Magnetic-Field Dependence of the Localization Length in Anderson Insulators

Using the conventional scaling approach as well as the renormalization group analysis in d = 2 + ε dimensions, we calculate the localization length ξ( B ) in the presence of a magnetic field B . For the quasi-1D case the results are consistent with a universal increase of ξ( B ) by a numerical factor when the magnetic field is in the range l ≪ l H ≲ ξ(0), l is the mean free path, l H is the magnetic length √ ℏ c / eB . However, for d ⩾ 2 where the magnetic field does cause delocalization there is no universal relation between ξ( B ) and ξ(0). The effect of spin-orbit interaction is briefly considered as well.