Exciton fractional Chern insulators in moir\'e heterostructures

Moir\'e materials have emerged as a powerful platform for exploring exotic quantum phases. While recent experiments have unveiled fractional Chern insulators exhibiting the fractional quantum anomalous Hall effect based on electrons or holes, the exploration of analogous many-body states with bosonic constituents remains largely uncharted. In this work, we predict the emergence of bosonic fractional Chern insulators arising from long-lived excitons in a moir\'e superlattice formed by twisted bilayer WSe$_2$ stacked on monolayer MoSe$_2$. Performing exact diagonalization on the exciton flat Chern band present in this structure, we establish the existence of Abelian and non-Abelian phases at band filling $\frac{1}{2}$ and $1$, respectively, through multiple robust signatures including ground-state degeneracy, spectral flow, many-body Chern number, and particle-cut entanglement spectrum. The obtained energy gap of $\sim 10$ meV for the Abelian states suggests a remarkably high stability of this phase. Our findings not only introduce a highly tunable and experimentally accessible platform for investigating bosonic fractional Chern insulators but also open a new pathway for realizing non-Abelian anyons.