Magnetic-Field Dependence of the Localization Length in Anderson Insulators

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 $\ell\ll{\ell_{\!{_H}}}\altξ(0)$, $\ell$ is the mean free path, ${\ell }_{{}_H}$ is the magnetic length $\sqrt{\hslash c/eB}$. 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.

arXiv comment4 pages, revtex, no figures; to be published in Europhysics Letters

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