Method of quasiclassical Green's functions in the theory of transport phenomena in superconducting mesoscopic structures

TL;DR

This paper introduces the matrix quasiclassical Green's functions method for analyzing transport in mesoscopic superconducting-normal metal structures, focusing on diffusive regimes and phase-coherent effects in multi-terminal setups.

Contribution

It presents a simplified set of equations for the diffusive and weak proximity effect regimes and applies them to calculate conductance and study Josephson effects in complex S/N structures.

Findings

Derived simplified equations for diffusive regimes

Calculated conductance of S/N structures

Identified conditions for observing Josephson effects

Abstract

A short introduction to the theory of matrix quasiclassical Green's functions is given and possible applications of this theory to transport properties of mesoscopic superconducting-normal metal (S/N) structures are considered. We discuss a simplified version of these equations in the diffusive regime and in the case of a weak proximity effect. These equations are used for the calculation of the conductance of different S/N structures. Long-range, phase-coherent effects are studied in a 4-terminal S/N/S structures under conditions when the Josephson critical current is negligible. It is shown that the Josephson effects may be observed in this system if an additional current flows through the N electrode.