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Strong-Coupling Theory of Impure Superconductors : Correspondence with Weak-Coupling Theory

Yong-Jihn Kim
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Abstract

We reconsider the ordinary impurity effect on the transition temperature $T_{c}$ of superconductors using the Eliashberg formalism. It is shown that the correspondence principle, which relates strong-coupling and weak-coupling theories, works only when Anderson's pairing condition between the time-reversed scattered-states is used. For an Einstein phonon model, the change of the electron density of states caused by the impurity scattering leads to a $T_{c}$ decrease proportional to ${1/ E_{F}τ}$ in the dirty limit. It is pointed out that the phonon-mediated interaction decreases by the same weak localization correction term as that of the conductivity. Accordingly, for strongly localized states the phonon-mediated interaction is exponentially small. We also discuss the case of Debye phonon model.

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Yong-Jihn Kim. 1997-12-26. Strong-Coupling Theory of Impure Superconductors : Correspondence with Weak-Coupling Theory. https://arxiv.org/abs/cond-mat/9712295

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