Electron-phonon effects in copper. II. Electrical and thermal resistivities and Hall coefficient

Abstract

The electrical and thermal resistivities ($\rho$ and $W$) and Hall coefficient ($R_H$) of pure and impure Cu are calculated. Realistic Korringa-Kohn-Rostocker energy bands and wave functions, experimental phonon frequencies, and Born—von Kármán eigenvectors, and the rigid-muffin-tin model for electron-phonon scattering are used to generate the velocities and scattering probabilities in the Bloch-Boltzmann equation, on a mesh of nearly 24000 points on the Fermi surface. The effect of impurities is approximated by an isotropic impurity scattering rate. Solutions for $\rho$, $W$, and $R_H$ are exhibited at three levels of accuracy: (1) the lowest-order variational approximation (LOVA) where the Fermi surface displaces rigidly; (2) a fully inelastic calculation where the distribution function is allowed arbitrary variations with energy (normal to Fermi surface) to reflect the inelasticity of electron-phonon scattering; (3) inelasticity plus somewhat increased angular freedom in the distribution function. For $\rho$ and $W$ we find that above $T=100\mathrm{}$ K the corrections to LOVA are negligible and that, except at the lowest temperatures $T\sim 20$ K, our angular corrections are negligible. For $R_H$ the lowest-order approximation is temperature independent and the addition of both inelasticity and increased angular freedom are not negligible at any temperature. Agreement with experiment for all three quantities is good throughout the range $T=10\mathrm{} \mathrm{to} 300$ K. The use of a phenomenological impurity relaxation time to study deviations from Matthiessen's rule in the electrical resistivity agrees qualitatively with experiment.