Localization in a random magnetic field: The semiclassical limit
- 15 August 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 50 (8) , 5272-5285
- https://doi.org/10.1103/physrevb.50.5272
Abstract
We study the two-dimensional electron gas in the presence of a random perpendicular magnetic field. We examine, in particular, the limit in which the correlation length of the random field is large compared to the typical magnetic length. In this limit, a semiclassical approach can be used to understand a large part of the energy spectrum. To investigate localization, we introduce a simplified model, in which electrons propagate coherently on a random network derived from the classical trajectories. The same network model (with different parameters) also represents electron motion in a uniform magnetic field and a random scalar potential, in a spin-degenerate Landau level. Requiring that the global phase diagram of our model be consistent with Khmelnitskii’s scaling flow for the quantum Hall effect, we argue that all electron states in a random magnetic field are localized in the semiclassical limit. We present the results of numerical simulations of the model in support of this conclusion.Keywords
This publication has 44 references indexed in Scilit:
- Effective field theory of electron motion in the presence of random magnetic fluxPhysical Review Letters, 1994
- Two-dimensional localization in the presence of random flux and the quantum Hall system at even-denominator filling fractionsPhysical Review B, 1993
- Single-particle motion in a random magnetic fluxPhysical Review B, 1993
- Localization problem of a two-dimensional lattice in a random magnetic fieldPhysical Review B, 1993
- Localization in a random magnetic field in 2DPhysical Review Letters, 1993
- Theory of the half-filled Landau levelPhysical Review B, 1993
- Metallic phase of the quantum Hall system at even-denominator filling fractionsPhysical Review B, 1992
- Electron hopping in the presence of random fluxPhysical Review B, 1992
- Normal-state properties of the uniform resonating-valence-bond statePhysical Review Letters, 1990
- Gapless fermions and gauge fields in dielectricsPhysical Review B, 1989