Coherence-length dependence of fluctuations in the conductance of normal-superconducting interfaces

Abstract

We compute sample-to-sample fluctuations in the electrical conductance GNS of mesoscopic normal-superconducting boundaries. If the superconductor is clean and the normal conductor diffusive, the rms deviation δGNS is approximately a factor of 2 larger than the universal value obtained for normal disordered conductors. This is consistent with predictions of random matrix theories and recent numerical simulations. If the normal material is clean, but the superconductor diffusive, the boundary conductance fluctuation is greater than δGNS, by an amount which increases as the superconducting coherence length decreases. For a diffusive normal material in contact with a dirty superconductor, δGNS is insensitive to weak disorder in the superconductor, but decreases in the extreme dirty limit, where quasiparticles within the superconductor become Anderson localized.