A Unified Model for Two Localisation Problems: Electron States in Spin-Degenerate Landau Levels, and in a Random Magnetic Field

TL;DR

This paper introduces a unified model that explains localization phenomena in two related magnetic systems, revealing critical behaviors and the universal localization of states in a random magnetic field.

Contribution

The paper presents a single model that unifies the understanding of localization in spin-degenerate Landau levels and in random magnetic fields, supported by scaling analysis and simulations.

Findings

Localization length diverges at two energies in spin-degenerate Landau levels

All states are localized in a two-dimensional random magnetic field with zero average

Critical behavior matches that of spin-split Landau levels

Abstract

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.