Dynamic screening and low-energy collective modes in bilayer graphene

We theoretically study the dynamic screening properties of bilayer graphene within the random-phase approximation assuming quadratic band dispersion and zero gap for the single-particle spectrum. We calculate the frequency-dependent dielectric function of the system and obtain the low-energy plasmon dispersion and broadening of the plasmon modes from the dielectric function. We also calculate the optical spectral weight (i.e., the dynamical structure factor) for the system. We find that the leading-order long-wavelength limit of the plasmon dispersion matches with the classical result for two-dimensional electron gas. However, contrary to electron-gas systems, the nonlocal plasmon dispersion corrections decrease the plasmon frequency. The nonlocal corrections are also different from the single-layer graphene. Finally, we also compare our results with the double-layer graphene system (i.e., a system of two independent graphene monolayers).