Quasiclassical theory of superconductivity: a multiple interface geometry

Abstract

The purpose of the paper is to suggest a new method which allows one to study multiple coherent reflection/transmissions by partially transparent interfaces (e.g. in multi-layer mesoscopic structures or grain boundaries in high-Tc&#39;s) in the framework of the quasiclassical theory of superconductivity. It is argued that typically the trajectory of the particle is a simply connected tree (no loops) with knots, i.e. the points where interface scattering events occur and ballistic pieces of the trajectory are mixed. A linear boundary condition for the 2-component trajectory &#34;wave function&#34; which factorizes matrix (retarded) Green&#39;s function, is formulated for an arbitrary interface, specular or diffusive. To show the usage of the method, the current response to the vector potential (the total superfluid density rho_s) of a SS&#39; sandwich with the different signs of the order parameter in S and S&#39;, is calculated. In this model, a few percent of reflection by the SS&#39; interface transforms the paramagnetic response (rho_s < 0) created by the zero-energy Andreev bound states near an ideal interface (see Fauchere et al. PRL, 82, 3336 (1999), cond-mat/9901112), into the usual diamagnetic one (rho_s >0).