Ab initiolattice dynamics and electron-phonon coupling of Bi(111)

Abstract

We present a comprehensive ab initio study of structural, electronic, lattice dynamical, and electron-phonon coupling properties of the Bi(111) surface within density functional perturbation theory. Relativistic corrections due to spin-orbit coupling are consistently taken into account. Changes of interatomic couplings are confined mostly to the first two bilayers, resulting in superbulk modes with frequencies higher than the optic bulk spectrum, and in an enhanced density of states at lower frequencies for atoms in the first bilayer. We give results for the momentum-dependent electron-phonon coupling of electronic states belonging to the two surface electronic bands along $\overline{\ensuremath{\Gamma}M}$ which cross the Fermi energy. For larger momenta, the lower surface band exhibits a moderate electron-phonon coupling of about 0.45, which is larger than the coupling constant of bulk Bi. For momenta close to $\overline{\ensuremath{\Gamma}}$, states of both surface bands show even stronger couplings because of interband transitions to bulk states near $\overline{\ensuremath{\Gamma}}$ around the Fermi level. For these cases, the state-dependent Eliashberg functions exhibit pronounced peaks at low energy and strongly deviate in shape from a Debye-type spectrum, indicating that an extraction of the coupling strength from measured electronic self-energies based on this simple model is likely to fail.