Anomalous valley Hall effect in two-dimensional valleytronic materials

The anomalous valley Hall effect (AVHE) can be used to explore and utilize valley degrees of freedom in materials, which has potential applications in fields such as information storage, quantum computing and optoelectronics. AVHE exists in two-dimensional (2D) materials possessing valley polarization (VP), and such 2D materials usually belong to the hexagonal honeycomb lattice. Therefore, it is necessary to achieve valleytronic materials with VP that are more readily to be synthesized and applicated experimentally. In this topical review, we introduce recent developments on realizing VP as well as AVHE through different methods, i.e., doping transition metal atoms, building ferrovalley heterostructures and searching for ferrovalley materials. Moreover, 2D ferrovalley systems under external modulation are also discussed. 2D valleytronic materials with AVHE demonstrate excellent performance and potential applications, which offer the possibility of realizing novel low-energy-consuming devices, facilitating further development of device technology, realizing miniaturization and enhancing functionality of them.