31 research outputs found
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, , 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 and .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
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 quantum Hall edge states
The spatial behavior of Landau levels (LLs) for the 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 . The nature of the transport depends crucially on
both the strength of the random component of and its mean
value . For , the governing parameter is ,
where is the correlation length of disorder and is the Larmor radius
in the field . While for the Drude theory applies, at
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 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
. In the regime the crossover between the snake-state
percolation and the percolation of the drift orbits with increasing
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 is
in good agreement with experimental data in the FQHE regime near .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