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 ($\Gamma$) 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 red-shift of ~150 $cm^{-1}$ and a 10x enhancement of the group velocity, together with a 5x increase in linewidths due to a 26x increase of the electron-phonon matrix elements. These effects persist for doping $2E_{F} < {\hbar}{\omega}_{ph}$ and are quenched at higher dopings. Near $\Gamma$, the excitonic effects are minor because of the gauge field nature of the electron-phonon coupling at small phonon momentum.