Anisotropic superconducting energy gap in Pb

Abstract

We have calculated directional electron-phonon effective distribution functions ${\ensuremath{\alpha}}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}^{2}(\ensuremath{\omega}){F}_{\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}}(\ensuremath{\omega})$ at many points on the Pb Fermi surface. From these distributions the zero-temperature energy gaps in superconducting Pb single crystals follow from one iteration of the directional Eliashberg equations. Anisotropic mass renormalization parameters are also determined. In the calculations, the Pb Fermi surface is obtained from a four-plane-wave model pseudopotential chosen to fit the de Haas-van Alphen data. The four-plane-wave electron states are used in evaluating the electron-phonon interaction which in addition depends on the lattice dynamics. This is taken from experiments on the dispersion curves for the phonons.