ELECTRON-PHONON SCATTERING CONTRIBUTIONS TO METALLIC RESISTIVITY AT 0K

Incorporating the quantum Boltzmann equation, with shielded electron-i on Coulomb interactions, the component of metallic electrical resistiv ity due to electron-phonon scattering is evaluated for the noble metal s and a restricted class of the alkali metals. In addition to Bloch's T-5 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 resi stivity is attributed to the interplay between Fermi-surface electrons and zero-point ion motion, inthe presence of an electric field, as we ll as to the inelastic nature of electron-phonon scattering. An estima te made of the temperature at which this residual component of resisti vity comes into play gives the criterion T much less than Theta(D)/5 f or the class of metals considered, where Theta(D) is the Debye tempera ture. It is further observed that this residual component of resistivi ty maintains nonsingular behavior of the Lorentz expansion for the ele ctron distribution function at low temperature. Our expression for res idual resistivity is given by (in the cgs system) [GRAPHICS] where S-1 (lambda) is a positive monotonic function of lambda. In the preceding expression, lambda varies as (n/Z(2))(1/6), Omega is the ion plasma fr equency, and n is the electron number density. The phonon speed and Fe rmi energy are written u and E(F), respectively. It is noted that rho( 0) scales as (Z(1/6)/nM(1/2))S-1(lambda), where M and Z are the ion ma ss and ion valence number respectively. At constant electron and ion n umber densities, po scales as M(-1/2). At these conditions, in the lim it that M-->infinity, Omega-->0 and, consistently, rho(o)-->0. A log-l og plot of the expression derived for resistivity, at various values o f lambda, clearly exhibits the three temperature intervals described a bove.