Considerable experimental evidence suggests a relation of high-temperature (high T_c) superconductivity to antiferromagnetism (AFM). To clarify this relationship, we have developed a novel approach in which a staggered i.e., alternating external magnetic field is applied to one-dimensional Hubbard and t-J Hamiltonians describing the strongly correlated electrons. The staggered field models the AFM background that exists in the real planar, high T_c materials. Applying both numerical and analytic techniques, we find that even modest staggered fields induce the formation of bound hole pairs thus enhancing the tendency to superconductivity in the strongly coupled limits of both the Hubbard and t-J models.

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.

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 silicon crystals, metal surfaces, metalization of hydrogen at high pressure, rare gas layers, simulations of solids and liquids as a function of temperature, and the fractional quantum Hall effect.

We study the interaction of an ``unconfined'' exciton with a quantum well via the center-of-mass (CM) motion and calculate the coupling of the CM and internal motion of the exciton due to the presence of a quantum well. The localization, binding, and oscillator strength of the unconfined exciton as functions of quantum-well width and the transition rate from the unconfined exciton to the lowest confined exciton are being studied. The result has direct bearing on the observed photoluminescence excitation spectrum. Interlayer exchange coupling in magnetic superlattices is studied with a realistic tight-bonding model. It is found that the coupling strength depends on the details of the band structures.

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.

We started a new direction of research in which we propose to use magnetic impurities as a diagnostic of the nature of the superconducting order. Thus, we have considered the regime in which the magnetic impurities act independently of one another. We have shown that the Kondo effect (the screening of the magnetic impurity) is pushed to intermediate values of the coupling constant between the normal excitations of a d _{x 2 -y 2} condensed state and a localized spin. The D-wave character of the condensate forces a mixing between angular momentum states, which always makes this a multichannel Kondo system. We showed that the electron T-matrix is sensitive to phase factors arising from angular momentum mixing. We are looking at these effects in tunneling.

Work on the mechanism of superconductivity has focused on the study of spontaneous breaking of time reversal invariance. Assuming that each CuO₂ plane exhibits spontaneous breaking of time reversal invariance, chiral antiferromagnetic exchange interactions between planes dynamically select a state in which adjoining planes have opposite chiralities and there is no breaking of time reversal. We further showed that, as the antiferromagnetic exchange interactions between planes increase beyond a critical value, pairs of planes prefer to be bound into local spin singlets: a spin gap state. We developed a Landau-type theory for this zero-temperature phase transition.

Common ground has been found in mesoscopic and strongly correlated systems. The merging of these highly dynamical fields has been propelled by great technological advances in microfabrication at the nanoscale. The geometrical restriction of the charge carriers to very narrow channels quantum wires or to small interfaces quantum dots between bulk leads enhance both the quantum mechanical and the correlation effects. We're developing theoretical tools to study strongly interacting one-dimensional systems of fermions with quantum impurities, constrictions and/or boundaries; a novel bosonization approach to consider the exact fermion boundary conditions; a method to compute fermion determinants and deriving an action for fermions coupled to boundary backscattering processes, and constructing the exact bosonized fermion operator.

T he program aims to provide theoretical understanding of various condensed matter systems and to develop field theories with applications both in condensed matter and particle physics. Present topics of investigation include: topology and anomalies in condensed matter and particle physics; superconductivity, superfluidity, and strongly correlated systems, high-temperature superconductors, disordered superconductors, states with fractional statistics and broken time reversal invariance and parity, application of Kac-Moody algebras and Chern-Simons theories to two- and one-dimensional systems, including the fractional quantum Hall effect, anyons, Kondo effect, and mesoscopic systems; phase transitions, cosmic strings, and related topics.

This project addresses the processes through which liquid crystalline order is established after a quench, e.g., from the isotropic to a nematic phase. Particular attention is paid to the role of topological defects during phase ordering Abelian defects in the case of uniaxial nematics and non-Abelian defects in the case of biaxial nematics. Future directions of this project include the investigation of macro scopic rheological properties, particularly the role of extended topological defects during shear flow.

This project addresses the properties of superconductors at length scales comparable to the coherence length. We have been exploring the impact of the size of the system on the rate at which supercurrent-altering dissipative fluctuations occur in narrow, small superconducting rings. We have also been exploring the nonlinear dynamics of the superconducting condensate near the critical supercurrent. In future work we shall examine the implications of coupling quasi-one-dimensional wires to superconducting electrodes, and also quasi-particle motion confined by a superconducting pair potential.

The central aim of this project is to provide a theoretical understanding of the properties of disordered condensed matter systems, such as randomly crosslinked macromolec ular networks (e.g., rubber) and covalently bonded random atomic networks (e.g., glass). The primary tools employed are statistical-mechanical: replica field theory for the static properties and MSR-stochastic field theory for the dynamical properties. Attention is focused on the transition to the amorphous solid state that emerges upon sufficient crosslinking or covalent bonding, and on the novel properties of this state, such as its resistance to shear deformations.

This is an investigation into the formation of large-scale structures in nonlinear systems far from equilibrium focusing on solidification and phase separation. We are developing novel computational techniques to study the long-time behavior of such systems.

We are studying nonequilibrium systems and their possible generic behavior using numerical and renormalization group methods. Specific systems include: phase separation renormalization group for asymptotics of partial differential equation and large deviation theory.

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.

A study is being made of (1) a new collective approach to the ultrasonic and thermal properties of glasses at low temperatures, which attempts to explain the puzzling quantitative universalities observed experimentally as a consequence of the interaction of large subvolumes via the strain field, (2) the properties of superfluid ³He-A at low temperatures in low magnetic field, including the magnetic resonance properties and the surface tension of the A-B interface, and (3) possible explanations for the intriguing behavior recently observed for third sound in ⁴He on a hydrogen substrate.

Studies are being made of (1) a model of c-axis transport in the high-temperature superconductors involving ``dynamical detuning'' of the hopping between CuO planes, (2) the interplay of the anisotropy of the pairing interaction and of the impurity scattering in ``exotic'' BCS-like states, and (3) novel Josephson-type tests for the order parameter symmetry.

The greatest challenges for first-principles computation of properties of materials are the difficult problems of electron correlation and thermal fluctuations. Our work includes development of methods for quantum Monte Carlo calculations on solids. We are also developing combined molecular dynamics/density functional methods, which have been used to study melting of carbon at ~4500K and prediction of the nature of the liquid, and the phase diagram of carbon as a function of temperature and pressure, which has been debated for decades. New ``linear scaling'' computational methods that can be applied to large systems are a focus of our current work.

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 full many-body electron problem in two-dimensional electron liquids and on clusters of silicon and carbon. Our primary work at present is development of efficient ``linear scaling'' and other algorithms for simulations of materials.

The goal is to make a practically usable unified statistical thermodynamics framework for nonequilibrium steady states. Fluctuation around steady states has been studied with the aid of large deviation theory. A phenomenological framework corresponding to thermodynamics has been partially constructed. The major effort in these days are made to make everything operationally (experimentally) well defined.

Construction of computationally efficient mesoscale models inspired us to consider the numerical schemes to solve partial differential equations (PDE) from the physics point of view. The key point is to try to capture the most important features of the phenomenon described by the PDE as accurately as possible on computers. Then, often the resultant discrete model becomes a good PDE solver. A Navier-Stokes equation solver was proposed long ago, and the idea has been extended to make a dispersion free wave equation solver.

This project has three major aims: (1) to make computationally efficient mesoscale models of various nonequilibrium systems, (2) to accelerate computational procedures with the aid of, e.g., renormalization group (RG) theory, and (3) to extract global features of a system with the aid of RG. We have found, for example, that the Boltzmann equation is a renormalization group equation. Numerical implementation of various renormalization group schemes applied to nonlinear systems and acceleration of molecular dynamics are among the goals.

We study the role of randomly placed nonmagnetic scatterers on the Kondo effect. Previous studies of this problem have focused on weak localization effects on Kondo scattering. Diffusive corrections were shown to give rise to a singular temperature dependence of the form, T ^d/2-2 (d the sample dimension), to the Kondo self-energy. We are explicitly considering the spin relaxation effect magnetic scatterers can produce in the diffusion and Cooperon propagators. We show that once these modified propagators are included as vertex corrections in the perturbation treatment of the Kondo self-energy, the singular temperature dependence arising from the diffusion poles cancels. Consequently, nonmagnetic scatterers at most modify the coefficient of the Kondo lnT resistivity, as recently measured by Blachly and Giordano.

We derive a stability condition for a local moment in the presence of an interacting sea of conduction electrons, modeled as a Luttinger liquid in which chirality and spin are coupled. We show that an Anderson-U defect in such an interacting system can be transformed onto a nearly Fermi liquid problem. We find that correlations among the conduction electrons stabilize the local moment phase. A Schrieffer-Wolff transformation is then performed and results in an anisotropic exchange interaction indicative of the Kondo effect in a Luttinger liquid. The ground-state properties of this model are then equivalent to those of the Kondo model in a Luttinger liquid.

This research involves formulating a model for the pair tunneling states observed by Ashoori and coworkers in GaAs quantum dots. We show that while GaAs is a weakly polar semiconductor, coupling to optical phonons is sufficiently strong to mediate a negative-U pairing state. The physical potential in which the two electrons are bound can be composed of a Si impurity and a parabolic well that originates from the potential created by the delta-dopants in the backing layer of the dot. Such a pair state breaks up at moderate magnetic field strengths ~ 2 T, as is seen experimentally, and is unstable when the confining radius of the dot is smaller than ~ 400Å.

This project is focused on study of magnetism in the high-temperature superconductors in order to gain deeper insight into its possible role in a mechanism for superconductivity. We recently proposed a magnetic scaling phase diagram for the high-temperature superconductors and presented evidence that several different superconductors exhibit quantitatively similar magnetic behavior (scaling property) despite being different in terms of their electronic and other properties. Further studies should ultimately allow us to determine precisely the extent to which this universal scaling theory describes magnetism in the high-temperature superconductors.