We describe an approach for calculations of phonon contributions to the electron spectral function, including both quasiparticle properties and satellites. The method is based on a cumulant expansion for the retarded one-electron Green's function and a many-pole model for the electron self-energy. Pole models are also used for the phonon density of states and the Eliashberg functions. Our calculations incorporate ab initio dynamical matrices and electron-phonon couplings from the density functional theory. Illustrative results are presented for several elemental metals and for Einstein and Debye models with a range of coupling constants. These are compared with experiment and other theoretical models. Estimates of corrections to Migdal's theorem are obtained by comparing with leading order contributions to the self-energy, and are found to be significant only for large electron-phonon couplings and low temperatures.

• Received 23 July 2014
• Revised 21 October 2014

DOI:https://doi.org/10.1103/PhysRevB.90.195135