Collective excitations of coupled electron-phonon systems are calculated for both monolayer and bilayer graphenes, taking into account the nonperturbative 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 ${\omega }_{pl}\approx {\omega }_{ph}$. The difference arises from the peculiar screening properties associated with chirality of graphene. Plasmon-phonon coupling explains the measured quasilinear plasmon dispersion in the long-wavelength limit, thus resolving a puzzle in the experimental observations.

• Received 20 August 2010

DOI:https://doi.org/10.1103/PhysRevB.82.195406