Disorder and Localization in the Lowest Landau Level

TL;DR

This paper investigates how disorder affects electron localization in a 2D electron gas under magnetic fields, showing that most states are localized with finite length and no universal localization exponent exists at low impurity levels.

Contribution

It provides a detailed analysis of localization properties in the lowest Landau level with short-range disorder, highlighting the absence of a universal localization exponent.

Findings

All states except at the Landau level are localized.

Localization length remains finite at low impurity concentrations.

No universal localization exponent is observed.

Abstract

We study the localization property of a two-dimensional noninteracting electron gas in the presence of randomly distributed short-range scatterers. We evaluate the participation number of the eigenstates obtained by exact diagonalization technique. At low impurity concentrations we obtain self-averaged values showing that all states, except those exactly at the Landau level, are localized with finite localization length. We conclude that there is no universal localization exponent and at least at low impurity concentrations localization length does not diverge.