Exploring the Fractional Quantum Anomalous Hall Effect in Moiré Materials: Advances and Future Perspectives.

The search for anyons, quasiparticles with fractional charge and exotic exchange statistics, has inspired the research of condensed matter physics for decades. Moiré materials, as superlattice systems characterized by tunable isolated topological flat bands, represent a vast material library, with the ability to adjust properties via various tuning knobs, and show particular suitability for investigating the physics of anyons. In the study of Hall effects, Moiré systems offer a distinctive platform to achieve various Hall effects such as the valley Hall effect, nonlinear Hall effect, quantum anomalous Hall effect, and fractional quantum anomalous Hall effect (FQAHE). Particularly, over the nearly four decades from the discovery of the integer quantum Hall effect in 1980 to the observation of the FQAHE in 2023, research on Moiré materials has advanced the development of condensed matter physics rapidly. The discovery of FQAHE contributes to the study of non-Abelian quasiparticles, which holds potential for applications in topological quantum computing. This review primarily reviews the experimental advances brought about by the emergence of Moiré material systems on the path to achieving the FQAHE as well as the technological transformations driven by advancements in recent device fabrication techniques. Furthermore, we highlight the critical challenges and provide perspectives for future research.