Superconducting Transition Temperature of Dirty Thin Films in Weakly Localized Regime

Our former investigation for the effects of localization on the superconducting critical temperature of thin films are extended to much dirty cases where τ -1 ≫ω D , ω D being the Debye frequency, but still in the weakly localized regime, i.e. \(/(2π EFτ){<}1\), E F and τ being the Fermi energy and the life time, respectively. The depression of the critical temperature to the first order in \(/(2π EFτ)\) is shown to be proportional to the inverse of the film thickness, 1/ d , i.e. to the sheet resistance \(R_{}\), in the wide range of the thickness within the present region of interest where \(√{ D/kBT}{}d{}l\), D being the diffusion constant, T the temperature and l the mean free path. The proportionality factor depends on the details of the interaction processes among electrons.