Anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted graphene systems

We study the anomalous Hall effect, magneto-optical properties, and nonlinear optical properties of twisted bilayer graphene aligned with hexagonal boron nitride substrate, as well as twisted double bilayer graphene systems. We show that non-vanishing valley polarizations in twisted graphene systems would give rise to the anomalous Hall effect, which can be tuned by in-plane magnetic fields. The valley polarized states are also associated with giant Faraday and Kerr rotations in the terahertz frequency regime. Moreover, we propose that the twisted graphene systems exhibit colossal nonlinear optical responses by virtue of the inversion-symmetry breaking, the small bandwidth, and the small excitation gaps of the systems. In twisted double bilayer graphene, we find that certain components of the nonlinear photo-conductivity tensor are directly proportional to the orbital magnetization of the system, which would exhibit remarkable hysteresis behavior in response to perpendicular magnetic fields.