Dynamical Properties of Quasiparticle Excitations in Metallic Copper

The results of experimental studies of the cyclotron masses associated with various orbits on the Fermi surface of copper are analyzed in terms of an interpolation scheme based on surfaces of constant energy that are constructed by the method of phase-shift analysis. Our results confirm that it is possible to construct surfaces of constant energy that are entirely consistent with experimental Fermi-surface and cyclotron-mass data. The variation of the quasiparticle velocity over the Fermi surface is determined from the experimental cyclotron masses. The anisotropy of the Fermi velocity is in excellent over-all agreement with the results of a similar calculation by Halse, and with recent experimental measurements by Doezema, Koch, and Strom. A comparison between the quasiparticle velocities and the velocities computed from a one-electron potential that has been constructed to fit optical and Fermi-surface data demonstrates that in copper the renormalization of the one-electron energy bands by the electron-phonon interaction varies significantly over the Fermi surface. We find that, for electronic states on the belly, the anisotropy of the renormalization factor is in good qualitative agreement with the predictions of a simple deformation-potential calculation, but that for states within a few degrees of the necks the deformation-potential approximation fails. Encouraged by the partial success of the deformation-potential calculation for virtual electron-phonon processes, we apply similar techniques to discuss the real processes that at low temperatures $T$ contribute a ($\frac{1}{T^3}$)-dependent term to the relaxation time for quasiparticle excitations. We propose a model to describe the variation of the electron-phonon relaxation time over the belly, but conclude that a first-principles calculation may be needed to investigate the relaxation time on the necks. At present there exist insufficient experimental data to allow a convincing test of the accuracy of the model, but it seems likely that our empirical deformation potential will be of value in the analysis of such data when they become available.