Thouless energy of a superconductor from non local conductance fluctuations

Abstract

We show that a spin-up electron from a normal metal entering a superconductor propagates as a composite object consisting of a spin-down hole and a pair in the condensate. This leads to a factorization of the non local conductance as two local Andreev reflections at both interfaces and one propagation in the superconductor, which is tested numerically within a one dimensional toy model of reflectionless tunneling. Small area junctions are characterized by non local conductance fluctuations. A treatment ignoring weak localization leads to a Thouless energy inverse proportional to the sample size, as observed in the numerical simulations. We show that weak localization can have a strong effect, and leads to a coupling between evanescent quasiparticles and the condensate by Andreev reflections ``internal'' to the superconductor.

11 pages, 12 figures, revised manuscript

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• Positive current cross-correlations in a highly transparent normal-superconducting beam splitter due to synchronized Andreev and inverse Andreev reflections
• Self-consistent microscopic calculations for non-local transport through nanoscale superconductors
• Non-local transport in normal-metal/superconductor hybrid structures: the role of interference and interaction
• Absence of split pairs in the cross-correlations of a highly transparent normal metal-superconductor-normal metal electron beam splitter
• Exchange-interaction of two spin qubits mediated by a superconductor
• Nonlocal transport mediated by nonlocal Hikami boxes: Condensation of evanescent quasiparticles injected into the superconducting gap
• Nonlocal transport through multiterminal diffusive superconducting nanostructures
• Non local Andreev reflection in a carbon nanotube superconducting quantum interference device
• Weak localization corrections to the thermal conductivity in $s$-wave superconductors
• Subgap tunneling via quantum-interference effect: insulators and charge density waves