Magnetic-Field Dependence of the Localization Length in Anderson Insulators

Details Magnetic-Field Dependence of the Localization Length in Anderson Insulators Magnetic-Field Dependence of the Localization Length in Anderson Insulators

1994-11-24

arxiv.org/abs/cond-mat/9411101v1

Europhys. Lett. 29 1995 49

Physics

Condensed Matter

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

Scientific paper

10.1209/0295-5075/29/1/009

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.

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