Chirality-induced Dynamic Kohn Anomalies in Graphene

We develop a theory for the renormalization of the phonon energy dispersion in graphene due to the combined effects of both Coulomb and electron-phonon (e-ph) interactions. We obtain the renormalized phonon energy spectrum by an exact analytic derivation of the phonon self-energy, finding three distinct Kohn anomalies (KAs) at the phonon wavevector $q = \omega/v, 2k_F\pm\omega/v$ for LO phonons and one at $q = \omega/v$ for TO phonons. The presence of these new KAs in graphene, in contrast to the usual KA $q = 2k_F$ in ordinary metals, originates from the dynamical screening of e-ph interaction (with a concomitant breakdown of the Born-Oppenheimer approximation) and the peculiar chirality of the graphene e-ph coupling.