Optical properties of twisted bilayer graphene

A twisted stack of two graphene layers (twisted bilayer graphene) exhibits an extremely long potential period arising from the Moir\'{e} interference between the layers. We calculate the optical absorption of twisted bilayer graphene in the absence of magnetic field and demonstrate that the spectroscopic characteristics serve as a fingerprint to identify the rotation angle between two layers\footnote{P. Moon and M. Koshino, Phys.\ Rev.\ B \textbf{87}, 205404 (2013).}. We explain the peculiar optical selection rule in terms of the symmetry of the effective Hamiltonian. We also investigate the effects of charging and gating on the optical spectrum\footnote{P. Moon, M. Koshino, and Y.-W. Son, in preparation}. In addition, we investigate the absorption spectrum and the selection rule for the fractal band regime (Hofstadter butterfly) in the presence of magnetic field. We demonstrate that the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum, and the optical selection rule has a nested self-similar structure as well\footnote{P. Moon and M. Koshino, arXiv:1308.0713 (2013)}.