Anisotropic Impure Superconductor and Resonance Scattering

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Abstract
We investigated both resonance scattering and impurity scattering effects in an anisotropic superconductor, extending the Markowitz-Kadanoff method for impurity scattering to the resonance scattering problem treated by Zuckerman. The decrease in Tc is computed; it contains both the resonance-scattering effect and the anisotropic part of the combination of resonance and impurity scattering. The decrease in the critical temperature is found to be a sum of the resonance effect and the mean free path effect in the anisotropic part for most physical cases, e. g. for Γ≫ kTc ≫ Ed and kTc ≫ Γ≫ Ed with nIǀVǀ2/(πkTc)2 ≫ 1; in the latter case there is a sharp decrease and in the former one a much weaker decrease. Here Γ is the broadening of the bound d state on each impurity due to the s-d interaction, Ed is the energy displacement of the d state from the Fermi level nI is the impurity density and V is the magnitude of the s-d interaction. The mean free path effect, appearing in the anisotropic term, is largely independent of the intrinsic properties of the impurities. However, for a few special situations, with the condition nIǀVǀ2/(πkTc)2 ≫ 1 for Γ≫ kTc ≳ Ed, Ed ≳ Γ≫ kTc and kTc ≫ Γ≫ Ed, the decrease in Tc has not only an isotropic resonance part, but also amalgamated resonance and mean free path effects in the anisotropic part. The problem of degeneracy of the d bound state is also investigated.

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