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

Journal article, 2021

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, momentumresolved 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-c. We find that V-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.