Electron-phonon interaction in bulk Pb: Beyond the Fermi surface

The electron-phonon interaction in bulk Pb and the influence of spin-orbit coupling (SOC) on the pairing strength are investigated within the density-functional theory and linear-response approach in the mixed-basis pseudopotential representation. We find that the SOC-induced modifications of both electronic bands and lattice vibrations result in striking changes in the phonon-induced scattering of excited electrons (holes). The strength of the momentum-averaged electron-phonon interaction lambda(E) ranges from 0 to 2.5 while the contribution to lambda(E) from particular electronic states can even exceed 4. It is found that the coupling strength is exceedingly strong for phonon-induced transitions between electronic states of p and d symmetry. The electron-phonon coupling in Pb also shows a band dependence which, in particular, results in two different sets of electron-phonon coupling parameters on the two sheets of the Fermi surface.