We have studied the electron-phonon interaction in aluminum using Fermi-surface-fitted 4-orthogonalized-plane-wave electron states, a realistic phonon spectrum, and integration mesh density varying with local Fermi-surface curvature. The resulting electron-mass enhancement $\lambda$ and thermal scattering rate ${\tau }^{-1\mathrm{}}$ are evaluated as functions of position on the Fermi surface, with the following results: (i) The agreement between observed and calculated cyclotron masses is improved slightly by the use of our anisotropic $\lambda$ rather than the average one. (ii) The anisotropy of $\lambda$ is determined predominantly by mixing coefficient variations, rather than by phonon anisotropy. (iii) The scattering rate ${\tau }^{-1\mathrm{}}$ exhibits order-of-magnitude variations over the Fermi surface at low temperatures. Its values at 5 K are within 50% of the experimentally observed ones everywhere, with considerably better agreement in free-electron regions. (iv) Deviations from the naively expected $T^3$ behavior are predicted: In free-electron regions, umklapp processes cause a more rapid increase than $T^3$ for temperatures above 15-25 K. On ridges, where the initial "$T^3$ coefficient" is very large, we find a slower increase. There results a washing out of anisotropy with increasing temperature. The results on $\lambda$ are in good agreement with those of a recent similar calculation; the ${\tau }^{-1\mathrm{}}$ results agree qualitatively but not quantitatively.

• Received 12 October 1976

DOI:https://doi.org/10.1103/PhysRevB.15.1850