Plasmon modes in 3-layer graphene structures: Inhomogeneity effects

We calculate the plasmon frequency and damping rate in a 3-layer graphene system made of parallel monolayer and bilayer graphene sheets using the random-phase-approximation dielectric function and taking into account the inhomogeneity of the dielectric background of the system. Numerical results show that two out-of-phase acoustic and one in-phase optical plasmon modes can be found from the zeroes of dynamical dielectric function of the structure. Plasmon frequencies and damping rate of plasma oscillations depend significantly on the inhomogeneity of environment, so plasmon curves become more distinctive from each other in single-particle excitation region, compared to the case of homogeneous medium. Finally, Plasmon dispersion patterns depend remarkably on the number (but not order) of bilayer graphene sheet constructing to the system.