Damping mechanism of terahertz plasmons in graphene on heavily doped substrate

Coupling of plasmons in graphene at terahertz frequencies with surface plasmons in a heavily doped substrate is studied theoretically. We reveal that a huge scattering rate may completely damp out the plasmons, so that proper choices of material and geometrical parameters are essential to suppress the coupling effect and to obtain the minimum damping rate in graphene. Even with the doping concentration 10¹⁹ - 10²⁰ cm^-3 and the thickness of the dielectric layer between graphene and the substrate 100nm, which are typical values in real graphene samples with a heavily doped substrate, the increase in the damping rate is not negligible in comparison with the acoustic-phonon-limited damping rate. Dependence of the damping rate on wavenumber, thicknesses of graphene-to-substrate and gate-to-graphene separation, substrate doping concentration, and dielectric constants of surrounding materials are investigated. It is shown that the damping rate can be much reduced by the gate screening, which suppresses the field spread of the graphene plasmons into the substrate.