Broken symmetries and localization lengths in Anderson insulators: Theory and experiment

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Abstract
Extending a random-matrix theory developed earlier, we show that breaking a basic symmetry in an Anderson insulator (e.g., time-reversal symmetry or spin-rotation symmetry) generically yields a multiplication of the localization length ξ by universal factors. Numerical calculations and magnetoconductance measurements in the Mott variable-range-hopping regime confirm that the removal of time-reversal symmetry by a magnetic field yields ξ→2ξ in the absence of spin-orbit scattering, and ξ→ξ/2 in the presence of spin-orbit coupling.