Empirical electron-phonon coupling constants and anisotropic electrical resistivity in hcp metals

Abstract

The Fermi-surface density of states N(0) and Drude-plasma-frequency tensor (${\Omega }_p^2$ ${)}_{\alpha \beta }$ =4π$e^2$N(0)〈$v_{\alpha }$ $v_{\beta }$〉 are calculated for 14 metallic elements with hcp structures. By comparison with measured anisotropic resistivity components ${\rho }_{\perp }$ and ${\rho }_{?}$, electron-phonon coupling constants are extracted. The resulting values of ${\lambda }_{\mathrm{tr}}$ compare reasonably well with λ from $T_c$ for the ten superconducting elements and provide new information on electron-phonon coupling for the four that are not. In particular, ${\lambda }_{\mathrm{tr}}$ for Mg is sufficiently low as to discourage a further search for superconductivity, whereas ${\lambda }_{\mathrm{tr}}$ for Sc and Y is sufficiently high (0.5–0.6) to require spin-fluctuation suppression of $T_c$ and motivate a low-T search for exotic superconductivity. Co is found to have very weak electron-phonon coupling in the majority-spin band and much stronger specific-heat enhancement in the minority-spin band. The anisotropy ${\rho }_{\mathrm{zz}}$/${\rho }_{\mathrm{xx}}$=${\rho }_{?}$/${\rho }_{\perp }$ is moderately well accounted for by the anisotropy of the Drude plasma frequency (${\Omega }_p^2$ ${)}_{\mathrm{xx}}$/(${\Omega }_p^2$ ${)}_{\mathrm{zz}}$ =〈$v_x^2$〉/〈$v_z^2$〉, except for the sp elements, which have significant scattering anisotropy (${\lambda }_{\mathrm{zz}}$/${\lambda }_{\mathrm{xx}}$≠1). A systematic onset of ‘‘resistivity saturation’’ (signifying a breakdown of Boltzmann theory) is found when the mean free path l≤10 Å. The onset occurs at a variable value 40<ρ<160 μΩ cm.