Diffusive superconductors beyond Usadel approximation: Electron-hole asymmetry and large photoelectric effect

TL;DR

This paper extends the quasiclassical formalism for diffusive superconductors by deriving anisotropic corrections to the Usadel equation, revealing effects like the photoelectric effect that are absent in the standard approximation.

Contribution

The authors derive anisotropic gradient corrections to the Usadel equation, enabling analysis of phenomena like the photoelectric effect in superconductors beyond the standard approximation.

Findings

Anisotropic corrections significantly impact the photoelectric effect in superconductors.

Charge imbalance and dc voltage are induced by external electromagnetic irradiation.

Magnetic impurities enhance the photoelectric effect, making it experimentally detectable.

Abstract

We extend the quasiclassical formalism for diffusive superconductors by deriving anisotropic (gradient) corrections to the Usadel equation. We demonstrate that in a number of physical situations such corrections may play a crucial role being responsible for the effects which cannot be recovered within the standard Usadel approximation. One of them is the so-called photoelectric effect in superconductors and superconducting-normal (SN) hybrid structures. Provided a superconducting part of the system is irradiated by an external ac electromagnetic field the charge imbalance develops and a non-vanishing dc voltage is induced across the SN interface. In the presence of magnetic impurities in a superconductor the magnitude of this effect becomes large and can easily be detected in modern experiments.