Multiple-scattering theory for clean superconducting layered structures

An exact expression is derived for the matrix Green's function of a clean superconducting layered structure with an arbitrary number of interfaces. A multiple-scattering approach is employed, in which the interfaces act as the scattering centres. Some initial applications of the theory to systems with transverse dimensions which vary from narrow to wide are given. The local 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 certain critical transverse widths the exact theory shows remarkable features not seen in the Andreev approximation. If the gap function for the systems is calculated self-consistently it turns out that for transverse dimensions smaller than twenty per cent of the superconducting coherence length, superconductivity is suppressed.