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We theoretically study the dynamic screening properties of bilayer graphenewithin the random phase approximation assuming quadratic band dispersion andzero gap for the single-particle spectrum. We calculate the frequency dependentdielectric function of the system and obtain the low energy plasmon dispersionand broadening of the plasmon modes from the dielectric function. We alsocalculate the optical spectral weight (i.e. the dynamical structure factor) forthe system. We find that the leading order long wavelength limit of the plasmondispersion matches with the classical result for 2D electron gas. However,contrary to electron gas systems, the non-local plasmon dispersion correctionsdecrease the plasmon frequency. The non-local corrections are also differentfrom the single layer graphene. Finally, we also compare our results with thedouble layer graphene system (i.e. a system of two independent graphenemonolayers).

Dynamic Screening and Low Energy Collective Modes in Bilayer Graphene