Superconductive proximity effect in interacting disordered conductors

Abstract

We present a general theory of the superconductive proximity effect in disordered normal--superconducting (N-S) structures, based on the recently developed Keldysh action approach. In the case of the absence of interaction in the normal conductor we reproduce known results for the Andreev conductance G_A at arbitrary relation between the interface resistance R_T and the diffusive resistance R_D. In two-dimensional N-S systems, electron-electron interaction in the Cooper channel of normal conductor is shown to strongly affect the value of G_A as well as its dependence on temperature, voltage and magnetic field. In particular, an unusual maximum of G_A as a function of temperature and/or magnetic field is predicted for some range of parameters R_D and R_T. The Keldysh action approach makes it possible to calculate the full statistics of charge transfer in such structures. As an application of this method, we calculate the noise power of an N-S contact as a function of voltage, temperature, magnetic field and frequency for arbitrary Cooper repulsion in the normal metal and arbitrary values of the ratio R_D/R_T.