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 nonvanishing 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.

• Received 7 June 2015

DOI:https://doi.org/10.1103/PhysRevB.92.014507