179 research outputs found
Thermally Activated Deviations from Quantum Hall Plateaus
The Hall conductivity of a two-dimensional electron system
is quantized in units of when the Fermi level is located in the
mobility gap between two Landau levels. We consider the deviation of
from a quantized value caused by the thermal activation of
electrons to the extended states for the case of a long range random potential.
This deviation is of the form . The prefactor
is equal to at temperatures above a characteristic
temperature . With the temperature decreasing below , decays according to a power law: . Similar results are valid for a fractional Hall
plateau near filling factor if is replaced by the fractional charge
.Comment: 4 pages in PostScript (figures included
Continuous Elastic Phase Transitions in Pure and Disordered Crystals
We review the theory of second--order (ferro--)elastic phase transitions,
where the order parameter consists of a certain linear combination of strain
tensor components, and the accompanying soft mode is an acoustic phonon. In
three--dimensional crystals, the softening can occur in one-- or
two--dimensional soft sectors. The ensuing anisotropy reduces the effect of
fluctuations, rendering the critical behaviour of these systems classical for a
one--dimensional soft sector, and classical with logarithmic corrections in
case of a two--dimensional soft sector. The dynamical critical exponent is , and as a consequence the sound velocity vanishes as , while the phonon damping coefficient is essentially
temperature--independent. Disorder may lead to a variety of precursor effects
and modified critical behaviour. Defects that locally soften the crystal may
induce the phenomenon of local order parameter condensation. When the
correlation length of the pure system exceeds the average defect separation
, a disorder--induced phase transition to a state with
non--zero average order parameter can occur at a temperature
well above the transition temperature of the pure crystal. Near
, the order--parameter curve, susceptibility, and specific heat appear
rounded. For the spatial inhomogeneity induces a static
central peak with finite width in the scattering cross section, accompanied
by a dynamical component that is confined to the very vicinity of the
disorder--induced phase transition.Comment: 26 pages, Latex (rs.sty now IS included), 11 figures can be obtained
from U.C. T\"auber ([email protected]); will appear in Phil. Trans. Roy.
Soc. Lond. A (October 1996
Continuous Versus First Order Transitions in Compressible Diluted Magnets
The interplay between disorder and compressibility in Ising magnets is
studied. Contrary to pure systems in which a weak compressibility drives the
transition first order, we find from a renormalization group analysis that it
has no effect on disordered systems which keep undergoing continuous transition
with rigid random-bond Ising model critical exponents. The mean field
calculation exhibits a dilution-dependent tricritical point beyond which, at
stronger compressibility the transition is first order. The different behavior
of XY and Heisenberg magnets is discussed.Comment: 16 pages, latex, 2 figures not include
Transport and Dephasing in a Quantum Dot: Multiply Connected Graph Model
Using the theory of diffusion in graphs, we propose a model to study
mesoscopic transport through a diffusive quantum dot. The graph consists of
three quasi-1D regions: a central region describing the dot, and two identical
left- and right- wires connected to leads, which mimic contacts of a real
system. We find the exact solution of the diffusion equation for this graph and
evaluate the conductance including quantum corrections. Our model is
complementary to the RMT-models describing quantum dots. Firstly, it reproduces
the universal limit at zero temperature. But the main advantage compared to
RMT-models is that it allows one to take into account interaction-induced
dephasing at finite temperatures. Besides, the crossovers from open to almost
closed quantum dots and between different regimes of dephasing can be described
within a single framework. We present results for the temperature dependence of
the weak localization correction to the conductance for the experimentally
relevant parameter range and discuss the possibility to observe the elusive
0D-regime of dephasing in different mesoscopic systems.Comment: 12 page
Peak Values of Conductivity in Integer and Fractional Quantum Hall Effect
The diagonal conductivity was measured in the Corbino geometry
in both integer and fractional quantum Hall effect (QHE). We find that peak
values of are approximately equal for transitions in a wide range
of integer filling factors , as expected in scaling theories of QHE.
This fact allows us to compare peak values in the integer and fractional
regimes within the framework of the law of corresponding states.Comment: 8 pages (revtex format), 3 postscript figure
Self-averaging in the random 2D Ising ferromagnet
We study sample-to-sample fluctuations in a critical two-dimensional Ising
model with quenched random ferromagnetic couplings. Using replica calculations
in the renormalization group framework we derive explicit expressions for the
probability distribution function of the critical internal energy and for the
specific heat fluctuations. It is shown that the disorder distribution of
internal energies is Gaussian, and the typical sample-to-sample fluctuations as
well as the average value scale with the system size like . In contrast, the specific heat is shown to be self-averaging with a
distribution function that tends to a -peak in the thermodynamic limit
. While previously a lack of self-averaging was found for the
free energy, we here obtain results for quantities that are directly measurable
in simulations, and implications for measurements in the actual lattice system
are discussed.Comment: 12 pages, accepted versio
Quantum Hall effect at low magnetic fields
The temperature and scale dependence of resistivities in the standard scaling
theory of the integer quantum Hall effect is discussed. It is shown that recent
experiments, claiming to observe a discrepancy with the global phase diagram of
the quantum Hall effect, are in fact in agreement with the standard theory. The
apparent low-field transition observed in the experiments is identified as a
crossover due to weak localization and a strong reduction of the conductivity
when Landau quantization becomes dominant.Comment: 4 pages, 2 figures, minor corrections, to appear in PR
Dynamical scaling at the quantum Hall transition: Coulomb blockade versus phase breaking
We argue that the finite temperature dynamics of the integer quantum Hall
system is governed by two independent length scales. The consistent scaling
description of the transition makes crucial use of two temperature critical
exponents, reflecting the interplay between charging effects and
interaction-induced dephasing. Experimental implications of the two-scale
picture are discussed.Comment: 4 pages, RevTeX, 1 figure included, minor changes, accepted in PR
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
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