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

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 semiconductors, 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.

Many-Particle Tunneling Effects and Resonant Processes in Mesoscopic Systems
D. K. Campbell,* G. R. Berman*
NATO Linkage Grant, NANO.LG 931602

Remarkable recent advances in materials science permit the construction of new "mesoscopic/nanoscale" materials with structures on the scale of 10-100 nm. These "quantum dots," "wires," and "layers" exhibit many new physical phenomena as nonlinear, quantum, and finite-size effects combine and compete. We have initiated three theoretical studies in this area: (1) correlated electron models for quantum dots and wires; (2) resonant processes in weak and strong electromagnetic fields; and (3) ground states and phase transitions in discrete quantum 1-D and 2-D systems, including the role of many-particle tunneling effects, diffusion, and quantum fluctuations. We will compare our results with experiments and seek applications in the designs of novel electronic devices.

Electronic Structure of Condensed Matter
D. M. Ceperley,* R. M. Martin,* F. H. Zong, M. Dewing, Y. Kim, T. Wilkens
National Science Foundation, DMR 94-22496

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.

Prediction of Macroscopic Properties of Liquid Helium from Computer Simulation
D. Ceperley,* N. Goldenfeld,* T. Chay, G. Bauer, E. Draeger
University of Illinois

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.

Theoretical Studies of Self-assembled Quantum Dots
Y. C. Chang,* D. M.-T. Kuo, J. Sun
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 continuum elastic theory combined with molecular dynamic studies. Properties of interest include photoluminescence, absorption, dark current, photoconductive gain, impurity levels, charging effects, and exciton states.

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.

Exchange Coupling in Magnetic Multilayers
Y. C. Chang,* L. Tsetseris, 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.

Electronic and Optical Properties of Surfaces and Heterostructures
Y.-C. Chang,* G. Li, L. Wei
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.

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 94-24511

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 = 1/2 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 = 1/2 are obtained by a flux-attachment procedure. We discuss the non-Abelian statistics of quasi-particles in the context of this effective field theory.

Andreev Reflection in the Fractional Quantum Hall Effect
E. Fradkin,* N. P. Sandler, C. Chamon
National Science Foundation, DMR 94-24511

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,* P. Goldbart, M. Stone, C. Chamon, H. Castillo, N. Sandler, G-S. Paraoanu, T. Stanescu, S. Kos
National Science Foundation, DMR 94-24511

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; geometric phases and their condensed matter implications; superfluids and superconductors, including vortex motion in dirty systems, quantum critical behavior of magnetic impurities in -wave superconductors; vulcanized matter and the vulcanization transition; structural glasses and network-forming systems, glassiness of superfluid helium-three in aerogel, shapes adopted by large biological macromolecules, and static and dynamic properties of polysoap macromolecules.

Electronic Liquid Crystal Phases of a Doped Mott Insulator
E. Fradkin,* S. Kivelson (UCLA), V. Emery (Brookhaven)
National Science Foundation, DMR 94-24511

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.

Exact Calculation of Multifractal Exponents of the Critical Wave Function of Dirac Fermions in a Random Magnetic Field
E. Fradkin,* H. Castillo, C. Chamon, P. M. Goldbart, C. Mudry (MIT)
National Science Foundation, DMR 94-24511

The multifractal scaling exponents are calculated for the critical wave function of a two-dimensional Dirac fermion in the presence of a random magnetic field. It is shown that the problem of calculating the multifractal spectrum maps into the thermodynamics of a static particle in a random potential. The multifractal exponents are simply given in terms of thermodynamic functions, such as free energy and entropy, which are argued to be self-averaging in the thermodynamic limit. These thermodynamic functions are shown to coincide exactly with those of a generalized random energy model, in agreement with previous results obtained using Gaussian field theories in an ultrametric space.

Distinct Universal Conductances in Tunneling to Quantum Hall States-The Role of Contacts
E. Fradkin,* C. Chamon
National Science Foundation, DMR 94-24511

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 = 1/3 FQH state which we show to be equivalent to the problem of tunneling between two G = 1/2 chiral Luttinger liquids. This system provides an experimental realization of this important exactly solvable case.

Overscreening of Magnetic Impurities in -wave Superconductors
E. Fradkin,* C. R. Cassanello
National Science Foundation, DMR 94-24511

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.

Liquid Crystal Phases of Quantum Hall Systems
E. Fradkin,* S. A. Kivelson (UCLA)
National Science Foundation, DMR94-24511

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 NŠ2 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.

Universal Structure of the Edge States of the Fractional Quantum Hall States
E. Fradkin,* A. Lopez (Instituto Balseiro, Argentina)
National Science Foundation, DMR94-24511

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=1/3, we calculate the noise in the tunneling current exactly for all voltages and temperatures and investigate the crossovers.

Landau-Ginzburg Theories for Non-Abelian Quantum Hall States
E. Fradkin,* C. Nayak (UCLA), K. Schoutens (Univ. of Amsterdam)
National Science Foundation, DMR94-24511

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.

Vulcanized Matter
P. M. Goldbart,* H. E. Castillo, W. Peng, K. Shakhnovich
National Science Foundation, DMR 94-24511

This project aims to develop a semimicroscopic theory of vulcanized matter, the prototypical example of such matter being randomly cross-linked 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. A recurrent theme is the utility of characterizing the matter via universal statistical distributions, such as the distribution of localization lengths. This approach is mandated by the essentially random character of the amorphous solid state that emerges upon sufficient vulcanization. Applications to a wide range of vulcanized media, including polymeric and low-molecular-weight varieties, are being constructed.

Superconductivity and Antiferromagnetism-Excitations and Dissipation
P. M. Goldbart,* D. E. Sheehy
U.S. Department of Energy, DE-FG02-96ER45439 (In cooperation with the Materials Research Laboratory)

This project aims to explore certain phenomenological implications of a recent approach to the physics of high-temperature superconducting materials: Zhang's SO(5) theory. It has been found that a novel type of excitation should arise in nearly superconducting antiferromagnets. These excitations resemble antiferromagnetic "hedgehogs" at large distances but are predominantly superconducting inside a core region. Their structure and experimental implications are currently being elucidated. It has also been found that Zhang's SO(5) theory implies an unusual type of dissipation mechanism via which supercurrent can decay. The relativity due to this mechanism, which involves orientation rather than amplitude order-parameter fluctuations, is being explored.

Bose-Einstein Condensed Alkali Gases-Current-carrying States and Their Decay
P. M. Goldbart,* E. J. Mueller, Y. Lyanda-Geller
National Science Foundation, DMR 94-24511

The ability to support metastable current-carrying states in multiply-connected settings is one of the prime signatures of superfluidity. This project aims to investigate such states theoretically for the case of trapped Bose condensed alkali gases, particularly with regard to the rate at which they decay via thermal fluctuations. It has been found that the lifetimes of metastable currents can be either longer or shorter than experimental time scales, depending on the experimental setting. Schemes for the experimental detection of metastable stages are being analyzed.

Equilibrium and Nonequilibrium Phenomena in Condensed Matter
N. Goldenfeld,* Y. Oono,* Q. Hou, G. Simms
National Science Foundation, DMR 93-14938

We are modeling phase transition kinetics, developing large deviation and fluctuations theories for nonequilibrium systems, and studying dynamic scaling in high-temperature superconductors. Ongoing projects include numerical renormalization group methods for PDEs and critical scaling in black hole formation.

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 B-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.

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

We are studying phase separation kinetics in helium-3/helium-4 mixtures by using path integral Monte Carlo methods and cell dynamic models. Our goal is to predict quantitatively the morphology generated during phase ordering from quantum mechanics alone, with as little experimental input as possible.

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.

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.

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.

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 Monte Carlo simulations of interacting electrons, and we have applied the method to study the doped fullerines. 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.

Theory of Solids, Surfaces, and Heterostructures
R. M. Martin,* E. Koch, I. Souza, B. Tuttle
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 included Monte Carlo simulations of the many-body electron problem in two-dimensional electron liquids and in the doped Fullerines. We are using density functional methods to study materials and developing new "linear scaling" algorithms for simulations of materials.

Local Pairing at U-Impurities in BCS Superconductor Liquid
P. Phillips,* I. Martin
National Science Foundation, DMR 95-10680; 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.

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.

Positive Magnetoresistance in Quasi-1-D Conductors
P. Phillips,* I. Martin
National Science Foundation, DMR95-10680, ACS-PRF 32374-AC5

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.

Landau Theory of Bi-Criticality in a Random Quantum Rotor System
P. Phillips,* D. Dalidovich
National Science Foundation, DMR98-12422, ACS-PRF 32374-AC5

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.