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.

我们研究了与六角形氮化硼衬底对齐的扭曲双层石墨烯以及扭曲双层双层石墨烯系统的异常霍尔效应，磁光特性和非线性光学特性。我们表明，在扭曲的石墨烯系统中不消失的谷极极化将引起异常霍尔效应，该效应可通过面内磁场进行调整。谷极化状态还与太赫兹频率范围内的巨大法拉第和克尔旋转有关。此外，我们提出扭曲的石墨烯系统表现出巨大的非线性光学响应，这归因于系统的反对称断裂，小带宽和小激发间隙。在双双层石墨烯中