46 research outputs found
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
Disorder and Quantum Fluctuations in Superconducting Films in Strong Magnetic Fields
We find that the upper critical field in a two-dimensional disordered
superconductor can increase essentially at low temperatures. This happens due
to the formation of local superconducting islands weakly coupled via the
Josephson effect. The distribution of the superconducting islands is derived.
It is shown that the value of the critical field is determined by the interplay
of the proximity effect and quantum phase fluctuations. We find that the shift
of the upper critical field is connected with the pinning properties of a
superconductor.Comment: 4 page
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
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-
Information about the Integer Quantum Hall Transition Extracted from the Autocorrelation Function of Spectral Determinants
The Autocorrelation function of spectral determinants (ASD) is used to probe
the sensitivity of a two-dimensional disordered electron gas to the system's
size L.
For weak magnetic fields ASD is shown to depend only trivially on L, which is
a strong indication that all states are localized.
From nontrivial dependence of ASD on L for infinite L at a Hall conductance
of 1/2 e^2/h we deduce the existence of critical wave functions at this point,
as long as the disorder strength does not exceed a critical value.Comment: 4 pages, one citation correcte
Scaling Theory of the Integer Quantum Hall Effect
The scaling theory of the transitions between plateaus of the Hall
conductivity in the integer Quantum Hall effect is reviewed. In the model of
two-dimensional noninteracting electrons in strong magnetic fields the
transitions are disorder-induced localization-delocalization transitions. While
experimental and analytical approaches are surveyed, the main emphasis is on
numerical studies, which successfully describe the experiments. The theoretical
models for disordered systems are described in detail. An overview of the
finite-size scaling theory and its relation to Anderson localization is given.
The field-theoretical approach to the localization problem is outlined.
Numerical methods for the calculation of scaling quantities, in particular the
localization length, are detailed. The properties of local observables at the
localization-delocalization transition are discussed in terms of multifractal
measures. Finally, the results of extensive numerical investigations are
compared with experimental findings.Comment: 96 pages, REVTeX 3, 28 figures, Figs. 8-24, 26-28 appended as
uuencoded compressed tarred PostScript files. Submitted to Rev. Mod. Phys