Magnetic-Field Dependence of the Localization Length in Anderson Insulators

TL;DR

This paper investigates how magnetic fields influence the localization length in Anderson insulators across different dimensions, revealing universal behavior in quasi-1D systems and non-universal effects in higher dimensions.

Contribution

It provides a detailed analysis of the magnetic field dependence of localization length using scaling and renormalization group methods, highlighting differences across dimensions.

Findings

In quasi-1D, magnetic field universally increases localization length.

In higher dimensions, magnetic field causes delocalization without a universal relation.

Spin-orbit interaction effects are briefly discussed.

Abstract

Using the conventional scaling approach as well as the renormalization group analysis in $d=2+\epsilon$ dimensions, we calculate the localization length $\xi(B)$ in the presence of a magnetic field $B$. For the quasi 1D case the results are consistent with a universal increase of $\xi(B)$ by a numerical factor when the magnetic field is in the range $\ell\ll{\ell_{\!{_H}}}\alt\xi(0)$, $\ell$ is the mean free path, ${\ell_{\!{_H}}}$ is the magnetic length $\sqrt{\hbar c/eB}$. However, for $d\ge 2$ where the magnetic field does cause delocalization there is no universal relation between $\xi(B)$ and $\xi(0)$. The effect of spin-orbit interaction is briefly considered as well.