Electronic structure and optical properties of twisted bilayer graphene calculated via time evolution of states in real space

Abstract

We investigate the electronic and optical properties of twisted bilayer graphene with arbitrary twist angles $\ensuremath{\theta}$. Our results are based on a method of evolving in time quantum states in lattice space. We propose an efficient scheme of sampling lattice nodes that helps to reduce significantly computational cost, particularly for tiny twist angles. We demonstrate the continuous variation of the density of states and the optical conductivity with respect to the twist angle. It indicates that the commensurability between the two graphene layers does not play an essential role in governing the electronic and optical properties. We point out that, for the twist angles roughly in the range $0.{1}^{\ensuremath{\circ}}l\ensuremath{\theta}l{3}^{\ensuremath{\circ}}$, the density of states in the vicinity of the Fermi energy exhibits the typical W shape with a small peak locating at the Fermi energy. This peak is formed as the merging of two van Hove peaks and reflects the appearance of states strongly localized in the AA-like region of moir\'e zones. When decreasing the twist angle to zero, the W shape is gradually transformed to the U shape, which is seen as the behavior of the density of states in the limit of $\ensuremath{\theta}\ensuremath{\rightarrow}{0}^{\ensuremath{\circ}}$.