Anomalous electron-phonon transport properties of impure metals. I. The electrical resistivity

The electron-phonon contribution rho(ep)(T, c) to the resistivity of an impure metal, or dilute metal alloy, can be drastically different from that of the ideally pure metal, rho(0)(ep)(T), if, in the region of the Fermi energy the conduction-electron relaxation time tau(0)(epsilon) for impurity seattering varies with energy epsilon on a scale comparable to or less than the Debye energy (h) over bar omega(D) Of the metal. This effect is a consequence of the sensitivity of the (inelastic) electron-phonon resistivity to any energy-dependent component in the nonequilibrium electron-distribution function. We present a working formula for the effect and indicate several important consequences for nontransitional metals containing magnetic or nonmagnetic transitional impurities. In the limit of small impurity concentrations c, the alloy and host electron-phonon resistivities are connected to the electron-diffusion thermopower S(T, c) of the alloy via the simple relation rho(ep)(T, c) similar or equal to rho(0)(ep)(T) {1 + ((h) over bar omega(D)/epsilon(F))(2) [S(T, c)/S-0(T)](2)}, where S-0 denotes the "free-electron" thermopower. More generallyt rho(ep)(T, c), and also rho(imp) (T, c), the resistivity resulting from impurity scattering, are expressed in terms of the first and second derivatives of tau(0) at the Fermi energy epsilon(F). The anomalous electron-phonon resistivity will cause sharp peaks to appear in the atomic-resistivity temperature curves of very dilute magnetic-impurity systems (e.g., CuFe, AuFe, AuMn). Experimentally, measurements of deviations from Matthiessen's rule should furnish useful information on the energy dependence of the electron-impurity scattering.