Anisotropy of the Fermi surface, Fermi velocity, many-body enhancement, and superconducting energy gap in Nb

Abstract

The detailed angular dependence of the Fermi radius ${\mathrm{k}}_{F}$, the Fermi velocity ${\mathrm{v}}_{F}$(k), the many-body enhancement factor \ensuremath{\lambda}(k), and the superconducting energy gap \ensuremath{\Delta}(k), for electrons on the Fermi surface of Nb are derived with use of the de Haas--van Alphen (dHvA) data of Karim, Ketterson, and Crabtree [J. Low Temp. Phys. 30, 389 (1978)], a Korringa-Kohn-Rostoker parametrization scheme, and an empirically adjusted band-structure calculation of Koelling. The parametrization is a nonrelativistic five-parameter fit allowing for cubic rather than spherical symmetry inside the muffin-tin spheres. The parametrized Fermi surface gives a detailed interpretation of the previously unexplained \ensuremath{\kappa}, \ensuremath{\alpha}', and \ensuremath{\alpha}'' orbits in the dHvA data. Comparison of the parametrized Fermi velocities with those of the empirically adjusted band calculation allow the anisotropic many-body enhancement factor \ensuremath{\lambda}(k) to be determined. Theoretical calculations of the electron-phonon interaction based on the tight-binding model agree with our derived values of \ensuremath{\lambda}(k) much better than those based on the rigid-muffin-tin approximation. The anisotropy in the superconducting energy gap \ensuremath{\Delta}(k) is estimated from our results for \ensuremath{\lambda}(k), assuming weak anisotropy.