanowire contacts or electrostatically depleted regions have been used for tunneling barriers for quantum dots. Coulomb blockade has been demonstrated successfully, showing 1.3 aF and 1.1 meV for the gate capacitance and the charging energy respectively. Studies of double quantum dots and spin-dependent effects are ongoing.   

Ballistic hole transport and spin-orbit effects in GaAs quantum wires

Studying the spin degree of freedom of charge carriers in semiconductors has become an area of significant current interest. Although spin-orbit coupling is extremely strong in p-type semiconductors such as GaAs, to date there have been only a limited number of experiments on holes in p-GaAs nanostructures. Here we present results from extremely high quality 1D hole quantum wires that show up to 10 clean and stable quantized conductance plateaus at B=0 [1.2]. The strong spin-orbit coupling leads to an extreme anisotropy of the Zeeman spin splitting of the 1D hole levels depending on whether the magnetic field is parallel or perpendicular to the quantum wire. Our results show that confining holes to a 1D system fundamentally alters their spin properties, and that it is possible to tune these properties by electrostatically changing the width of the 1D system [3]. [1] O. Klochan, \textit{et al}, Appl. Phys. Lett. \textbf{89}, 092105 (2006). [2] R. Danneau, \textit{et al}, Appl. Phys. Lett. \textbf{88}, 012107 (2006) [3] R. Danneau, \textit{et al}, Phys. Rev. Lett., \textbf{97} 026403 (2006).   

Quantum dots in graphene

We suggest a way of confining quasiparticles by an external potential in a small region of a graphene strip. Transversal electron motion plays a crucial role in this confinement. Properties of thus obtained graphene quantum dots are investigated theoretically for different types of the boundary conditions at the edges of the strip. The (quasi)bound states exist in all systems considered. At the same time, the dependence of the conductance on the gate voltage carries an information about the shape of the edges.   

Microwave Conductivity of Silicon Nanowire Arrays

We have measured the microwave conductivity spectra of silicon nanowire (SiNW) parallel arrays from room temperature to 4K. ~Doped (n-type and p-type) and nominally undoped SiNWs were synthesized by vapor-liquid-solid growth and assembled by AC dielectrophoresis into parallel arrays spanning the electrodes of coplanar waveguides (CPWs). ~The CPW complex reflection and transmission coefficients were measured from 0.1 to 50 GHz. ~Measurements of identical bare CPWs were utilized to calculate the frequency dependent complex conductivity and power dissipation of the SiNW arrays and provide estimates of these quantities for individual SiNWs in this configuration. The conductivity of the undoped SiNWs is purely imaginary, indicating a bound charge response. The doped SiNWs have a real component that, upon preliminary analysis, increases with frequency consistent with free charge disorder effects. No loss is measured for the undoped SiNWs, but loss due to the doped SiNWs is consistently measured and increases with frequency. *Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.   

Persistent mobility edges and anomalous quantum diffusion in order-disorder separated quantum films

A novel concept of order-disorder separated quantum films is proposed for the design of ultra-thin quantum films of a few atomic layers thick with unconventional transport properties. The concept is demonstrated through studying an atomic bilayer comprised of an ordered layer and a disordered layer. Without the disordered layer or the ordered layer, the system is a conducting two-dimensional (2D) crystal or an insulating disordered 2D electron system. Without the order-disorder phase separation, a disordered bilayer is insulating under large disorder. In an order-disorder separated atomic bilayer, however, we show that the system behaves remarkably different from the conventional ordered or disordered electron systems, exhibiting metal-insulator transitions with persistent mobility edges and super-diffusive anomalous quantum diffusion. Application of the model to double-layer graphene systems will be discussed.