Superconductivity in Transition Metals with Nonmagnetic Impurities

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Abstract
The two-band model proposed by Suhl, Matthias and Walker for the theory of superconductivity of pure transition metals is extended to the transition metals in the presence of nonmagnetic impurities. It is found that the theory of superconductivity in the two-band model is rather sensitive to the choice of the cutoffs of the pairing interactions, in contrast to our expectations in the one-band model. That is, if ωss = ωdd = ωsd ≡ωD, Tc always decreases with increasing impurity concentration and has a complete isotope effect. Furthermore if ωss = ωdd ≠ωsd (ωss = ωD), Tc always decreases of increases with the impurity concentration according to the case of |α| ≪ 1 or α> 1, respectively, and does not necessarily have the complete isotope effect, where ωss, ωdd and ωsd are the cutoffs for interactions giving a pairing of s-s, d-d and s-d electrons and α is a certain constant given by the pairing interaction, the density of states and the cutoffs. Besides, if ωss = ωdd ≠ωsd (ωss = ωD), VssVdd ≪ V2sd and α> 1, there may exist the phase transition of some kind (maybe of first order) at a certain impurity concentration, where Vss, Vdd and Vsd are the strength of the pairing interactions. Thus we note here that the choice of the cutoffs of the pairing interactions is physically important for the study of superconducting transition metals.

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