Self consistent charge-current in a mesoscopic region attached to superconductor leads

TL;DR

This paper studies how the electric potential profile inside a mesoscopic region connected to superconductors influences the current-voltage characteristics and electronic population, using a self-consistent Keldysh Green functions approach.

Contribution

It introduces a self-consistent method to analyze potential profiles and their effects on transport in mesoscopic superconductor systems, extending previous models.

Findings

Potential profiles significantly modify I-V curves.

Electronic populations are affected by potential profile behavior.

Model results align with experimental observations.

Abstract

We investigate the behavior of a electric potential profile inside a mesoscopic region attached to a pair of superconducting leads. It turns out that ${\rm I}-V$ characteristic curves are strongly modified by this profile. In addition, the electronic population in the mesoscopic region is affected by the profile behavior. We discuss the single particle current and the mesoscopic electronic population within the non-equilibrium Keldysh Green functions technique. The Keldysh technique results are further converted in a self consistent field (SFC) problem by introducing potential profile modifications as proposed by Datta. Evaluation of ${\rm I}-V$ characteristics are presented for several values of the model parameters and comparison with current experimental results are discussed.