Fluctuations of the Josephson current and electron-electron interactions in superconducting weak links

Abstract

We derive a microscopic effective action for superconducting contacts with arbitrary transmission distribution of conducting channels. Provided fluctuations of the Josephson phase remain sufficiently small our formalism allows to fully describe fluctuation and interaction effects in such systems. As compared to the well studied tunneling limit our analysis yields a number of qualitatively new features which occur due to the presence of subgap Andreev bound states in the system. We investigate the equilibrium supercurrent noise and evaluate the electron-electron interaction correction to the Josephson current across superconducting contacts. At T=0 this correction is found to vanish for fully transparent contacts indicating the absence of Coulomb effects in this limit.