Thomas-Fermi-Poisson theory of screening for latterally confined and unconfined two-dimensional electron systems in strong magnetic fields

We examine within the self-consistent Thomas-Fermi-Poisson approach the low-temperature screening properties of a two-dimensional electron gas (2DEG) subjected to strong perpendicular magnetic fields. Numerical results for the unconfined 2DEG are compared with those for a simplified Hall bar geometry realized by two different confinement models. It is shown that in the strongly non-linear screening limit of zero temperature the total variation of the screened potential is related by simple analytical expressions to the amplitude of an applied harmonic modulation potential and to the strength of the magnetic field.Comment: 12 pages, 12 figure

Density-functional theory of quantum wires and dots in a strong magnetic field

We study the competition between the exchange and the direct Coulomb interaction near the edge of a two-dimensional electron gas in a strong magnetic field using density-functional theory in a local approximation for the exchange-energy functional. Exchange is shown to play a significant role in reducing the spatial extent of the compressible edge channel regions obtained from an electrostatic description. The transition from the incompressible edge channels of the Hartree-Fock picture to the broad, compressible strips predicted by electrostatics occurs within a narrow and experimentally accessible range of confinement strengths.Comment: 24 pages latex and 10 postscript figures in self extracting fil

Ensemble density functional theory of the fractional quantum Hall effect

We develop an ensemble density functional theory for the fractional quantum Hall effect using a local density approximation. Model calculations for edge reconstructions of a spin-polarized quantum dot give results in good agreement with semiclassical and Hartree-Fock calculations, and with small system numerical diagonalizations. This establishes the usefulness of density functional theory to study the fractional quantum Hall effect, which opens up the possibility of studying inhomegeneous systems with many more electrons than has heretofore been possible.Comment: Improved discussion of ensemble density functional theory. 4 pages plus 3 postscript figures, uses latex with revtex. Contact [email protected]

Quantized Thermal Transport in the Fractional Quantum Hall Effect

We analyze thermal transport in the fractional quantum Hall effect (FQHE), employing a Luttinger liquid model of edge states. Impurity mediated inter-channel scattering events are incorporated in a hydrodynamic description of heat and charge transport. The thermal Hall conductance, $K_H$, is shown to provide a new and universal characterization of the FQHE state, and reveals non-trivial information about the edge structure. The Lorenz ratio between thermal and electrical Hall conductances {\it violates} the free-electron Wiedemann-Franz law, and for some fractional states is predicted to be {\it negative}. We argue that thermal transport may provide a unique way to detect the presence of the elusive upstream propagating modes, predicted for fractions such as $\nu=2/3$ and $\nu=3/5$.Comment: 6 pages REVTeX, 2 postscript figures (uuencoded and compressed

Imaging of Low Compressibility Strips in the Quantum Hall Liquid

Using Subsurface Charge Accumulation scanning microscopy we image strips of low compressibility corresponding to several integer Quantum Hall filling factors. We study in detail the strips at Landau level filling factors $\nu =$ 2 and 4. The observed strips appear significantly wider than predicted by theory. We present a model accounting for the discrepancy by considering a disorder-induced nonzero density of states in the cyclotron gap.Comment: 5 pages, 3 figure

Electron correlation effects in a wide channel from the ν=1\nu =1 quantum Hall edge states

The spatial behavior of Landau levels (LLs) for the $nu=1$ quantum Hall regime at the edge of a wide channel is studied in a self-consistent way by using a generalized local density approximation proposed here. Both exchange interaction and strong electron correlations, due to edge states, are taken into account. They essentially modify the spatial behavior of the occupied lowest spin-up LL in comparison with that of the lowest spin-down LL, which is totally empty. The contrast in the spatial behavior can be attributed to a different effective one-electron lateral confining potentials for the spin-split LLs. Many-body effects on the spatially inhomogeneous spin-splitting are calculated within the screened Hartree-Fock approximation. It is shown that, far from the edges, the maximum activation energy is dominated by the gap between the Fermi level and the bottom of the spin-down LL, because the gap between the Fermi level and the spin-up LL is much larger. In other words, the maximum activation energy in the bulk of the channel corresponds to a highly asymmetric position of the Fermi level within the gap between spin-down and spin-up LLs in the bulk. We have also studied the renormalization of the edge-state group velocity due to electron correlations. The results of the present theory are in line with those suggested and reported by experiments on high quality samples.Comment: 9 pages, 4 figure

A Unified Model for Two Localisation 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.Comment: 7 pages (RevTeX 3.0) plus 4 postscript figure

Semiclassical theory of transport in a random magnetic field

We study the semiclassical kinetics of 2D fermions in a smoothly varying magnetic field $B({\bf r})$. The nature of the transport depends crucially on both the strength $B_0$ of the random component of $B({\bf r})$ and its mean value $\bar{B}$. For $\bar{B}=0$, the governing parameter is $\alpha=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $\alpha\ll 1$ the Drude theory applies, at $\alpha\gg 1$ most particles drift adiabatically along closed contours and are localized in the adiabatic approximation. The conductivity is then determined by a special class of trajectories, the "snake states", which percolate by scattering at the saddle points of $B({\bf r})$ where the adiabaticity of their motion breaks down. The external field also suppresses the diffusion by creating a percolation network of drifting cyclotron orbits. This kind of percolation is due only to a weak violation of the adiabaticity of the cyclotron rotation, yielding an exponential drop of the conductivity at large $\bar{B}$. In the regime $\alpha\gg 1$ the crossover between the snake-state percolation and the percolation of the drift orbits with increasing $\bar{B}$ has the character of a phase transition (localization of snake states) smeared exponentially weakly by non-adiabatic effects. The ac conductivity also reflects the dynamical properties of particles moving on the fractal percolation network. In particular, it has a sharp kink at zero frequency and falls off exponentially at higher frequencies. We also discuss the nature of the quantum magnetooscillations. Detailed numerical studies confirm the analytical findings. The shape of the magnetoresistivity at $\alpha\sim 1$ is in good agreement with experimental data in the FQHE regime near $\nu=1/2$.Comment: 22 pages REVTEX, 14 figure

Observation of two relaxation mechanisms in transport between spin split edge states at high imbalance

Using a quasi-Corbino geometry to directly study electron transport between spin-split edge states, we find a pronounced hysteresis in the I-V curves, originating from slow relaxation processes. We attribute this long-time relaxation to the formation of a dynamic nuclear polarization near the sample edge. The determined characteristic relaxation times are 25 s and 200 s which points to the presence of two different relaxation mechanisms. The two time constants are ascribed to the formation of a local nuclear polarization due to flip-flop processes and the diffusion of nuclear spins.Comment: Submitted to PR