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 responsi
ble 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.
We demonstrate that thermoelectric currents in superconducting bilayers with a spin-active interface are controlled by the two competing processes. On one hand, spin-sensitive quasiparticle scattering at such interface generates electron-hole imbalan
ce and yields orders-of-magnitude enhancement of the thermoelectric effect in the system. On the other hand, this electron-hole imbalance gets suppressed in the superconductor bulk due to electron scattering on non-magnetic impurities. As a result, large thermoelectric currents can only flow in the vicinity of the spin-active interface and decay away from this interface at a distance exceeding the electron elastic mean free path $ell$. The magnitude of the thermoelectric effect reaches its maximum provided $ell$ becomes of order of the total bilayer thickness.
