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Plasmon-phonon coupled modes in graphene tuned by the carrier concentration of the semiconductor substrates

The interaction between graphene plasmons and surface phonons of a semiconductor substrate is investigated, which can be efficiently controlled by the carrier injection of the substrate. The energy and lifetime of surface phonons in a substrate depend a lot on the carrier concentration, which provides a new machanism to tune plasmon-phonon coupled modes (PPCMs). More specifically, the dispersion and lifetime of PPCMs can be controlled by the carrier concentration change of the substrate. The energy of PPCMs for a given momentum increases as the carrier concentration of a substrate increases. On the other hand, the momentum of PPCMs for a given energy decreases when the carrier concentration of the substrate increases. Lifetime of PPCMs is always larger than the intrinsic lifetime of graphene plasmons without plasmon-phonon coupling.