Multiple-scattering theory for clean superconducting layered structures

An exact expression is derived for the matrix Green's function of a clean s uperconducting layered structure with an arbitrary number of interfaces. A multiple-scattering approach is employed, in which the interfaces act as th e scattering centres. Some initial applications of the theory to systems wi th transverse dimensions which vary from narrow to wide are given. The loca l density of states is calculated for an SNS and for an SNSNS junction ('S' standing for a superconducting layer and 'N' for a normal layer). For cert ain critical transverse widths the exact theory shows remarkable features n ot seen in the Andreev approximation. If the gap function for the systems i s calculated self-consistently it turns out that for transverse dimensions smaller than twenty per cent of the superconducting coherence length, super conductivity is suppressed.