Dielectric screening and plasmons in AA-stacked bilayer graphene

The screening properties and collective excitations (plasmons) in AA-stacked bilayer graphene are studied within the random phase approximation (RPA). Whereas long lived plasmons in single layer graphene and in AB-stacked bilayer graphene can exist only in doped samples, we find that coherent plasmons can disperse in AA-stacked bilayer graphene {\it even in the absence of doping}. Moreover, we show that the characteristic low energy dispersion relation is unaffected by changes in the number of carriers, unless the chemical potential of the doped sample exceeds the inter-layer hopping energy. We further consider the effect of an external electric field applied perpendicular to the layers, and show how the dispersion of the modes can be tuned by the application of a gate voltage.