Spin-orbit scattering for localized electrons: Absence of negative magnetoconductance

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Abstract
The distribution of hopping conductances in the strongly localized regime in the presence of both a magnetic field and spin-orbit (SO) scattering is calculated via an analytic independent-directed-path formalism, and a locator expansion which includes all correlations between paths. Both methods lead to a positive magnetoconductance for all strengths of SO scattering, contrary to recent random-matrix theory predictions. Extensive numerical simulations demonstrate that the crossover from negative to positive magnetoconductance occurs as the system size exceeds the localization length.