Suppression of Superconductivity in Disordered Films: Interplay of Two-Dimensional Diffusion and Three-Dimensional Ballistics

Suppression of the critical temperature in homogeneously disordered superconducting films is a consequence of the disorder-induced enhancement of Coulomb repulsion. We demonstrate that for the majority of thin films studied now this effect cannot be completely explained under the assumption of two-dimensional diffusive nature of electron motion. The main contribution to the suppression of Tc arises from the correction to the electron-electron interaction constant coming from small scales of the order of the Fermi wavelength that leads to the critical temperature shift δTc/Tc0 ∼ − 1/kFl, where kF is the Fermi momentum and l is the mean free path. Thus almost for all superconducting films that follow the fermionic scenario of Tc suppression with decreasing the film thickness, this effect is caused by the proximity to the three-dimensional Anderson localization threshold and is controlled by the parameter kFl rather than the sheet resistance of the film.