Superconducting Transition Temperature of Dirty Thin Films in Weakly Localized Regime

Abstract

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. h⁄(2πE_Fτ)<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 h⁄(2πE_Fτ) is shown to be proportional to the inverse of the film thickness, 1⁄d, i.e. to the sheet resistance (Remark: Graphics omitted.), in the wide range of the thickness within the present region of interest where \sqrthD⁄k_BT>>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.