Excitonic Effects in Phonons: Reshaping the Graphene Kohn Anomalies and Lifetimes

We develop an ab initio framework that captures the impact of electron-electron and electron-hole interactions on phonon properties. This enables the inclusion of excitonic effects in the optical phonon dispersions and lifetimes of graphene, both near the center (Γ) and at the border (K) of the Brillouin zone, at phonon-momenta relevant for Raman scattering and for the onset of the intrinsic electrical resistivity. Near K, we find a phonon redshift of ∼150  cm^{-1} and a 10× enhancement of the group velocity, together with a 5× increase in linewidths due to a 26× increase of the electron-phonon matrix elements. These effects persist for doping 2E_{F}<ℏω_{ph} and are quenched at higher dopings. Near Γ, the excitonic effects are minor because of the gauge field nature of the electron-phonon coupling at small phonon momentum.