Cumulant expansion for phonon contributions to the electron spectral function

TL;DR

This paper introduces a cumulant expansion method combined with a many-pole model to accurately compute phonon effects on the electron spectral function, including quasiparticles and satellites, using ab initio data.

Contribution

It presents a novel approach integrating cumulant expansion with a many-pole model and ab initio calculations for phonon contributions to electron spectral functions.

Findings

Method accurately reproduces experimental spectral features.

Significant corrections to Migdal's theorem occur at high coupling and low temperatures.

Results agree well with experimental data and other models.

Abstract

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. The electron-phonon couplings are calculated from the Eliashberg functions, and the phonon density of states is obtained from a Lanczos representation of the phonon Green's function. Our calculations incorporate ab initio dynamical matrices and electron-phonon couplings from the density functional theory code ABINIT. 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 at low temperatures.