Low-temperature transport properties of the alkali metals. I. The electron-phonon interaction

Abstract

The form of the electron-phonon matrix element is calculated for metals with non-spherical Fermi surfaces by using electron wave functions, which are linear combinations of two plane waves, as in the model of nearly free electrons. Numerical calculations are made with the use of the ‘twelve cone’ approximation to the Brillouin zone. It is shown that, if the Fermi surface bulges towards the zone faces, there is a significant increase in the probability of Umklapp scattering of electrons, the increase depending on the amount of distortion of the Fermi surface, and on the symmetry properties of the electron wave functions. The increase in Umklapp scattering has important consequences for calculations of the resistivities of metals, and particularly for calculations of the ‘phonon drag’ contribution to the thermo-electric power.