Localization and Delocalization in Dirty Superconducting Wires

Abstract

We present Fokker-Planck equations that describe transport of heat and spin in dirty unconventional superconducting quantum wires. Four symmetry classes are distinguished, depending on the presence or absence of time-reversal and spin-rotation invariance. In the absence of spin-rotation symmetry, heat transport is anomalous in that the mean conductance decays like $1/\sqrt{L}$ instead of exponentially fast for large enough length $L$ of the wire. The Fokker-Planck equations in the presence of time-reversal symmetry are solved exactly and the mean conductance for quasiparticle transport is calculated for the crossover from the diffusive to the localized regime.