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Plasmon-phonon coupling in graphene

Collective excitations of coupled electron-phonon systems are calculated for both monolayer and bilayer graphene, taking into account the non-perturbative Coulomb coupling between electronic excitations in graphene and the substrate longitudinal optical phonon modes. We find that the plasmon-phonon coupling in monolayer graphene is strong at all densities, but in bilayer graphene the coupling is significant only at high densities satisfying the resonant condition $ω_{pl} \approx ω_{ph}$. The difference arises from the peculiar screening properties associated with chirality of graphene. Plasmon-phonon coupling explains the measured quasi-linear plasmon dispersion in the long wavelength limit, thus resolving a puzzle in the experimental observations.