Breakdown of the Concentration Expansion for the Zero-Temperature Impurity Resistivity

Abstract

Transport coefficients for classical gases do not possess simple expansions in powers of the density. A similar phenomenon occurs in the problem of expressing the zero-temperature resistivity of a metal as a function of ${n}_{i}$, the density of impurities. Both semiclassical and quantum-mechanical treatments reveal that the resistivity $\ensuremath{\rho}$ breaks down at order ${{n}_{i}}^{3}$. The leading term of the breakdown is of the form ${{n}_{i}}^{3}$ $\mathrm{ln}{n}_{i}$.