Fractional Chern insulator states in multilayer graphene moiré superlattices

ZQ Guo and X Lu and B Xie and JP Liu, PHYSICAL REVIEW B, 110, 075109 (2024).

DOI: 10.1103/PhysRevB.110.075109

In this work, we theoretically study the fractional Chern insulator (FCI) states in rhombohedral multilayer graphene moir & eacute; superlattices. We start from the highest energy scale (similar to 2 similar to 2 eV) of the continuum model, and construct a renormalized low-energy model that applies to a lower cutoff similar to 0 . 15 eV using a renormalization group approach. Then, we study the ground states of the renormalized low-energy model at filling 1 under the Hartree-Fock approximation in the presence of tunable but self-consistently screened displacement field D with several experimentally relevant background dielectric constants E r . Focusing on the pentalayer moir & eacute; graphene system, two competing Hartree-Fock states are obtained at filling 1, which give rise to two types topologically distinct isolated flat bands with Chern numbers 1 and 0, respectively. By hole-doping the isolated topological flat bands, both Laughlin-type and composite- fermion-type FCI states can be obtained through exact-diagonalization calculations at different fractional filling factors, which exhibit quantitative consistency with experimental measurements. We further explore the correlated topological states in generic rhombohedral multilayer graphene moir & eacute; superlattices, and find that FCI states may also emerge in tetralayer and hexalayer moir & eacute; graphene systems.

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