Phonons in ultrathin Bi(111) films: Role of spin-orbit coupling in electron-phonon interaction

The vibrational properties of ultrathin Bi(111) films have been calculated by applying density functional perturbation theory with and without the inclusion of spin-orbit interaction. Phonon dispersion curves of dynamically stable bilayers are presented and analyzed. Surprisingly, the Rayleigh mode is found to have the largest amplitude on the second atomic layer.Moreover an optical surface phonon branch is found to be localized above the optical band and confined within the first surface bilayer. The analysis of this mode as a function of the number of bilayers allows one to estimate the contribution of the spin-orbit coupling to the electron-phonon interactions.