Correlation Effects and Superconductivity in Dilute Alloys with Localized States

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Abstract
We study the effect of transitional impurities on the superconducting critical temperature of normal metals: we restrict our considerations to the impurities which give rise to virtual bound states (localized states) but do not have magnetic moments. We use Gor'kov's method to study the superconducting state and Anderson's Hamiltonian to describe the impurity effect. The virtual bound state gives two contributions to the decrease of the critical temperature. The first one, pointed out by Zuckermann, is due to the resonance scattering only, and hence depends on the relaxation time of the conduction electrons; the second one, which is studied here in detail, is produced by the Coulomb interaction within the localized states. In fact, because of the admixture of localized and conduction states, a part of this Coulomb repulsion appears in the interaction of conduction states and then changes the binding energy of a pair. It is shown that our problem is connected with the study of Schrieffer and Mattis on correlation effects; in particular, we find that the same effective Coulomb interaction determines the properties of the system. Finally, we compare our formulas with the experimental results for Al- and Zn-base alloys. A reasonable agreement is found.