19 research outputs found
The Quantum Hall Effect: Unified Scaling Theory and Quasi-particles at the Edge
We address two fundamental issues in the physics of the quantum Hall effect:
a unified description of scaling behavior of conductances in the integral and
fractional regimes, and a quasi-particle formulation of the chiral Luttinger
Liquids that describe the dynamics of edge excitations in the fractional
regime.Comment: 11 pages, LateX, 2 figures (not included, available from the
authors), to be published in Proceedings of the International Summer School
on Strongly Correlated Electron Systems, Lajos Kossuth University, Debrecen,
Hungary, Sept 199
Disordered Critical Wave functions in Random Bond Models in Two Dimensions -- Random Lattice Fermions at without Doubling
Random bond Hamiltonians of the flux state on the square lattice are
investigated. It has a special symmetry and all states are paired except the
ones with zero energy. Because of this, there are always zero-modes. The states
near are described by massless Dirac fermions. For the zero-mode, we can
construct a random lattice fermion without a doubling and quite large systems (
up to ) are treated numerically. We clearly demonstrate that
the zero-mode is given by a critical wave function. Its multifractal behavior
is also compared with the effective field theory.Comment: 4 pages, 2 postscript figure
Quantized Anomalous Hall Effect in Two-Dimensional Ferromagnets - Quantum Hall Effect from Metal -
We study the effect of disorder on the anomalous Hall effect (AHE) in
two-dimensional ferromagnets. The topological nature of AHE leads to the
integer quantum Hall effect from a metal, i.e., the quantization of
induced by the localization except for the few extended states
carrying Chern number. Extensive numerical study on a model reveals that
Pruisken's two-parameter scaling theory holds even when the system has no gap
with the overlapping multibands and without the uniform magnetic field.
Therefore the condition for the quantized AHE is given only by the Hall
conductivity without the quantum correction, i.e., .Comment: 5 pages, 4 figures, REVTe
One-Dimensional Extended States in Partially Disordered Planar Systems
We obtain analytically a continuum of one-dimensional ballistic extended
states in a two-dimensional disordered system, which consists of compactly
coupled random and pure square lattices. The extended states give a marginal
metallic phase with finite conductivity in a wide energy
range, whose boundaries define the mobility edges of a first-order
metal-insulator transition. We show current-voltage duality,
scaling of the conductivity in parallel magnetic field and
non-Fermi liquid properties when long-range electron-electron interactions are
included.Comment: 4 pages, revtex file, 3 postscript file
Fredholm Indices and the Phase Diagram of Quantum Hall Systems
The quantized Hall conductance in a plateau is related to the index of a
Fredholm operator. In this paper we describe the generic ``phase diagram'' of
Fredholm indices associated with bounded and Toeplitz operators. We discuss the
possible relevance of our results to the phase diagram of disordered integer
quantum Hall systems.Comment: 25 pages, including 7 embedded figures. The mathematical content of
this paper is similar to our previous paper math-ph/0003003, but the physical
analysis is ne
Energy spectra, wavefunctions and quantum diffusion for quasiperiodic systems
We study energy spectra, eigenstates and quantum diffusion for one- and
two-dimensional quasiperiodic tight-binding models. As our one-dimensional
model system we choose the silver mean or `octonacci' chain. The
two-dimensional labyrinth tiling, which is related to the octagonal tiling, is
derived from a product of two octonacci chains. This makes it possible to treat
rather large systems numerically. For the octonacci chain, one finds singular
continuous energy spectra and critical eigenstates which is the typical
behaviour for one-dimensional Schr"odinger operators based on substitution
sequences. The energy spectra for the labyrinth tiling can, depending on the
strength of the quasiperiodic modulation, be either band-like or fractal-like.
However, the eigenstates are multifractal. The temporal spreading of a
wavepacket is described in terms of the autocorrelation function C(t) and the
mean square displacement d(t). In all cases, we observe power laws for C(t) and
d(t) with exponents -delta and beta, respectively. For the octonacci chain,
0<delta<1, whereas for the labyrinth tiling a crossover is observed from
delta=1 to 0<delta<1 with increasing modulation strength. Corresponding to the
multifractal eigenstates, we obtain anomalous diffusion with 0<beta<1 for both
systems. Moreover, we find that the behaviour of C(t) and d(t) is independent
of the shape and the location of the initial wavepacket. We use our results to
check several relations between the diffusion exponent beta and the fractal
dimensions of energy spectra and eigenstates that were proposed in the
literature.Comment: 24 pages, REVTeX, 10 PostScript figures included, major revision, new
results adde
Quasi-localized states in disordered metals and non-analyticity of the level curvature distribution function
It is shown that the quasi-localized states in weakly disordered systems can
lead to the non-analytical distribution of level curvatures. In 2D systems the
distribution function P(K) has a branching point at K=0. In quasi-1D systems
the non-analyticity at K=0 is very weak, and in 3D metals it is absent at all.
Such a behavior confirms the conjecture that the branching at K=0 is due to the
multi-fractality of wave functions and thus is a generic feature of all
critical eigenstates. The relationsip between the branching power and the
multi-fractality exponent is derived.Comment: 4 pages, LATE
Weak levitation of 2D delocalized states in a magnetic field.
The deviation of the energy position of a delocalized state from the center
of Landau level is studied in the framework of the Chalker-Coddington model. It
is demonstrated that introducing a weak Landau level mixing results in a shift
of the delocalized state up in energy. The mechanism of a levitation is a
neighboring - Landau level - assisted resonant tunneling which ``shunts'' the
saddle-points. The magnitude of levitation is shown to be independent of the
Landau level number.Comment: Latex file (12 pages) + 3 Postscript figures
THE ANOMALOUS DIFFUSION IN HIGH MAGNETIC FIELD AND THE QUASIPARTICLE DENSITY OF STATES
We consider a disordered two-dimensional electronic system in the limit of
high magnetic field at the metal-insulator transition. Density of states close
to the Fermi level acquires a divergent correction to the lowest order in
electron-electron interaction and shows a new power-law dependence on the
energy, with the power given by the anomalous diffusion exponent . This
should be observable in the tunneling experiment with double-well GaAs
heterostructure of the mobility at temperatures of and voltages of .Comment: 12 pages, LATEX, one figure available at request, accepted for
publication in Phys. Rev.
Chiral Random Matrix Model for Critical Statistics
We propose a random matrix model that interpolates between the chiral random
matrix ensembles and the chiral Poisson ensemble. By mapping this model on a
non-interacting Fermi-gas we show that for energy differences less than a
critical energy the spectral correlations are given by chiral Random
Matrix Theory whereas for energy differences larger than the number
variance shows a linear dependence on the energy difference with a slope that
depends on the parameters of the model. If the parameters are scaled such that
the slope remains fixed in the thermodynamic limit, this model provides a
description of QCD Dirac spectra in the universality class of critical
statistics. In this way a good description of QCD Dirac spectra for gauge field
configurations given by a liquid of instantons is obtained.Comment: 21 pages, 3 figures, Latex; added two references and minor
correction