11 research outputs found
Integer Quantum Hall Effect for Lattice Fermions
A two-dimensional lattice model for non-interacting fermions in a magnetic
field with half a flux quantum per plaquette and levels per site is
considered. This is a model which exhibits the Integer Quantum Hall Effect
(IQHE) in the presence of disorder. It presents an alternative to the
continuous picture for the IQHE with Landau levels. The large limit can be
solved: two Hall transitions appear and there is an interpolating behavior
between the two Hall plateaux. Although this approach to the IQHE is different
from the traditional one with Landau levels because of different symmetries
(continuous for Landau levels and discrete here), some characteristic features
are reproduced. For instance, the slope of the Hall conductivity is infinite at
the transition points and the electronic states are delocalized only at the
transitions.Comment: 9 pages, Plain-Te
Hall Resistivity and Dephasing in the Quantum Hall Insulator
The longstanding problem of the Hall resistivity rho(x,y) in the Hall
insulator phase is addressed using four-lead Chalker-Coddington networks.
Electron interaction effects are introduced via a finite dephasing length. In
the quantum coherent regime, we find that rho(x,y) scales with the longitudinal
resistivity rho(x,x), and they both diverge exponentially with dephasing
length. In the Ohmic limit, (dephasing length shorter than Hall puddles' size),
rho(x,y) remains quantized and independent of rho(x,x). This suggests a new
experimental probe for dephasing processes.Comment: RevTeX, 4 pages, 3 figures included with epsf.st
On the Relevance of Disorder for Dirac Fermions with Imaginary Vector Potential
We consider the effects of disorder in a Dirac-like Hamiltonian. In order to
use conformal perturbation theory, we argue that one should consider disorder
in an imaginary vector potential. This affects significantly the signs of the
lowest order eta functions. We present evidence for the existence of two
distinct universality classes, depending on the relative strengths of the gauge
field verses impurity disorder strengths. In one class all disorder is driven
irrelevant by the gauge field disorder.Comment: 4 pages, 1 figure. New version has expanded and improved discussion
of why one should consider an imaginary vector potential in a physical
localization problem. Factors of 2 in beta functions corrected. References
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Duality and Universality for the Chern-Simons bosons
By mapping the relativistic version of the Chern-Simons-Landau-Ginzburg
theory in 2+1 dimensions to the 3D lattice Villain x-y model coupled with the
Chern-Simons gauge field, we investigate phase transitions of Chern-Simons
bosons in the limit of strong coupling. We construct algebraically exact
duality and flux attachment transformations of the lattice theories,
corresponding to analogous transformations in the continuum limit. These
transformations are used to convert the model with arbitrary fractional
Chern-Simons coefficient to a model with either zero or one.
Depending on this final value of , the phase transition in the original
model is either in the universality class of the 3D x-y model or a
``fermionic'' universality class, unless the irrelevant corrections of cubic
and higher power in momenta render the transition of the first order.Comment: 14 two-column pages, revtex 3.0, multicol and epsf.sty (optional),
one PostScript figure, Submitted to Phys. Rev. B The changes intended to
simplify the arguments and eliminate logical gaps. We also show how the
filling factor is changed by the duality transformatio
Integer Quantum Hall Effect in Double-Layer Systems
We consider the localization of independent electron orbitals in double-layer
two-dimensional electron systems in the strong magnetic field limit. Our study
is based on numerical Thouless number calculations for realistic microscopic
models and on transfer matrix calculations for phenomenological network models.
The microscopic calculations indicate a crossover regime for weak interlayer
tunneling in which the correlation length exponent appears to increase.
Comparison of network model calculations with microscopic calculations casts
doubt on their generic applicability.Comment: 14 pages, 12 figures included, RevTeX 3.0 and epsf. Additional
reference
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