Diffusion on the Fermi-Surface and the Conductivity of Metals

Abstract

The transport phenomena in metals, such as the electrical and the thermal conductivity, are treated as a kind of the diffusion of electrons on the Fermi-surface. Gruneisen's well-known formula is gained for the electrical conductivity σ, and as for the thermal conductivity κ the expression \begin{aligned} \kappa{=}\sigma T\frac{\pi^{2}}{3}\left(\frac{k}{e}\right)^{2}\bigg/\left\{1+\left(\frac{\theta}{T}\right)^{2}\left(\frac{K}{q_{0}}\right)^{2}\int_{0}^{\theta/T}\frac{x^{3}dx}{\mathrm{e}^{x}-\mathrm{e}^{-x}}\bigg/\int_{0}^{\theta/T}\frac{x^{5}dx}{(\mathrm{e}^{x}-1)(1-\mathrm{e}^{-x})}\right\} \end{aligned} is obtained. In this equation θ denotes the Debye temperature, K and q 0 are the maximum wave numbers of electrons and phonons respectively.