Detailed microscopic calculation of phonon-mediated electron-electron scattering in aluminum.

Abstract

The phonon-mediated electron-electron scattering rate has been calculated in Al using a realistic band structure and phonon spectrum. The electron-phonon contribution has also been calculated as an extension of previous calculations to provide a detailed Fermi-surface map and special orbit averages for comparison with experiment. Comparison with recent radio-frequency size-effect data in which the two contributions are resolved on three orbits yields agreement in both magnitude and anisotropy for both contributions. The calculated electron-electron scattering rate at points exhibits surprisingly large anisotropy (up to an order of magnitude), which is masked in part by orbit averaging but which could, in principle, be measured experimentally. We argue that the Coulomb interaction, whose contribution is known to be much smaller in Al, is also much less anisotropic. Therefore, an anisotropic ${\mathit{T}}^{2}$ contribution to the scattering rate persisting to low temperatures should be, at least in the simple metals, a signature of the phonon-mediated scattering mechanism.