3,298 research outputs found
Spectral Properties of the Chalker-Coddington Network
We numerically investigate the spectral statistics of pseudo-energies for the
unitary network operator U of the Chalker--Coddington network. The shape of the
level spacing distribution as well the scaling of its moments is compared to
known results for quantum Hall systems. We also discuss the influence of
multifractality on the tail of the spacing distribution.Comment: JPSJ-style, 7 pages, 4 Postscript figures, to be published in J.
Phys. Soc. Jp
Universality in an integer Quantum Hall transition
An integer Quantum Hall effect transition is studied in a modulation doped
p-SiGe sample. In contrast to most examples of such transitions the
longitudinal and Hall conductivities at the critical point are close to 0.5 and
1.5 (e^2/h), the theoretically expected values. This allows the extraction of a
scattering parameter, describing both conductivity components, which depends
exponentially on filling factor. The strong similarity of this functional form
to those observed for transitions into the Hall insulating state and for the
B=0 metal- insulator transition implies a universal quantum critical behaviour
for the transitions. The observation of this behaviour in the integer Quantum
Hall effect, for this particular sample, is attributed to the short-ranged
character of the potential associated with the dominant scatterers
Network Models of Quantum Percolation and Their Field-Theory Representations
We obtain the field-theory representations of several network models that are
relevant to 2D transport in high magnetic fields. Among them, the simplest one,
which is relevant to the plateau transition in the quantum Hall effect, is
equivalent to a particular representation of an antiferromagnetic SU(2N) () spin chain. Since the later can be mapped onto a ,
sigma model, and since recent numerical analyses of the
corresponding network give a delocalization transition with ,
we conclude that the same exponent is applicable to the sigma model
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
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
Floating of Extended States and Localization Transition in a Weak Magnetic Field
We report results of a numerical study of non-interacting electrons moving in
a random potential in two dimensions in the presence of a weak perpendicular
magnetic field. We study the topological properties of the electronic
eigenstates within a tight binding model. We find that in the weak magnetic
field or strong randomness limit, extended states float up in energy. Further,
the localization length is found to diverge at the insulator phase boundary
with the same exponent as that of the isolated lowest Landau band (high
magnetic field limit).Comment: RevTex, 4 pages, 3 figures available upon reques
Localization and conductance fluctuations in the integer quantum Hall effect: Real--space renormalization group approach
We consider the network model of the integer quantum Hall effect transition.
By generalizing the real--space renormalization group procedure for the
classical percolation to the case of quantum percolation, we derive a closed
renormalization group (RG) equation for the universal distribution of
conductance of the quantum Hall sample at the transition. We find an
approximate solution of the RG equation and use it to calculate the critical
exponent of the localization length and the central moments of the conductance
distribution. The results obtained are compared with the results of recent
numerical simulations.Comment: 17 pages, RevTex, 7 figure
The Quantum Hall Effect in Drag: Inter-layer Friction in Strong Magnetic Fields
We study the Coulomb drag between two spatially separated electron systems in
a strong magnetic field, one of which exhibits the quantum Hall effect. At a
fixed temperature, the drag mimics the behavior of in the quantum
Hall system, in that it is sharply peaked near the transitions between
neighboring plateaux. We assess the impact of critical fluctuations near the
transitions, and find that the low temperature behavior of the drag measures an
exponent that characterizes anomalous low frequency dissipation; the
latter is believed to be present following the work of Chalker.Comment: 13 pages, Revtex 2.0, 1 figure upon request, P-93-11-09
Effect of screening of the Coulomb interaction on the conductivity in the quantum Hall regime
We study variable range hopping in the quantum Hall effect regime in the
presence of a metallic gate parallel to the plane of a two-dimensional electron
gas. Screening of the Coulomb interaction by the gate causes the partial
``filling'' of the Coulomb gap in the density of localized states. At low
enough temperatures this leads to a substantial enhancement and a new
temperature behavior of the hopping conductivity. As a result, the diagonal
conductivity peaks become much wider. The power law dependence of the width of
the peaks on the temperature changes: the corresponding exponent turns out to
be twice as small as that for gateless structures. The width dependences on the
current in non-ohmic regime and on the frequency for the absorption of the
electromagnetic waves experience a similar modification. The experimental
observation of the crossovers predicted may demonstrate the important role of
the Coulomb interaction in the integer quantum Hall regime.Comment: 14 pages + 3 figures by request preprint TPI-MINN-93/58-
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