Localization of electrons in two-dimensional spatially-correlated random magnetic fields

TL;DR

This study investigates electron localization in a 2D plane with spatially-correlated random magnetic fields, finding no metal-insulator transition and showing all states are localized, with eigenstates exhibiting multifractal properties.

Contribution

It provides the first detailed analysis of localization in correlated random magnetic fields, challenging previous claims of a metal-insulator transition and characterizing eigenstates' multifractality.

Findings

No metal-insulator transition observed.

All states are localized in the presence of disorder.

Eigenstates show multifractal behavior with unique dimensions.

Abstract

The localization properties of electrons moving in a plane perpendicular to a spatially-correlated static magnetic field of random amplitude and vanishing mean are investigated. We apply the method of level statistics to the eigenvalues and perform a multifractal analysis for the eigenstates. From the size and disorder dependence of the variance of the nearest neighbor energy spacing distribution, $P_{W,L}(s)$, a single branch scaling curve is obtained. Contrary to a recent claim, we find no metal-insulator-transition in the presence of diagonal disorder. Instead, as in the uncorrelated random magnetic field case, conventional unitary behavior (all states are localized) is observed. The eigenstates at the band center, which in the absence of diagonal disorder are believed to belong to the chiral unitary symmetry class, are shown to exhibit a $f(\alpha)$-distribution for not too weak random fields. The corresponding generalized multifractal dimensions are calculated and found to be different from the results known for a QHE-system.