Quantum anomalous Hall effect in rhombohedral multilayer graphene/h-BN moiré superlattices

The recent observation of robust quantum anomalous Hall (QAH) effects in rhombohedral multilayer graphene (RMG) aligned with hexagonal boron nitride (-BN) has established a highly versatile platform for correlated topological matter. This review synthesizes the experimental and theoretical progress in understanding these interaction-driven topological phases, with particular emphasis on the filling factor. Experimentally, the landscape has rapidly expanded from initial Chern insulators in trilayer systems to fully quantized QAH states in thicker systems. Theoretically, it is generally understood that moiré potential and electron-electron interaction cooperate and lead to the formation of isolated Chern bands and spontaneous symmetry breaking, producing the QAH effect in such systems. Theoretical calculations also raised important questions, such as the formation of an interaction-driven topological phase known as an anomalous Hall crystal (AHC). This review covers the experimental hallmarks, the theoretical frameworks-including continuum models and many-body approaches-and the ensuing physical picture that reconciles the roles of interactions, displacement fields, and the moiré potentials. Finally, open questions and future directions are discussed, highlighting the role of RMG/-BN systems as a platform for correlated topological quantum matter.