Penetration Depth in Impure Superconductors

Abstract

The equation giving the current density as a functional of the vector potential for an impurity superconductor derived by Mattis and Bardeen is used to compute the temperature dependence of the penetration depth of impure superconductors. Results of calculations for different values of the ratio of the coherence distance to the mean free path and also for different values of the ratio of the coherence distance to the London penetration depth are given. The results are applied to tin as an example, and appreciable deviations from the ${[1-{\left(\frac{T}{T_c}\right)}^4]}^{-\frac{1}{2}}$ temperature dependence of the penetration depth are found for all values of the mean free path.