Electronic structure and optical properties of twisted multilayer graphene

We study the electronic and optical properties of twisted trilayer and tetralayer graphene structures using a combination of tight-binding and density-functional theory methods. Band structures, densities of states, and optical absorption spectra are calculated for a variety of layer stackings and twisting angles. Systematic trends of all properties are obtained and compared to the more well known case of twisted bilayer graphene. For trilayer and tetralayer structures, we find, respectively, two and three well-defined absorption peaks in the infrared/visible range that shift with twisting angle, in contrast to the single peak observed in bilayer graphene. In addition, systems containing Bernal-stacked layers present an extra peak in the infrared which is related to transitions between parabolic bands and does not shift with twisting angle. The observed trends may be used to identify the twisting angle and the number of layers in multilayer graphene samples. In particular, magic angles are predicted for the trilayer and tetralayer structures.