Anisotropy correction to the electrical resistivity of ideally pure potassium

Abstract

At 3K the calculated change in the resistivity obtained by Hayman and Carbotte (see ibid., vol.2, p.915 (1972)) using Ziman's one-iteration approximation (1961) to the solution of the linearised Boltzmann equation is three times as large as that obtained by Ekin and Bringer (see Phys. Rev. B., vol.7, p.4468 (1973)) using the variational technique with a rather simple trial function. In an attempt to resolve the discrepancy between two widely used techniques, the Boltzmann equation was iterated to convergence to determine accurately the anisotropic relaxation time tau (k) as a function of position on the Fermi surface. It was found that the variational result for tau (k) is in good agreement with the accurate one except on those parts of the Fermi surface that are least heavily weighted in a calculation of the electrical resistivity; on the other hand, the Ziman one-iteration solution is much too anisotropic, at least for the temperature range considered. The electrical resistivity calculated with the accurately determined anisotropic relaxation times is only marginally better than the variational result. The same applies to the effective number of carriers in the Hall effect.