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

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.