General Boundary Conditions for Quasiclassical Theory of Superconductivity in the Diffusive Limit: Application to Strongly Spin-polarized Systems

TL;DR

This paper derives comprehensive boundary conditions for the diffusive quasiclassical theory of superconductivity, enabling accurate modeling of proximity effects in heterostructures involving strongly spin-polarized materials like half-metals.

Contribution

It provides the first complete boundary conditions for Usadel theory with arbitrary spin polarization, transmission, and spin-dependent scattering, including complex spin textures and channel mixing.

Findings

Derived boundary conditions valid for any spin polarization and interface scattering.

Applied the theory to superconductor/half-metal/superconductor junctions.

Predicted $0$ junction behavior under specific interface conditions.

Abstract

Boundary conditions in quasiclassical theory of superconductivity are of crucial importance for describing proximity effects in heterostructures between different materials. Although they have been derived for the ballistic case in full generality, corresponding boundary conditions for the diffusive limit, described by Usadel theory, have been lacking for interfaces involving strongly spin-polarized materials, such as e.g. half-metallic ferromagnets. Given the current intense research in the emerging field of superconducting spintronics, the formulation of appropriate boundary conditions for the Usadel theory of diffusive superconductors in contact with strongly spin-polarized ferromagnets for arbitrary transmission probability and arbitrary spin-dependent interface scattering phases has been a burning open question. Here we close this gap and derive the full boundary conditions for quasiclassical Green functions in the diffusive limit, valid for any value of spin polarization, transmission probability, and spin mixing angles (spin-dependent scattering phase shifts). It allows also for complex spin textures across the interface and for channel off-diagonal scattering (a necessary ingredient when the numbers of channels on the two sides of the interface differ). As an example we derive expressions for the proximity effect in diffusive systems involving half-metallic ferromagnets. In a superconductor/half-metal/superconductor Josephson junction we find $\phi_0$ junction behavior under certain interface conditions.