Fractional Chern insulators in moiré flat bands with high Chern numbers

Recent discoveries of zero-field fractional Chern insulators in moir\'e materials have attracted intensive research interest. However, most current theoretical and experimental attempts focus on Chern bands with Chern number $|C|=1$, in analogy to the Landau levels. Here, we propose candidate material systems for realizing fractional Chern insulators with higher Chern numbers. The material setup involves $\mathrm{\ensuremath{\Gamma}}$-valley twisted homobilayer transition metal dichalcogenides in proximity to a magnetic skyrmion lattice. The skyrmion exchange potential induces a flat band with a high Chern number $C=\ensuremath{-}2$. Using the momentum-space projected exact diagonalization method, we perform a comprehensive study at various filling factors, confirming the generalized Jain sequence. Our research provides theoretical guidance on realizing unconventional fractional Chern insulators beyond the Landau level picture.