Plasmon modes in double bilayer graphene heterostructures

We investigate the plasmon frequency and decay rate in a double bilayer graphene (DBLG) heterostructure made of two bilayer graphene (BLG) flakes separated by a spacer of thickness d. Calculations are carried out at zero temperature, within the random phase approximation, taking into account the inhomogeneity of the dielectric background of the system. Analytical expressions for plasmon frequencies are obtained by using the long wavelength expansions of the response and bare Coulomb interaction functions. We find that at long-wavelength limit, the acoustic (optical) plasmon mode shows the linear (square-root) energy dispersion and the inhomogeneity of dielectric background decreases the frequencies of both plasmon branches as in the case of DLG. The carrier density, spacer thickness and background dielectric constant affect remarkably on plasmon frequency and decay rate.