Electron-phonon interaction in cubic systems: Application to niobium

Abstract

To a good approximation the electron-phonon coupling parameter $\lambda$, 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, ${\left(M〈{\omega }^2〉\right)}^{-1\mathrm{}}$, and a purely electronic factor $\eta$. This latter quantity is determined by the band structure and the electron-phonon matrix elements. In this paper we develop a method of calculating $\eta$ from first principles making only the rigid muffin-tin approximation to describe the electron-phonon coupling. As an illustration we evaluate $\eta$ 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 $T_c$.