Electron-phonon interaction in cubic systems: Application to niobium

Abstract

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 ${T}_{c}$.