Ab initiocalculation of the phonon-induced contribution to the electron-state linewidth on the Mg(0001) surface versus bulk Mg

Abstract

We report a detailed ab initio study of the electron-phonon (e-ph) interaction contribution to the linewidth ${\ensuremath{\Gamma}}_{\mathrm{e}\text{\ensuremath{-}}\mathrm{ph}}({ϵ}_{\mathbf{k},i})$ of electron and hole states for bulk magnesium and the Mg(0001) surface. The calculations are based on density functional theory and linear response approach. For bulk Mg, we find a large contribution of optical phonons to the Eliashberg spectral function and to ${\ensuremath{\Gamma}}_{\mathrm{e}\text{\ensuremath{-}}\mathrm{ph}}({ϵ}_{\mathbf{k},i})$. The e-ph coupling parameter $\ensuremath{\lambda}$ at the Fermi level (mass enhancement parameter) has been found to be $\ensuremath{\lambda}=0.30$. In the case of the surface, we have focused on the study of the $\overline{\ensuremath{\Gamma}}$ and $\overline{M}$ surface states for which we find $\ensuremath{\lambda}=0.28$ and $\ensuremath{\lambda}=0.38$, respectively. We show an important role of the Rayleigh vibrational mode in the e-ph coupling in the $\overline{\ensuremath{\Gamma}}$ surface state. These results are in a very good agreement with tunneling spectroscopic data and recent photoemission measurements of $\ensuremath{\lambda}$.