Theory of Nonhomogeneous Superconductors

Abstract

A variational principle is developed for calculating the properties of nonhomogeneous superconducting systems at finite temperatures. The quantity varied is the energy-gap function as it occurs in the Gor'kov equations, and the correct Green's function is obtained by minimization of the thermodynamic potential. The calculation may be simplified by expanding the potential in powers of the energy-gap function or by a technique of analytic continuation. The former is easier but can be used only near the transition temperature, while the latter is valid at all temperatures. The variational procedure is used to calculate the transition temperatures of superposed-film systems, using a one-parameter model to describe the intermetallic potential barrier. The results agree well with the experimental data and indicate that barrier effects are important. The theory is valid for all mean free paths and is in accord with the phenomenological analysis of Hilsch and Hilsch.