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