SELF-CONSISTENT THEORY FOR THE DC JOSEPHSON EFFECT IN A SUPERCONDUCTING STM JUNCTION

We present a microscopic theory for the DC Josephson tunnelling curren ts between a superconducting STM tip and the surface of a superconduct or. Within this theory, the spatial variation of the order parameter i n the presence of a stationary current is calculated in a self-consist ent way at the interface region. The Hamiltonian modelling this system is written in a tight-binding representation and the superconducting state is treated in a mean-field (BCS-like) approximation. We use a no n-equilibrium Green functions technique for the calculation of the pha se-parameter profile and currents. The results are analyzed as a funct ion of the tip-sample distance, tunnelling current intensity, total ph ase gradient through the interface and coherence length of the superco nductors. The effects of self-consistency are found to be crucial in t he close-contact regime when the tip-sample junction has a bottle-neck geometry.