Abstract
A new set of basis functions is introduced, consisting of products of Fermi-surface harmonics and polynomials in the energy . The former are orthonormal on the Fermi surface, and the latter are orthonormal with weight function . In terms of this set the exact semiclassical Boltzmann equation takes a particularly simple form, giving a matrix equation which can probably be truncated at low order to high accuracy. The connection with variational methods is simple. Truncating at a 1 × 1 matrix gives the usual variational solution where is assumed proportional to for electrical conductivity and for thermal conductivity. Explicit equations are given for the matrix elements of the scattering operator for the case of phonon scattering, and a perturbation formula for is given which is accurate for weak anisotropy. The matrix elements are simple integrals over spectral functions which generalize the electron-phonon spectral function used in superconductivity theory. Analogies are described between Boltzmann theory and Eliashberg theory for of superconductors. The intimate relations between high-temperature resistance and the - or -wave transition temperature are made explicit.
- Received 23 January 1978
DOI:https://doi.org/10.1103/PhysRevB.17.3725
©1978 American Physical Society