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 nonmonotonous. We discuss the key differences of the ballistic and semiballistic regimes to the fully diffusive case.

• Received 16 June 2021
• Revised 5 August 2021
• Accepted 16 August 2021

DOI:https://doi.org/10.1103/PhysRevB.104.104502

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

Published by the American Physical Society