Euler parametrization of Eilenberger equations

Abstract

We suggest a parametrization of the quasiclassical equations of superconductivity which takes into account the boundary conditions on quasiclassical Green's functions. The resultant equations have a simple structure and permit numeric treatment of one-dimensional problems for arbitrary strength of the boundary potential. Both cases of absence and presence of the current through the system are discussed. We apply the technique to calculate the effect of the current through the interface with small reflectivity separating two superconductors. Contrary to the case of low transparency (conventional Josephson effect) the phase jump is not located at the interface. Rather it is distributed near the interface within characteristic range of the order of zero-temperature coherence length xi(0) (clean limit) or mean free path I (dirty limit).