Role of electron-phonon interactions versus electron-electron interactions in the broadening mechanism of the electron and hole linewidths in bulk Be

We report on ab initio study of electron-phonon (e-ph) and electron-electron (e-e) interactions in bulk Be. The calculations show that the e-ph coupling parameter lambda varies from 0.01 to 1.02 as a function of electron energy and momentum, lambda=0.21 at the Fermi level as averaged over momenta. The e-ph contribution Gamma e-ph to the electrons and holes lifetime broadening also manifests clear dependence on the momentum and energy of an electron state. We demonstrate that the e-ph coupling matrix elements strongly affect the Eliashberg function especially for low phonon frequencies. By using the Debye model relation between Gamma e-ph and lambda the characteristic Debye frequency omega D is obtained in good agreement with the experimental one. The e-e contribution to the lifetime broadening is evaluated from the imaginary part of the electron self-energy computed within a GW approximation