Superconductivity Suppression in Disordered Films: Interplay of Proximity to the Two- and Three-Dimensional Localization

We revisit the problem of superconductivity suppression in homogeneously disordered thin films. Andersons theorem stating that the critical temperature is insensitive to the degree of disorder is violated in the vicinity of the Anderson localization transition. For strongly disordered films, the interplay between disorder and interaction effectively suppresses the BCS coupling constant, thereby reducing the critical temperature. For strictly 2D films, superconductivity suppression is coming from large scales (similar to the 2D localization), and summation of the leading logarithms can be performed with the help of Finkelsteins renormalization group. For thicker and sufficiently dirty films, there exists an additional effect originating from small scales (similar to the 3D localization). We calculate the corresponding contribution to the shift of the critical temperature and discuss its importance in the context of experimental situation.