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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 -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=-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.
Wang et al. (Fri,) studied this question.