Self-Consistent Theory of Superconducting Mesoscopic Weak Links

TL;DR

This paper develops a microscopic, self-consistent model for superconducting mesoscopic weak links, analyzing their transport properties and excitation spectra across various regimes using the Bogoliubov-de Gennes equations and Green functions.

Contribution

It introduces a detailed self-consistent theoretical framework for superconducting weak links, bridging point contact and extended channel regimes with numerical solutions.

Findings

Maximum Josephson current depends on transmission coefficient and length.

Transition from point contact to long channel regimes analyzed.

Spectra and transport properties vary with system parameters.

Abstract

A microscopic model for describing a superconducting mesoscopic weak link is presented. We consider a model geometry consisting of a narrow channel coupled to wider superconducting electrodes which act as reservoirs fixing the asymptotic values of the complex order parameter. For this model, the Bogoliubov-de Gennes equations are discretized and solved self-consistently using a non-equilibrium Green functions formalism. The transport properties and the electronic excitation spectra of this system are studied for the different regimes that can be reached by varying parameters like coherence length, constriction length, normal transmission coefficient and temperature. We study in detail the transition from the point contact limit to the infinite channel length case, analyzing the maximum Josephson current that can be sustained by the weak link as a function of its transmission coefficient and length.