Long-range coherence and mesoscopic transport in N-S metallic structures

TL;DR

This paper reviews mesoscopic transport phenomena in diffusive normal-superconductor structures, highlighting the proximity effect, long-range coherence, and characteristic energy scales like the Thouless energy, with implications for conductance and magnetoresistance.

Contribution

It provides a comprehensive review of how Andreev reflection and the proximity effect influence mesoscopic transport and coherence in N-S structures, emphasizing the role of the Thouless energy.

Findings

Conductivity is locally enhanced by the proximity effect.

Re-entrant conductance behavior occurs at low energies.

Magnetoresistance oscillates with temperature, indicating long-range coherence.

Abstract

We review the mesoscopic transport in a diffusive proximity superconductor made of a normal metal (N) in metallic contact with a superconductor (S). The Andreev reflection of electrons on the N-S interface is responsible for the diffusion of electron pairs in N. Superconducting-like properties are induced in the normal metal. In particular, the conductivity of the N metal is locally enhanced by the proximity effect. A re-entrance of the metallic conductance occurs when all the energies involved (e.g. temperature and voltage) are small. The relevant characteristic energy is the Thouless energy which is $\hbar$ divided by the diffusion time for an electron travelling throughout the sample. In loop-shaped devices, a 1/T temperature-dependent oscillation of the magnetoresistance arises with a large amplitude from the long-range coherence of low-energy pairs.