Dynamical conductivity of AA-stacked bilayer graphene

We calculate the dynamical conductivity of AA-stacked bilayer graphene as a function of frequency and in the presence of a finite chemical potential due to charging. Unlike the monolayer, we find a Drude absorption at charge neutrality in addition to an interband absorption with onset of twice the interlayer hopping energy. At finite doping, the interband absorption exhibits two edges, which depend on both chemical potential and interlayer hopping energy. We study the behavior as a function of varying chemical potential relative to the interlayer hopping energy scale and compute the partial optical sum. The results are contrasted with the previously published case of AB stacking. While we focus on in-plane conductivity, we also provide the perpendicular conductivity for both AB and AA stacking. We also examine conductivity for other variations with AA stacking, such as AAA-stacked trilayer. Based on proposed models for topological insulators discussed in the literature, we also consider the effect of spin-orbit coupling on the optical properties of an AA-stacked bilayer, which illustrates the effect of an energy gap opening at points in the band structure.