Transfer-matrix description of heterostructures involving superconductors and ferromagnets

TL;DR

This paper develops a comprehensive theoretical framework using quasiclassical Green's functions and t-matrix boundary conditions to describe heterostructures involving superconductors and spin-polarized materials, applicable to various transmission regimes.

Contribution

It introduces a t-matrix based boundary condition approach that unifies ballistic and diffusive regimes and connects with existing scattering-matrix methods.

Findings

Formulated boundary conditions for arbitrary interface transmission and spin scattering.

Unified description for ballistic and diffusive heterostructures.

Demonstrated advantages of the t-matrix approach over traditional methods.

Abstract

Based on the technique of quasiclassical Green's functions, we construct a theoretical framework for describing heterostructures consisting of superconductors and/or spin-polarized materials. The necessary boundary conditions at the interfaces separating different metals are formulated in terms of hopping amplitudes in a t-matrix approximation. The theory is applicable for an interface with arbitrary transmission and exhibiting scattering with arbitrary spin dependence. Also, it can be used in describing both ballistic and diffusive systems. We establish the connection between the standard scattering-matrix approach and the existing boundary conditions, and demonstrate the advantages offered by the t-matrix description.