Electron-phonon scattering contributions to metallic resistivity at 0 K

Incorporating the quantum Boltzmann equation, with shielded electron-ion Coulomb interactions, the component of metallic electrical resistivity due to electron-phonon scattering is evaluated for the noble metals and a restricted class of the alkali metals. In addition to Bloch's T5 contribution at low temperature and canonical T dependence at high temperature, a component of resistivity stemming from electron-phonon scattering is found to survive in the limit T→0. This residual resistivity is attributed to the interplay between Fermi-surface electrons and zero-point ion motion, in the presence of an electric field, as well as to the inelastic nature of electron-phonon scattering. An estimate made of the temperature at which this residual component of resistivity comes into play gives the criterion T<ΘD/5 for the class of metals considered, where ΘD is the Debye temperature. It is further observed that this residual component of resistivity maintains nonsingular behavior of the Lorentz expansion for the electron distribution function at low temperature. Our expression for residual resistivity is given by ρ0=(3π2/8)[kBΘD/mu2ℎ(ℎΩ)2/E3F]S1 (λ), where S1(λ) is a positive monotonic function of λ. In the last expression, λ varies as (n/Z2)1/6, Ω is the ion plasma frequency, and n is the electron number density. The phonon speed and Fermi energy are written u and EF, respectively. It is noted that ρ0 scales as (Z1/6/nM1/2)S1(λ), where M and Z are the ion mass and ion valence number respectively. At constant electron and ion number densities, ρ0 scales as M-1/2