Quasiclassical theory of charge transport across mesoscopic normal metal-superconducting heterostructures with current conservation

TL;DR

This paper develops a quasiclassical, self-consistent theory for charge transport in mesoscopic superconductor-normal metal heterostructures, capturing phenomena beyond the diffusive limit and analyzing the effects of interface transparency and mean-free path.

Contribution

It introduces a comprehensive approach that extends beyond the diffusive limit to include ballistic and semi-ballistic regimes, ensuring current conservation in mesoscopic superconducting systems.

Findings

Superconductivity breaks down at a critical bias voltage $V_c$.

The critical voltage $V_c$ increases with reduced interface transparency.

The dependence of $V_c$ on mean-free path is non-monotonous.

Abstract

We consider the steady-state nonequilibrium behavior of mesoscopic superconducting wires connected to normal-metal reservoirs. Going beyond the diffusive limit, we utilize the quasiclassical theory and perform a self-consistent calculation that guarantees current conservation through the entire system. Going from the ballistic to the diffusive limit, we investigate several crucial phenomena such as charge imbalance, momentum-resolved nonequilbrium distributions, and the current-to-superflow conversion. Connecting to earlier results for the diffusive case, we find that superconductivity can break down at a critical bias voltage $V_\mathrm{c}$. We find that $V_\mathrm{c}$ generally increases as the interface transparency is reduced, while the dependence on the mean-free path is non-monotonous. We discussthe key differences of the ballistic and semi-ballistic regimes to the fully diffusive case.