Moiré fractional Chern insulators from topological bosons and trivial fermions

Recent realizations of fermionic fractional Chern insulators (FCIs) and anomalous Hall crystals have established moiré systems as a powerful platform for exploring correlated topological phases. Here, we predict the emergence of robust bosonic topological order arising from long-lived interlayer excitons consisting of holes in twisted bilayer WSe₂ and electrons in an additional MoSe₂ layer. In particular, exact diagonalization reveals that realistic long-range interactions stabilize Laughlin and non-Abelian Moore–Read states at filling factors 1/2 and 1 of the exciton Chern band present in this system. In parallel, we uncover Laughlin-like fermionic FCIs in topologically trivial bands of twisted multilayer graphene, where a strongly inhomogeneous quantum geometry drives topological order independent of band topology. Together, these results highlight the extraordinarily rich landscape of moiré quantum matter, encompassing both bosonic and fermionic topological order shaped by quantum geometry.