Non-adiabatic phonon self-energy due to electrons with finite linewidths

TL;DR

This paper introduces a theoretical framework for calculating non-adiabatic phonon self-energy considering electrons with finite linewidths, improving agreement with experimental data and including intra-band electronic transitions.

Contribution

The authors develop a spectral Green's function formalism that incorporates finite electron linewidths into phonon self-energy calculations, capturing intra-band transitions at all wavevectors.

Findings

Finite electron linewidths significantly alter phonon linewidth predictions.

Intra-band electronic transitions are crucial for accurate phonon linewidths.

Results with finite linewidths match experimental data better than infinitesimal linewidth models.

Abstract

We develop the theory of the non-adiabatic phonon self-energy arising from coupling to electrons with finite linewidths using the spectral representation of Green's functions. Our formalism naturally includes the contribution from the intra-band electronic transitions (as well as the inter-band ones) at all electron wavevectors to the phonon linewidths, which is forbidden for zone-center optical phonons if infinitesimal electron linewidths are used. As a proof of principle, we use the theory to calculate the linewidth of the double-degenerate, zone-center optical $E_{\rm 2g}$ phonons of graphene as a function of the chemical potential. The calculated phonon linewidths obtained with finite electron linewidths differ significantly from those obtained with infinitesimal electron linewidths even at low temperatures. Intra-band electronic transitions play an important role in making this difference. Moreover, only the results accounting for the finite electron linewidths are in quantitative agreement with the available experimental data. The presented formalism is suitable for first-principles calculations.