Fractional quantum anomalous Hall effect in moiré fractional Chern insulators

Fractional Chern insulators (FCIs) generalize the fractional quantum Hall effects of Landau levels to lattice systems in the absence of an external magnetic field, which arise from the interplay between strong electron-electron interactions and non-trivial topology. Despite extensive theoretical proposals over more than a decade, realizing intrinsic FCIs in realistic materials has remained a long-standing challenge, owing to stringent requirements on band flatness, topology and quantum geometry. Advances in two-dimensional moiré superlattices have overcome these obstacles, enabling observations of the fractional quantum anomalous Hall effect. In this Perspective, we review the theoretical foundations of FCIs and discuss their experimental realizations in moiré materials, with a focus on two complementary platforms: twisted MoTe₂ and rhombohedral multilayer graphene/hexagonal boron nitride moiré superlattices. We highlight the distinct physical mechanisms underlying FCIs in these systems, outline open questions concerning their microscopic origin and stability and discuss future opportunities towards new FCIs and non-Abelian topological order in quantum materials.