Exact formula with two dynamically screened electron-phonon couplings for positive phonon-linewidths approximations

TL;DR

This paper derives an exact formula for phonon linewidths using dressed electron-phonon couplings, addressing nonadiabatic and correlation effects, and clarifies the correctness of DFT calculations without double counting, also extending to nonequilibrium cases.

Contribution

It introduces a novel exact formula for phonon linewidths that incorporates screening effects and proves the validity of DFT approaches without double counting, including nonequilibrium extensions.

Findings

The formula ensures positivity of phonon linewidths.

It confirms DFT calculations are free from double counting issues.

Extension to nonequilibrium scenarios with a rigorous phononic Boltzmann equation.

Abstract

In this paper, we present an exact formula for the phonon linewidths involving only dressed electron-phonon couplings and ensuring the positivity property. The formula is designed to account for both nonadiabatic and correlation effects, and it provides an alternative proof that Density Functional Perturbation Theory calculations of phonon linewidths are not affected by a double counting of screening diagrams. Furthermore, we extend the treatment to nonequilibrium scenarios and offer a rigorous justification for employing the phononic Boltzmann equation.