Fractional Chern insulators in moir\'e flat bands with high Chern numbers

TL;DR

This paper proposes a new material setup involving twisted transition metal dichalcogenides and skyrmion lattices to realize fractional Chern insulators with high Chern numbers, expanding beyond traditional Landau level systems.

Contribution

It introduces a novel candidate system for high Chern number fractional Chern insulators and confirms their properties through comprehensive numerical analysis.

Findings

High Chern number flat bands induced by skyrmion exchange potential

Confirmation of generalized Jain series at various fillings

Guidance for experimental realization of unconventional fractional Chern insulators

Abstract

Recent discoveries of zero-field fractional Chern insulators in moir\'e materials have attracted intensive research interests. However, most current theoretical and experimental attempts focus on systems with low Chern number bands, 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 $\Gamma$-valley twisted homobilayer transition metal dichalcogenides in proximity to a 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 series. Our research provides theoretical guidance on realizing unconventional fractional Chern insulators beyond the Landau level picture.