Optical Properties of AA-Stacked Bilayer Graphene
Theoretical predictions of the AC conductivity of both monolayer and Bernal-stacked bilayer graphene have largely been in agreement with experimental observations. Due to the recent realization of AA-stacked samples, we provide theoretical predictions for this system. We begin this thesis with a review of the optical properties of graphene and provide a brief discussion of the previously studied Bernal-stacked bilayer. We then calculate the optical conductivity of AA-stacked bilayer graphene as a function of frequency for several interesting cases. We are primarily interested in the case of finite doping due to charging. Unlike the monolayer, we see a Drude absorption at charge neutrality as well as an interband absorption with strength twice that of the monolayer background conductivity which onsets at twice the interlayer hopping energy. We examine the behaviour as we vary the chemical potential relative to the interlayer hopping energy scale and compute the partial optical sum. We also consider the effect of adding a bias across the layers and find it serves merely to renormalize the interlayer hopping parameter. While interested in the in-plane conductivity we also provide the perpendicular conductivity of the AA-stacked bilayer. We then extend the ideas to the AAA-stacked trilayer. Based on proposed models for topological insulators discussed in the literature, we consider the effect of spin orbit coupling in both one and two layers on the optical properties of the AA-stacked bilayer which illustrates the effect of opening an energy gap in the band structure.