Current-carrying states in superconducting multilayers with Josephson interlayer coupling for temperatures close to T_c0: A microscopic theory

We present a complete, self-consistent, microscopic description of current-carrying states in all sorts of superconducting multilayers with interlayer Josephson coupling near the bulk critical temperature, T_c0: superconductor-insulator (SI) superlattices with or without intrabarrier exchange interactions and nonmagnetic impurities inside superconducting (S) layers, pure structures with point-contact-type interlayer coupling, superconductor–normal-metal (SN) superlattices with an arbitrary concentration of nonmagnetic impurities, and SN superlattices in the dirty limit with paramagnetic impurities inside N barriers. We have obtained closed analytical expressions for the Josephson current as a function of an S layer thickness, a. For all these systems drastic deviations from a single-junction case were found: a reduction of the critical Josephson current j_c for pure SI superlattices with a<~ξ₀, nontrivial current-phase dependence for multilayers with point-contact-type coupling and a<~ξ₀, and nontrivial temperature dependence of j_c for SN superlattices. Mathematically, our approach is based solely on the use of a microscopic free-energy functional. For a≫ξ₀, we reduce this functional to a Ginzburg-Landau-type functional with an extra term accounting for the interface free energy. For SI superlattices, in an appropriate limit this latter reduces to a Lawrence-Doniach-type functional with microscopically defined coefficients.