Localized description of superconductivity in narrow-band metals

A. Birnboim*, H. Gutfreund

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

A localized description of superconductivity in narrow-band metals, proposed by Appel and Kohn, is applied to the calculation of the phonon-exchange vertex in three transition metals. The essence of this description is the formulation of the equation for the vertex function in the Wannier representation and the assumption of a contact interaction, in which the two electrons in a Cooper pair scatter together from site to site. The value of the vertex function at =0 plays the same role in determining Tc as the coupling parameter in the BCS or McMillantheory. The phonon-exchange vertex is calculated for V, Nb, and Ta, assuming that the d electrons occupy the threefold degenerate 25 band. The calculation makes use of tabulated atomic wave functions and potentials, and of measured phonon frequency distributions. The electron-phonon interaction is described within the so-called modified tight-binding approximation, in which the zeroth-order electron wave functions follow adiabatically the vibrating ions. The values of the phonon-exchange vertex at =0 are compared with given by McMillan and correct orders of magnitude are obtained with reasonable screening of the atomic potentials. The validity of the contact approximation is checked numerically.

Original languageEnglish
Pages (from-to)139-146
Number of pages8
JournalPhysical Review B
Volume9
Issue number1
DOIs
StatePublished - 1974

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