Self-consistently renormalized quasiparticles under the electron-phonon interaction

Abstract

Combining ab initio techniques and the analytic properties of the electron Green's function, we outline a method for calculating quasiparticle properties under the electron-phonon interaction. The presented scheme is a generalization of the work by Engelsberg and Schrieffer [Phys. Rev. 131, 993 (1963)] to finite temperatures and is suitable for being applied to complex materials, where the electronic and vibrational properties are calculated from first principles. We show that under some circumstances, the low-energy dynamical properties are well described by quasiparticles, but at the same time the renormalization effects on quasiparticle lifetimes and energies can be very important. The bare second-order perturbative (such as Fermi's golden rule) results for the self-energy are compared with self-consistent ones. The theory is first illustrated with the simple Einstein and Debye models at finite temperatures. Thereafter we consider realistic materials such as the $1\ifmmode\times\else\texttimes\fi{}1$ hydrogen-covered (deuterium-covered) W(110) surface and the superconductor ${\text{MgB}}_{2}$.