Interpolation-Scheme Calculation of Electron-Phonon Interaction in Noble and Transition Metals: Copper

Abstract

A simple method for evaluating the electron-phonon interaction matrix elements, and hence the point-mass enhancement and the relaxation time of quasiparticles, is proposed for the transition metals. The method is based essentially on the Bloch model of the electron-phonon interactions and is similar to a pseudopotential formulation with modification to account for the presence of $d$ electrons in the conduction bands and the resulting anisotropy of the above quantities. The results obtained by applying our theory to copper, based on the combined interpolation scheme with explicit inclusion of the screening effects based on Lindhard's formulation and of the contributions from transverse and longitudinal phonons and from umklapp processes, are in fair quantitative agreement with those obtained from a phenomenological interpretation of the experimental cyclotron-mass data of Lee and with the calculations of Nowak based on an empirical phase-shift formulation.