Generalized boundary conditions for the circuit theory of mesoscopic transport

TL;DR

This paper extends the circuit theory of mesoscopic transport to include hybrid systems with normal metals, ferromagnets, and superconductors, providing a unified framework for complex spin-dependent and superconducting phenomena.

Contribution

It introduces a generalized expression for the current between nodes in hybrid systems, accommodating superconducting and ferromagnetic elements and interfaces.

Findings

Derived a universal formula for matrix current in hybrid systems.

Simplified results for weak ferromagnets and magnetic tunnel junctions.

Enhanced the applicability of circuit theory to complex mesoscopic systems.

Abstract

The circuit theory of mesoscopic transport provides a unified framework to describe spin-dependent or superconductivity-related phenomena. We extend this theory to hybrid systems of normal metals, ferromagnets and superconductors. Our main result is an expression for the current through an arbitrary contact between two general isotropic "nodes", which is suitable to describe the presence of superconducting and ferromagnetic elements in the system, as well as magnetically active interfaces/contacts. In certain cases (weak ferromagnet and magnetic tunnel junction) we derive transparent and simple results for the matrix current.