Berry curvature-induced emerging magnetic response in two-dimensional materials

The magnetic response in a two-dimensional material has received increasing attention in recent years. The magnetic effects and related quantum transport originate from Berry curvature, which is associated with crystal symmetry and many quantum effects including electrons’ orbital magnetism, spin-orbit coupling, and magnetoelectricity. The importance of studying the magnetic response in the two-dimensional material lies in two aspects. First, the magnetic response of two-dimensional material provides a platform to investigate the coupling between the above-mentioned intrinsic quantum effects and their couplings. Second, it possesses the potential applications in energy-efficient quantum and spintronic devices. Here, we review the experimental research progress made in recent years. In particular, we focus on the research progress of the valley Hall and magnetoelectric effect, quantum non-linear Hall effect, anomalous Hall, and quantum anomalous Hall effect in two-dimensional materials such as graphene, transition-metal chalcogenides, and twisted bilayer graphene. For each session, we first introduce these phenomena and their underlying physics by using crystal symmetries and band structures. Then, we summarize the experimental results and identify unsolved problems. At last, we provide an outlook in this emerging research direction.