The theory of the residual resistance of copper

Abstract

Cohen & Heine (1958) have suggested that the addition of impurities to Cu drives the Fermi surface out of contact with the zone boundary. Since the scattering of electrons by impurities is sensitive to the form of the wave function, and to the density of states, both of which depend on the nearness of the electron wave vector to the zone boundary, there should be anomalies in the transport properties. For example, the function $\sigma $($\scr{E}$) (conductivity as a function of energy), should have a discontinuity of slope at the point where the energy surfaces just break contact. An attempt is made to calculate $\sigma $($\scr{E}$), using a simple heuristic form of electron wave function, and allowing for the strong directional anisotropy of the scattering by a screened Coulomb potential. It is shown that there could be a small resistance minimum, of the sort observed in some alloys of Cu, but the associated anomaly in the thermopower comes out with the wrong sign. The experimental properties of the resistance minimum are discussed in the light of this theory, and a programme of further experimental and theoretical research is proposed.