Superconductivity suppression 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 in the assumption of two-dimensional diffusive nature of electrons motion. The main contribution to the \(T_c\) suppression 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 \(\delta T_c/T_{c0} \sim - 1/k_Fl\), where \(k_F\) is the Fermi momentum and \(l\) is the mean free path. Thus almost for all superconducting films that follow the fermionic scenario of \(T_c\) 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 \(k_F l\) rather than the sheet resistance of the film.