Substrate carrier concentration dependent plasmon-phonon coupled modes at the interface between graphene and semiconductors

The coupled modes between graphene plasmons and surface phonons of a semiconductor substrate are investigated, which can be efficiently controlled by carrier injection of the substrate. A new physical mechanism on tuning plasmon-phonon coupled modes (PPCMs) is proposed due to the fact that the energy and lifetime of substrate surface phonons depend a lot on the carrier concentration. Specifically, the change of dispersion and lifetime of PPCMs can be controlled by the carrier concentration of the substrate. The energy of PPCMs for a given momentum increases as the carrier concentration of the substrate increases. On the other hand, the momentum of PPCMs for a given energy decreases when the carrier concentration of the substrate increases. The lifetime of PPCMs is always larger than the intrinsic lifetime of graphene plasmons without plasmon-phonon coupling.