Derek K. K. Lee

Unified model for two localization problems: Electron states in spin-degenerate Landau levels and in a random magnetic field.

A single model is presented which represents both of the two apparently unrelated localisation problems of the title. The phase diagram of this model is examined using scaling ideas and numerical simulations. It is argued that the localisation length in a spin-degenerate Landau level diverges at two distinct energies, with the same critical behaviour as in a spin-split Landau level, and that all states of a charged particle moving in two dimensions, in a random magnetic field with zero average, are localised.

Interaction picture density matrix quantum Monte Carlo

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samples the N-body thermal density matrix and hence provides access to exact properties of many-particle quantum systems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substantial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system of much recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness error at finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally, we provide benchmark calculations for a four-electron system, comparing our results to previous work where possible.

Spin textures, screening, and excitations in dirty quantum Hall ferromagnets.

We study quantum Hall ferromagnets in the presence of a random electrostatic impurity potential. Describing these systems with a classical nonlinear sigma model and using analytical estimates supported by results from numerical simulations, we examine the nature of the ground state as a function of disorder strength, Delta, and deviation, deltanu, of the average Landau level filling factor from unity. Screening of an impurity potential requires distortions of the spin configuration, and in the absence of Zeeman coupling there is a disorder-driven, zero-temperature phase transition from a ferromagnet at small Delta and /deltanu/ to a spin glass at larger Delta or /deltanu/. We examine ground-state response functions and excitations.

Dynamics of thermalization in small Hubbard-model systems.

We study numerically the thermalization and temporal evolution of a two-site subsystem of a fermionic Hubbard model prepared far from equilibrium at a definite energy. Even for very small systems near quantum degeneracy, the subsystem can reach a steady state resembling equilibrium. This occurs for a nonperturbative coupling between the subsystem and the rest of the lattice where relaxation to equilibrium is Gaussian in time, in sharp contrast to perturbative results. We find similar results for random couplings, suggesting such behavior is generic for small systems.

Dissipation and tunneling in quantum Hall bilayers.

We discuss the interplay between transport and intrinsic dissipation in quantum Hall bilayers, within the framework of a simple thought experiment. We compute, for the first time, quantum corrections to the semiclassical dynamics of this system. This allows us to reinterpret tunneling measurements on these systems. We find a strong peak in the zero-temperature tunneling current that arises from the decay of Josephson-like oscillations into incoherent charge fluctuations. In the presence of an in-plane field, resonances in the tunneling current develop an asymmetric line shape.

Possibility of a Metallic Phase in Granular Superconducting Films

We investigate the possibility of finding a zero-temperature metallic phase in granular superconducting films. We are able to identify the breakdown of the conventional treatment of these systems as dissipative Bose systems. We do not find a metallic state at zero temperature. At finite temperatures, we find that the system exhibit crossover behaviour which may have implications for the analysis of experimental results. We also investigate the effect of vortex dissipation in these systems.

Transport phenomenology for a holon - spinon fluid

We propose that the normal-state transport in the cuprate superconductors can be understood in terms of a two-fluid model of spinons and holons. In our scenario, the resistivity is determined by holon dynamics while magnetotransport involves the recombination of holons and spinons to form physical electrons. Our model implies that the Hall transport time, as defined by Anderson and Ong, is a measure of the electron lifetime, which is shorter than the longitudinal transport time. We predict a strong increase in linewidth with increasing temperature in photoemission. Our model also suggests that the AC Hall effect is controlled by the transport time.

Degenerate Bose liquid in a fluctuating gauge field.

We study the effect of a strongly fluctuating gauge field on a degenerate Bose liquid, relevant to the charge degrees of freedom in doped Mott insulators. We find that the superfluidity is destroyed. The resulting metallic phase is studied using quantum Monte Carlo methods. Gauge fluctuations cause the boson world lines to retrace themselves. We examine how this world-line geometry affects the physical properties of the system. In particular, we find a transport relaxation rate of the order of 2kT, consistent with the normal state of the cuprate superconductors. We also find that the density excitations of this model resemble that of the full tJ model.

Network model of localization in a random magnetic field

We consider a multichannel network model to study the localization problem of noninteracting fermions in a random magnetic field with zero average. We argue that the number of channels {ital M} is even. After averaging over the randomness, the network is mapped onto {ital M} coupled SU(2{ital N}) spin chains in the {ital N}{r_arrow}0 limit. In the large conductance limit {ital g}={ital M}({ital e}{sup 2}/2{pi}{h_bar}) ({ital M}{much_gt}2), it turns out that this system is equivalent to a particular representation of the U(2{ital N})/U({ital N}){times}U({ital N}) sigma model ({ital N}{r_arrow}0) {ital without} a topological term. The beta function {beta}(1/{ital M}) of this sigma model in the 1/{ital M} expansion is consistent with the previously known {beta}({ital g}) of the unitary ensemble. These results and further arguments support the conclusion that all the states are localized.

Single-electron induced surface plasmons on a topological nanoparticle

It is rarely the case that a single electron affects the behaviour of several hundred thousands of atoms. Here we demonstrate a phenomenon where this happens. The key role is played by topological insulators—materials that have surface states protected by time-reversal symmetry. Such states are delocalized over the surface and are immune to its imperfections in contrast to ordinary insulators. For topological insulators, the effects of these surface states will be more strongly pronounced in the case of nanoparticles. Here we show that under the influence of light a single electron in a topologically protected surface state creates a surface charge density similar to a plasmon in a metallic nanoparticle. Such an electron can act as a screening layer, which suppresses absorption inside the particle. In addition, it can couple phonons and light, giving rise to a previously unreported topological particle polariton mode. These effects may be useful in the areas of plasmonics, cavity electrodynamics and quantum information.