Imaginary parts of coupled electron and phonon propagators

Abstract

Quasiparticle and phonon damping rates due to the electron-phonon and Coulomb interactions are obtained directly from the self-energy formalism of strong-coupling theory. This accounts for all processes involving phonon or quasiparticle decay into a single particle-hole pair, or quasiparticle decay by emission or absorption of a single real phonon. The two quasiparticle decay modes are treated on a common footing, without ad hoc separation, by accounting fully for the dynamics of the phonon propagator and the Coulomb vertex—the latter by expansion of the four-point Coulomb vertex function. The results are shown to be expressible in terms of only the physical (i.e., fully renormalized) energies and coupling constants, and are written in terms of spectral functions such as ${\alpha }^2$F(ω) and its generalizations. Expansion of these in powers of a phonon linewidth parameter distinguishes (in lowest orders) between quasiparticle decay modes involving real and virtual phonons. However, the simplest prescription for calculating decay rates involves an effective scattering amplitude in which this distinction is not made.