A Chern-Simons Effective Field Theory for the Pfaffian Quantum Hall State
E. Fradkin,* C. Nayak (UCSB), A. Tsvelik (Oxford Univ.), F. Wilczek (IAS-Princeton Univ.)
National Science Foundation, DMR 98-17941

We present a low-energy effective field theory describing the universality class of the Pfaffian quantum Hall state. To arrive at this theory, we observe that the edge theory of the Pfaffian state of bosons at n = 1z is an SU(2)2 Kac-Moody algebra. It follows that the corresponding bulk effective field theory is an SU(2)2 Chern-Simons theory with coupling constant K = 2. The effective field theories for other Pfaffian states, such as the fermionic one at n = 1z are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasi-particles in the context of this effective field theory.

Adaptive Grid Methods for Phase Field Models of Microstructure Development
N. Goldenfeld,* J. Dantzig (Mech. & Indus. Engr.), N. Provatas
National Aeronautics and Space Administration, NAG 8-1249

We are developing adaptive grid methods for solving asymptotically efficient phase field models of microstructure development. Present applications include free dendritic growth, directional solidification, and eutectic growth.

Andreev Interferometry as a Probe of the Pseudogap State
P. M. Goldbart,* D.E. Sheehy
U.S. Department of Energy, DE-FG02-96ER45439 (In cooperation with the Materials Research Laboratory)

Schemes for probing the so-called pseudogap state of high-temperature superconductors are being addressed in the context of tunneling from mesoscopic contacts. The primary issue being explored is this: To what extent can contributions to the conductance that are sensitive to the phase of the superconductivity be employed to measure spatial superconducting correlations in the pseudogap state?

Andreev Reflection and Spectral Geometry
P. M. Goldbart,* I. Adagideli
U.S. Department of Energy, DE-FG02-96ER45439 (In cooperation with the Materials Research Laboratory)

The aim of this project is to explore the dynamics of quasi-particles propagating near normal-to-superconductor interfaces. The central theme is Andreev reflection: the mechanism by which low-energy electron quasi-particles impinging on a superconducting region are retroreflected from it and converted into hole quasi-particles, their velocities and charges thereby being reversed. This reflection phenomenon plays a striking role in the context of Andreev billiards (i.e., normal metal structures surrounded by superconductor) in which quasi-particles are confined by Andreev reflection (rather than conventional reflection). In this setting, the connection between the geometry of region of confinement and the spectrum of available quantal energy levels represent a rich and fascinating new theme in the venerable subject of spectral geometry.

Andreev Reflection in the Fractional Quantum Hall Effect
E. Fradkin,* N. P. Sandler, C. Chamon
National Science Foundation, DMR 98-17941

We study the reflection of electrons and quasi-particles on point-contact interfaces between fractional quantum Hall (FQH) states and normal metals (leads), as well as interfaces between two FQH states with mismtached filling fractions. We classify the processes taking place at the interface in the strong coupling limit. In this regime a set of quasi-particles can decay into quasi-holes on the FQH side and charge excitations on the other side of the junction. This process is analogous to an Andreev reflection in normal-metal/superconductor interfaces.

Applications of Field Theory to Condensed Matter Physics
E. Fradkin,* M. Stone, S. Kos
National Science Foundation, DMR 98-17941

This program is aimed at advancing the theoretical understanding of a variety of condensed matter systems, each involving many strongly coupled degrees of freedom. Attention is primarily focused on the following areas: electronic liquid crystal phases in Mott insulators; the quantum Hall effect; superfluids and superconductors, including vortex motion in dirty systems, quantum critical behavior of magnetic impurities in D-wave superconductors.

Aspects of Cuprate Superconductivity
A. J. Leggett,* R. Ramazashvili, H. Westfahl, M. Turlakov, V. Lukic
NSF Science and Technology Center for Superconductivity; John D. and Catherine T. MacArthur Foundation; University of Illinois Center for Advanced Study

We are exploring a scenario for cuprate superconductivity in which a major factor is the reduction, due to increased screening by the Cooper pairs, of the long-wavelength, mid-infrared-frequency part of the Coulomb interaction. In addition, independently of this scenario, we are attempting to explain the c-axis transport properties of the cuprates and are looking at some problems associated with the 'pseudogap' regime and with the peculiar features resulting from the existence of gap nodes.

Charge Transport in Manganites and the Role of Quantal Phases
P. M. Goldbart,* Y. Lyanda-Geller, M.B. Salamon
U.S. Department of Energy, DE-FG02-96ER45439 (In cooperation with the Materials Research Laboratory)

Charge transport in manganites is investigated theoretically, with particular attention being paid to the neighborhood of the ferromagnet-to-paramagnet phase transition. The extent to which inelastically assisted carrier hopping between states localized by magnetic disorder provides the dominant transport mechanism is being examined. In the context of the anomalous Hall effect, the roles played by the Pancharatnam and spin-orbit quantal phases are being studied.

Computational Methods for Materials
R. M. Martin,* E. Koch, in collaboration with O. E. Gunnarsson, Max Planck Institute, Stuttgart, and the Humboldt Foundation, Germany
University of Illinois

We have developed a new method for quantum Monte Carlo simulations of interacting electrons, and we have applied the method to study the doped fullerenes. The key feature is that the bands crossing the Fermi surface are degenerate, which leads to new effects not present in one-band models. Our work shows that the actual systems are near a metal-insulator transition and are metallic only because of the degeneracy.

Distinct Universal Conductances in Tunneling to Quantum Hall States-The Role of Contacts
E. Fradkin,* C. Chamon
National Science Foundation, DMR 98-17941

We have shown that different universal values can be obtained for the two-terminal conductance of a fractional quantum Hall state. We have also shown that devices with different types of contacts between the reservoir and the FQH state lead to distinct universal values of saturation conductance which are rational multiples of e2/h. We have demonstrated that the problem of tunneling between an electron gas and a fractional quantum Hall state through an impurity is exactly equivalent to the problem of tunneling between a chiral Fermi liquid and a chiral Luttinger liquid. We are investigating in detail the case of tunneling to a n = 1{ FQH state which we show to be equivalent to the problem of tunneling between two G = 1z chiral Luttinger liquids. This system provides an experimental realization of this important exactly solvable case.

Electronic Liquid Crystal Phases of a Doped Mott Insulator
E. Fradkin,* S. Kivelson (UCLA), V. Emery (Brookhaven)
National Science Foundation, DMR 98-17941

The character of the ground state of an antiferromagnetic insulator is fundamentally altered upon addition of even a small amount of charge. The added charge agglomerates along domain walls at which the spin correlations suffer a p phase shift. In two dimensions, these domain walls are 'stripes' which are either insulating, or conducting. Here it is shown that a transition to a charge density wave (CDW) is eliminated if the zero-point energy of transverse stripe fluctuations is sufficiently large in comparison to the CDW coupling between stripes. As a consequence, there exist novel electronic quantum liquid crystal phases which constitute new states of matter and which can be either a high-temperature superconductor or two-dimensional anisotropic 'metallic' non-Fermi liquids.

Electronic Structure of Condensed Matter
D. M. Ceperley,* R. M. Martin,* F. H. Zong, M. Dewing, Y. Kim, T. Wilkens
National Science Foundation, DMR 98-02373

The goals of our research are to develop computational methods for condensed matter starting from the fundamental many-body equations. The primary methods used are quantum Monte Carlo simulations, which can find exact properties of many-body systems, and density functional methods, which can be applied to diverse solids and liquids. We are combining these approaches to create new methods and to test the accuracy of calculations on materials. Current research includes studies of electron fluids, metalization of hydrogen at high pressure, simulations of solids and liquids as a function of temperature, and atoms in strong magnetic fields.

Electronic and Optical Properties of Surfaces and Heterostructures
Y.-C. Chang,* G. Li, R. Furstenberg
University of Illinois

This project concentrates on theoretical studies of electronic and optical properties of semiconductor surfaces and heterostructures by using a newly developed first-principle pseudopotential method in planar-orbital basis (products of two-dimensional plane waves and one-dimensional Gaussian functions). The method is efficient and accurate and well suited for treating layered systems. In particular, we are investigating the work functions, hydrogen passivation, and optical responses of various semiconductor surfaces. Planar Wannier functions can be constructed directly from Bloch states expressed in terms of planar orbitals and they can be used for modeling of realistic heterostructure devices.

Equilibrium and Nonequilibrium Phenomena in Condensed Matter
N. Goldenfeld,* Y. Oono
National Science Foundation,DMR-99-70690

We are developing renormalization group methods for spatially extended dynamical systems, including fluid turbulence, phase ordering and pattern formation problems. We are also investigating the critical phenomena in high-temperature superconductors, the role of phase fluctuations, and the pseudogap state.

Exchange Coupling in Magnetic Multilayers
Y. C. Chang,* J. Velev
University of Illinois

We performed theoretical studies of the interlayer exchange coupling (IEC) in magnetic multilayer (Co/Cu and Fe/Cr) systems, taking into account the realistic band structures. We also investigated the magnetic layer thickness dependence of IEC in magnetic multilayers in which the extremal points of the Fermi surfaces for the spacer and magnetic material do not coincide. We showed that the oscillation period is determined by a stationary condition that depends on the mixed geometry of Fermi surfaces for both materials. The giant magnet resistance (GMR) effect will be investigated next.

Experimentally Oriented Studies of Basic Conceptual Issues in the Foundations of Quantum Mechanics
A. J. Leggett*
John D. and Catherine T. MacArthur Foundation

We are studying the application of the quantum-mechanical formalism to the description of various experiments that severely test one's understanding of its meaning. In addition, we study possible alternative explanations of ostensibly relevant experiments in the literature.

Landau Theory of Bi-Criticality in a Random Quantum Rotor System
P. Phillips,* D. Dalidovich
National Science Foundation, DMR98-12422; American Chemical Society

We considered here a generalization of the random quantum rotor model in which each rotor is characterized by an M-component vector spin. We focused on the case not considered previously, namely when the distribution of exchange interactions has non-zero mean. Inclusion of nonzero mean permits ferromagnetic and superconducting phases for M=1 and M=2, respectively. We found that generally, the Landau theory for this system can be recast as a zero-mean problem in the presence of a magnetic field. At finite temperature, we found that the qualitative features of the phase diagram, for M=1, were identical to what is observed experimentally in the random magnetic alloy LiHoxY(1-x)F4.

Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
E. Fradkin,* C. Nayak (UCLA), K. Schoutens (Univ. of Amsterdam)
National Science Foundation, DMR 98-17941

We construct Landau-Ginzburg effective field theories for fractional quantum Hall states which exhibit non-Abelian statistics. We rely on a Meissner construction which increases the level of a non-Abelian Chern-Simons theory while simultaneously projecting out the unwanted degrees of freedom of a concomitant enveloping Abelian theory. We describe this construction in the context of a system of bosons at Landau level filling factor n=1, where the non-Abelian symmetry is a dynamically-generated SU(2)2 continuous extension of the discrete particle-hole symmetry of the lowest Landau level.

Liquid Crystal Phases of Quantum Hall Systems
E. Fradkin,* S. A. Kivelson (UCLA)
National Science Foundation, DMR 98-17941

Recent measurements of the longitudinal resistivity of a two-dimensional electron gas (2DEG) in large magnetic fields have revealed that these systems have a very large anisotropy presumably driven by electron-electron interactions. We show that at T+0 and for fractionally filled Landau level with index N?2 the 2DEG is in a dynamical stripe phase, an electronic liquid crystal, and that it behaves like a smectic. We propose that the observed reentrant integer quantum Hall plateaus are nematic phases of the stripes.

Local Pairing at U-Impurities in BCS Superconductor Liquid
P. Phillips,* I. Martin
American Chemical Society

We analyzed the role d-electrons on Anderson U-impurities play in superconductivity in a metal alloy. We find that phonon coupling at impurities counteracts the traditional effects that dominate T c suppression in the nonmagnetic limit. In some cases, we find that nonmagnetic impurities can enhance T c. Qualitative agreement is found between the predicted increase and the experimental data for VI-VI degenerate semiconductors doped with Tl or In. In the Kondo limit, a Fermi liquid analysis reveals that it is the enhancement in the density of states arising from the Kondo resonance that counteracts pair-weakening.

Low-Energy Quasi-Particle States near Extended Scatterers in d-Wave Superconductors
P. M. Goldbart,* I. Adagideli, A. Shnirman, A. Yazdani
U.S. Department of Energy, DE-FG02-96ER45439 (In cooperation with the Materials Research Laboratory)

Low-energy states, arising from the scattering of quasi-particles by single-particle potentials in d-wave superconductors, are being explored theoretically, using both general ideas from supersymmetric quantum mechanics and studies of specific microscopic models. The idea that sign-variations in the superconducting pair-potential lead to such states can thus be extended beyond its original setting of boundary scattering to the broader context of scattering by general single-particle potentials, such as those due to impurities.

Mesoscopic Phenomena in Bose-Einstein Condensed Alkali-Metal Gases
P. M. Goldbart,* Y. Lyanda-Geller
U.S. Department of Energy, DE-FG02-96ER45439 (In cooperation with the Materials Research Laboratory)

Mesoscopic phenomena-including population oscillations and persistent currents driven by quantal phases-are being explored theoretically in the context of multiply-connected Bose-Einstein systems composed of trapped alkali-metal gas atoms. These atomic phenomena are bosonic analogues of electronic persistent currents in normal metals and Little-Parks oscillations in superconductors.

Novel Coexisting Density Wave Ground States and Superconductivity in Organic Charge Transfer Solids
D. K. Campbell,* R. T. Clay, S. Mazumdar (Arizona)
National Science Foundation, DMR 97-12765; IBM Corp., Shared University Research Program; National Center for Supercomputing Applications

We have demonstrated the existence of a new exotic ground state in strongly correlated, 2-D electronic materials: a novel, insulating bond-order/charge density wave state (BCDW) in the commensurate 1|-filled band that persists for all anisotropies within the 2-D lattice, in contradiction to the noninteracting electron prediction of the vanishing of density waves in 2-D for non-1z-filled bands. Our results have implications for experiments in the organic charge transfer solids (CTS), where they explain the observation of a 'mysterious' coexistence of density waves, clarify the optical conductivity of the 'metallic' state, and suggest an approach to the observed organic superconductivity.

Optical Properties of Semiconductor Quantum Wires grown by the SILO Process
Y.-C. Chang,* L. Li
National Science Foundation, ECS 96-17153

Band structures and optical matrix elements of strained multiple quantum wires (QWRs) are investigated theoretically via the effective bond-orbital model, which takes into account the effects of valence-band anisotropy and band mixing. The Ga1-xInxAs QWRs grown by strain-induced lateral ordering (SILO) are considered. Long wavelength Ga1-xInxAs QWR lasers have been fabricated via a single-step MBE technique which uses the SILO process. Low threshold current and high optical anisotropy have been achieved. Multiaxial strains for the QWR (combinations of biaxial strains in the [001] and [011] planes) are considered. Our calculated anisotropy in optical matrix elements is in good agreement with the experimental results.

Overscreening of Magnetic Impurities in -wave Superconductors
E. Fradkin,* C. R. Cassanello
National Science Foundation, DMR 98-17941

We consider the screening of a magnetic impurity in a wave superconductor. The properties of the state lead to an unusual behavior in the impurity magnetic susceptibility, the impurity specific heat, and in the quasi-particle phase shift which can be used to diagnose the nature of the condensed state. We construct an effective theory for this problem and show that there is a quantum phase transition from an unscreened impurity state to an overscreened Kondo state at a critical value which varies with , the superconducting gap away from the nodes. In the overscreened phase, the impurity Fermi level and the amplitude of the ground state singlet vanish at like \exp (-const/) / and respectively. We derive the scaling laws for the susceptibility and specific heat in the overscreened phase.

Positive Magnetoresistance in Quasi-1-D Conductors
P. Phillips,* I. Martin
American Chemical Society

We study the problem of the origin of the resistivity maximum and the positive magnetoresistance in quasi-1-D conductors. At high temperatures, we argued that transport is governed by inelastic scattering while at low temperatures the conductance decays exponentially with the electron dephasing length. The crossover between these regimes occurs at the temperature at which the elastic and inelastic scattering times become equal. This model was in quantitative agreement with the organic conductor TTT2I{3-\d}. Within this model, we also showed that on the insulating side, the positive magnetoresistance of the form (H/T)2 observed in TTT2I{3-\d} and other quasi-1-D conductors is explained by the role spin-flip scattering plays in the electron dephasing rate.

Prediction of Macroscopic Properties of Liquid Helium from Computer Simulation
D. Ceperley,* N. Goldenfeld,* T. Chay, G. Bauer, E. Draeger
University of Illinois; National Aeronautics and Space Administration, NRA-94-OLMSA-05

This research is concerned with fundamental aspects of helium and quantum fluids in general; we are addressing outstanding problems in the current understanding of relevant phenomena such as Bose condensation, superfluidity, and phase transitions, as well as of theoretical issues such as the inference of bulk properties of matter from the study of finite clusters. The theoretical issues involved in helium systems are of direct relevance to understanding other many-body quantum systems such as correlated electronic systems.

Quantum Fluctuation Effects in Spin-Peierls Models
D. K. Campbell,* A. W. Sandvik
National Science Foundation, DMR 97-12765; IBM Corp.; Shared University Research Program; National Center for Supercomputing Applications

We have studied the spin-Peierls transition in a Heisenberg chain coupled to optical bond phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling exceeds a critical value, which is nonzero. Using sum rules, we show that the phonon spectral function has divergent (for N approaching infinity) weight extending to zero frequency for couplings below the critical coupling. The equal time phonon-phonon correlations decay with distance r as 1/r.

Quasi-One-dimensional Correlated Electronic Materials
D. K. Campbell,* A. W. Sandvik, R. T. Clay, P. Sengupta
National Science Foundation, DMR 97-12765; IBM Corp., Shared University Research Program; National Center for Supercomputing Applications

In recent years, increasing computing power and significant progress in numerical algorithms have brought true many-body computational methods to the point at which quantitatively accurate results can be obtained for one-dimensional (1-D) systems involving simultaneously strong electron-electron and electron-phonon interactions. At the same time, significant experimental advances have been made for quasi-1-D electronic materials, such as conjugated polymers, Bechgaard salts, and high Tc cuprate superconductors, in terms of both materials synthesis and preparation and physical characterization and measurement. Our research, comparing the results of detailed numerical studies with experimental data, focuses on a systematic theoretical investigation of 1-D lattice many-body models, including the important Peierls-Hubbard and spin-Peirels models.

Studies of Anomalous Heat Conductivity in Classical Lattices
D. K. Campbell,* T. Prosen (Ljubljana)
University of Illinois

Under quite general conditions, we have proven that for classical many-body lattice Hamiltonians in one dimension (1-D) total momentum conservation implies anomalous conductivity in the sense of the divergence of the Kubo expression for the thermal conductivity. Our results provide rigorous confirmation and explanation of many of the existent 'surprising' numerical studies of anomalous conductivity in classical 1-D lattices, including the celebrated Fermi-Pasta-Ulam problem.

Superconductivity in a Two-dimensional Electron Gas
P. Phillips,* Y. Wan, I. Martin, S. Knysh, D. Dalidovich
National Science Foundation, DMR98-12422

Kravchenko and colleagues observed unexpectedly that a two-dimensional electron gas in zero magnetic field can be a conductor. This was surprising as the conventional theory of metals precludes the presence of a metallic state at zero temperature in 2-D. We argued that the new conducting phase in 2-D is in fact a superconductor with an inhomogeneous charge density. The similarity of the transport data with that of known insulator-superconductor transitions, the existence of a critical magnetic field, and the proximity of the conducting phase to an electron crystal state in which strong charge retardation effects can lead to Cooper pair formation are why we support superconductivity.

Superfluidity and Phase Coherence in Very Degenerate Atomic Gases
A. J. Leggett,* C. Lobo, J. Hahm, S. Ashhab, S. Paraoanu, G. Warner
National Science Foundation, DMR 96-14133

Studies are being made of the superfluid density of an arbitrary many-body system, possible phase-coherence and interference experiments in Bose-condensed atomic gases, superfluidity in very degenerate dilute Fermi gases, and thermal transport in the ultralow-temperature regime of superfluid 3He.

Theoretical Studies of Self-assembled Quantum Dots
Y. C. Chang,* D. M.-T. Kuo, J. Sun, G. Qing
U.S. Air Force, YCC 2059-S. CAL MURI

We calculate the electronic and optical properties of quantum dots grown on semiconductor substrates, including the effects of strain distribution. The stress-strain field in these heterostructures will be determined by a valence-force field model combined with molecular dynamic studies. Properties of interest include photoluminescence, absorption, dark current, photoconductive gain, impurity levels, charging effects, and exciton states.

Theory of Polysoap Molecules
P. M. Goldbart,* A. Halperin
National Science Foundation, INT96 03228

This project aims to develop a theory of systems containing flexible macromolecules into which amphiphilic monomers have been covalently incorporated. This combination leads to polysoaps, an interesting class of materials central in many industrial settings, from oil-recovery to paper-coating. Incorporating amphiphilic monomers induces striking modifications of the spatial configurations of the polymers. What were featureless random coils now exhibit a remarkable hierarchy of self-organization: the surfactants incorporated into the polymers aggregate into micelles, thus imparting organization to the polymer itself. Due to this self-organization, essentially all paradigms describing the behavior of polymers (above the chemical level) will need to be significantly modified.

Theory of Random Solids
P. M. Goldbart,* H. E. Castillo, W. Peng, K. Shakhnovich
National Science Foundation, DMR 99-75187

This project aims to develop a semimicroscopic theory of vulcanized matter, the prototypical example of such matter being randomly crosslinked macromolecular networks (e.g., rubber). The central challenges are to construct theoretical approaches to static and dynamical aspects of the structure of vulcanized matter, as well as its response to external perturbations, and to do so at the mean-field level of approximation and beyond. A recurrent theme is the utility of characterizing the matter via universal statistical distributions, such as the distribution of localization lengths. Applications to a wide range of vulcanized media, including polymeric and low-molecular-weight varieties, are being constructed.

Theory of Solids, Surfaces, and Heterostructures
R. M. Martin,* U. Stephan, D. Sanchez-Portal, I Souza
U.S. Department of Energy, DE-FG02-96ER45439 (In cooperation with the Materials Research Laboratory)

We are developing theoretical methods to describe the electronic structure of solids and applying them to the calculation of properties of crystalline solids, surfaces, and interfaces. Recent work has focused on development of new linear scaling 'order N' algorithms for first-principles simulations of materials. We have applied the methods to predict the structures and the electronic states of amorphous silicon and carbon and other materials. We have developed new methods to treat electric polarization and are applying these methods to complex oxide ferroelectrics and magnetic systems.

Universal Structure of the Edge States of the Fractional Quantum Hall States
E. Fradkin,* A. Lopez (Instituto Balseiro, Argentina)
National Science Foundation, DMR 98-17941

An effective theory for the bulk fractional quantum Hall states on the Jain sequences on closed surfaces is developed, and we show that it has a universal form whose structure does not change from fraction to fraction. The structure of this effective theory follows from the condition of global consistency of the flux attachment transformation on closed surfaces. We derive the theory of the edge states on a disk. For a fully polarized 2-D electron gas, the edge states for all the Jain filling fractions n=p(2np+1) have only one propagating edge field that carries both energy and charge, and two nonpropagating edge fields responsible for the statistics of the excitations. The tunneling density of states for all the Jain states scales with frequency as w(1-n)n.

What Do Noise Measurements Reveal about Fractional Charge in Fractional Quantum Hall Liquids?
E. Fradkin,* N. Sandler, C. de C. Chamon
NSF Science and Technology Center for Superconductivity

We calculated the noise in the tunneling current through junctions between two 2-D electron gases (2DEG) in inequivalent Laughlin fractional quantum Hall (FQH) states, as a function of voltage and temperature. We take measurements of suppressed shot noise levels of tunneling currents through a quantum point contact (QPC) in terms of tunneling of fractionally charged states and in terms of solitons of the coupled system. The charge of the soliton is, in units of the electron charge, the harmonic average of the filling fractions of the individual Laughlin states, and it coincides with the saturation value of the differential conductance of the QPC. For a QPC between states at filling fractions n=and n=1{, we calculate the noise in the tunneling current exactly for all voltages and temperatures and investigate the crossovers.