Rigid Muffin-tin Approximation Research Articles

Theory of energy bands and related properties of 4d-transition metals. II. The electron-phonon matrix element, superconductivity and ion core enhancement

For pt.I see ibid., vol.7, p.613 (1977). The variation of the electronic contribution eta to the electron-phonon mass enhancement is studied across the 4d transition metal series within the Gaspari-Gyorffy rigid muffin tin (RMT) approximation. The pd and df matrix elements are expressed in terms of band parameters. It is shown that hybridization enhances the p density of states for Nb, but reduces it for transition metals to the right of the series, whose superconductivity is, therefore, determined by df scattering which still remains dominant even after a 50% reduction by screening of the RMT results. The importance of the ion core in enhancing the scattering through orthogonality constraints and reduction in effective screening, is illustrated by studying the large volume dependence of eta shown by the early transition metals and rare earths.

Electron-phonon interaction in cubic systems: Application to niobium

To a good approximation the electron-phonon coupling parameter $\ensuremath{\lambda}$, which determines the superconducting transition temperature ${T}_{c}$ and the electron-phonon mass enhancement, may be written as the product of two factors: one which depends upon the phonon frequencies, ${(M〈{\ensuremath{\omega}}^{2}〉)}^{\ensuremath{-}1}$, and a purely electronic factor $\ensuremath{\eta}$. This latter quantity is determined by the band structure and the electron-phonon matrix elements. In this paper we develop a method of calculating $\ensuremath{\eta}$ from first principles making only the rigid muffin-tin approximation to describe the electron-phonon coupling. As an illustration we evaluate $\ensuremath{\eta}$ for Nb and discuss the significance of the calculation with regard to the validity of describing the electron-phonon interaction in transition metals by the rigid muffin-tin approximation. We also attempt to isolate those features of the band structure which appear to have the strongest effect on ${T}_{c}$.