Superconducting proximity effect and charging effect on the normal transport in normal-metal (semiconductor) wire

We theoretically investigated superconducting proximity corrections of the conductance of a mesoscopic metal wire in terms of the Kubo-formula. In diagrammatic expression, the electromagnetic response kernel is quite similar to that of reproducible conductance fluctuation However, the proximity correction modifies the average conductance of the wire even though the latter gives a mesoscopic fluctuation. This Kubo-formula expression is applicable to the analysis of charging effects on the proximity correction in a superconductor(S)/Mesoscopic-normal-metal-wire(N) hybrid system with a very small S/N interface. Although the charging effect exponentially suppresses Andreev reflections at the S/N interface, the proximity correction survives. We propose an experiment to confirm this charging effect, where a degenerated semiconductor is used as the normal-metal wire. The proximity correction can be picked from the entire conductance as the magnetoconductance of an interferometer, and the charging effect is depicted by a gate control of the superconducting island. The semiconductor interferometer is more promising than a metallic one because the conductance without the proximity effect is bigger.