Cumulant expansion for phonon contributions to the electron spectral function

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.

References in corpus (2)

• Theoretical X-Ray Absorption Debye-Waller Factors
• Many-pole model of inelastic losses in x-ray absorption spectra

Cited by in corpus (5)

• Finite temperature Green's function approach for excited state and thermodynamic properties of cool to warm dense matter
• Nonperturbative self-consistent electron-phonon spectral functions and transport
• Beyond-quasiparticle transport with vertex correction: self-consistent ladder formalism for electron-phonon interactions
• Many-body Green's function approaches to the doped Fröhlich solid: Exact solutions and anomalous mass enhancement
• Applicability of the cumulant expansion method for the calculation of transport properties in electron-phonon systems