Electron-phonon interaction effects in tantalum

The results of calculations for a number of electron-phonon interaction effects for tantalum are presented. The calculations are based on Korringa-Kohn-Rostoker energy bands, Born–von Kármán phonons, and the rigid-muffin-tin approximation for the electron-phonon matrix element. The calculated Eliashberg spectral function ${\alpha }^2$F is compared with the earlier tunneling data of Shen and the proximity tunneling data of Wolf et al. The calculated and tunneling transverse-phonon peaks agree well, but the height of the tunneling longitudinal-phonon peak is smaller than the calculated results. The calculated electron-phonon coupling parameter λ is 0.88, which is larger than the λ determined from superconducting tunneling and superconducting $T_c$ measurements, but is slightly smaller than the λ determined from electronic specific-heat measurements. Calculated phonon linewidths along various symmetry directions are presented. The temperature dependence of the electrical resistivity due to phonon scattering is calculated in the lowest-order variational approximation and it agrees with experiment. The point-contact spectral function of Kulik, G(ω), is determined and compared with ${\alpha }^2$F(ω). The agreement between calculated and measured electronic specific heat and high-temperature electrical resistivity gives strong support to the validity of the rigid-muffin-tin approximation for electron-phonon matrix elements. The main disagreement between calculated and measured results is for superconducting properties for which an ad hoc Coulomb interaction ${\mu }^{\mathrm{*}}$ must be used.