241 research outputs found
Integer quantum Hall effect of interacting electrons: dynamical scaling and critical conductivity
We report on a study of interaction effects on the polarization of a
disordered two-dimensional electron system in a strong magnetic field. Treating
the Coulomb interaction within the time-dependent Hartree-Fock approximation we
find numerical evidence for dynamical scaling with a dynamical critical
exponent z=1 at the integer quantum Hall plateau transition in the lowest
Landau level. Within the numerical accuracy of our data the conductivity at the
transition and the anomalous diffusion exponent are given by the values for
non-interacting electrons, independent of the strength of the interaction.Comment: Minor changes. Final version to be published in Phys. Rev. Lett. June
2
Liouvillian Approach to the Integer Quantum Hall Effect Transition
We present a novel approach to the localization-delocalization transition in
the integer quantum Hall effect. The Hamiltonian projected onto the lowest
Landau level can be written in terms of the projected density operators alone.
This and the closed set of commutation relations between the projected
densities leads to simple equations for the time evolution of the density
operators. These equations can be used to map the problem of calculating the
disorder averaged and energetically unconstrained density-density correlation
function to the problem of calculating the one-particle density of states of a
dynamical system with a novel action. At the self-consistent mean-field level,
this approach yields normal diffusion and a finite longitudinal conductivity.
While we have not been able to go beyond the saddle point approximation
analytically, we show numerically that the critical localization exponent can
be extracted from the energetically integrated correlation function yielding
in excellent agreement with previous finite-size scaling
studies.Comment: 9 pages, submitted to PR
Wave-packet dynamics at the mobility edge in two- and three-dimensional systems
We study the time evolution of wave packets at the mobility edge of
disordered non-interacting electrons in two and three spatial dimensions. The
results of numerical calculations are found to agree with the predictions of
scaling theory. In particular, we find that the -th moment of the
probability density scales like in dimensions. The
return probability scales like , with the generalized
dimension of the participation ratio . For long times and short distances
the probability density of the wave packet shows power law scaling
. The numerical calculations were performed
on network models defined by a unitary time evolution operator providing an
efficient model for the study of the wave packet dynamics.Comment: 4 pages, RevTeX, 4 figures included, published versio
Metal-insulator transitions in anisotropic 2d systems
Several phenomena related to the critical behaviour of non-interacting
electrons in a disordered 2d tight-binding system with a magnetic field are
studied. Localization lengths, critical exponents and density of states are
computed using transfer matrix techniques. Scaling functions of isotropic
systems are recovered once the dimension of the system in each direction is
chosen proportional to the localization length. It is also found that the
critical point is independent of the propagation direction, and that the
critical exponents for the localization length for both propagating directions
are equal to that of the isotropic system (approximately 7/3). We also
calculate the critical value of the scaling function for both the isotropic and
the anisotropic system. It is found that the isotropic value equals the
geometric mean of the two anisotropic values. Detailed numerical studies of the
density of states for the isotropic system reveals that for an appreciable
amount of disorder the critical energy is off the band center.Comment: 6 pages RevTeX, 6 figures included, submitted to Physical Review
Scaling in the Integer Quantum Hall Effect: interactions and low magnetic fields
Recent developments in the scaling theory of the integer quantum Hall effect
are discussed. In particular, the influence of electron-electron interactions
on the critical behavior are studied. It is further argued that recent
experiments on the disappearance of the quantum Hall effect at low magnetic
fields support rather than disprove the scaling theory, when interpreted
properly.Comment: 13 pages, invited talk at DPG spring meeting, Regensburg, March 2000,
to appear in Advances in Solid State Physics, ed. B. Krame
Streda-like formula in spin Hall effect
A generalized Streda formula is derived for the spin transport in spin-orbit
coupled systems. As compared with the original Streda formula for charge
transport, there is an extra contribution of the spin Hall conductance whenever
the spin is not conserved. For recently studied systems with quantum spin Hall
effect in which the z-component spin is conserved, this extra contribution
vanishes and the quantized value of spin Hall conductivity can be reproduced in
the present approach. However, as spin is not conserved in general, this extra
contribution can not be neglected, and the quantization is not exact.Comment: 4 pages, no figur
Charged particles in random magnetic fields and the critical behavior in the fractional quantum Hall effect
As a model for the transitions between plateaus in the fractional Quantum
Hall effect we study the critical behavior of non-interacting charged particles
in a static random magnetic field with finite mean value. We argue that this
model belongs to the same universality class as the integer Quantum Hall
effect. The universality is proved for the limiting cases of the lowest Landau
level, and slowly fluctuating magnetic fields in arbitrary Landau levels. The
conjecture that the universality holds in general is based on the study of the
statistical properties of the corresponding random matrix model.Comment: 11 pages, Revtex 3.0, no figures, to appear in PR
Isolated resonances in conductance fluctuations in ballistic billiards
We study numerically quantum transport through a billiard with a classically
mixed phase space. In particular, we calculate the conductance and Wigner delay
time by employing a recursive Green's function method. We find sharp, isolated
resonances with a broad distribution of resonance widths in both the
conductance and the Wigner time, in contrast to the well-known smooth
conductance fluctuations of completely chaotic billiards. In order to elucidate
the origin of the isolated resonances, we calculate the associated scattering
states as well as the eigenstates of the corresponding closed system. As a
result, we find a one-to-one correspondence between the resonant scattering
states and eigenstates of the closed system. The broad distribution of
resonance widths is traced to the structure of the classical phase space.
Husimi representations of the resonant scattering states show a strong overlap
either with the regular regions in phase space or with the hierarchical parts
surrounding the regular regions. We are thus lead to a classification of the
resonant states into regular and hierarchical, depending on their phase space
portrait.Comment: 2 pages, 5 figures, to be published in J. Phys. Soc. Jpn.,
proceedings Localisation 2002 (Tokyo, Japan
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