Stationary transport in mesoscopic hybrid structures with contacts to superconducting and normal wires. A Green's function approach for multiterminal setups

TL;DR

This paper extends Green's function methods to analyze stationary quantum transport in hybrid normal-superconducting structures, revealing flux-sensitive Andreev states and their relation to Cooper pairs in superconducting rings.

Contribution

It introduces a generalized Green's function approach for multiterminal hybrid structures with normal and superconducting components.

Findings

Equilibrium currents in normal rings are flux-sensitive.

Andreev states respond similarly to Cooper pairs with zero momentum.

Method enables detailed analysis of hybrid S-N structures.

Abstract

We generalize the representation of the real time Green's functions introduced by Langreth and Nordlander [Phys. Rev. B 43 2541 (1991)] and Meir and Wingreen [Phys. Rev. Lett. 68 2512 (1992)] in stationary quantum transport in order to study problems with hybrid structures containing normal (N) and superconducting (S) pieces. We illustrate the treatment in a S-N junction under a stationary bias and investigate in detail the behavior of the equilibrium currents in a normal ring threaded by a magnetic flux with attached superconducting wires at equilibrium. We analyze the flux sensitivity of the Andreev states and we show that their response is equivalent to the one corresponding to the Cooper pairs with momentum q=0 in an isolated superconducting ring.