Energy-level statistics and localization of 2d electrons in random magnetic fields

TL;DR

This paper investigates the localization of 2D electrons in random magnetic fields using energy-level statistics, finding evidence for localized states contrary to some previous proposals of extended states.

Contribution

It provides a finite size scaling analysis of energy-level statistics showing that electrons are localized in the presence of random magnetic fields, challenging earlier claims of extended states.

Findings

Electrons are localized in the studied model.

Energy-level statistics indicate no extended states.

Contradicts previous proposals of extended states in this system.

Abstract

Using the method of energy-level statistics, the localization properties of electrons moving in two dimensions in the presence of a perpendicular random magnetic field and additional random disorder potentials are investigated. For this model, extended states have recently been proposed to exist in the middle of the band. In contrast, from our calculations of the large-$s$ behavior of the nearest neighbor level spacing distribution $P(s)$ and from a finite size scaling analysis we find only localized states in the suggested energy and disorder range.