Fractional quantum anomalous Hall effect in rhombohedral multilayer graphene with a strong displacement field

Abstract

We investigate the fractional quantum anomalous Hall (FQAH) effect in rhombohedral multilayer graphene (RnG) in the presence of a strong applied displacement field. We first introduce the interacting model of RnG, which includes the noninteracting continuum model and the many-body Coulomb interaction. We then discuss the integer quantum anomalous Hall (IQAH) effect in RnG and the role of the Hartree-Fock approach in understanding its appearance. Next, we explore the FQAH effect in RnG for $n=3$--$6$ using a combination of constrained Hartree-Fock and exact diagonalization methods. We characterize the stability of the FQAH phase by the size of the FQAH gap and find that RnG generally has a stable FQAH phase, although the required displacement field varies significantly among different $n$ values. Our work establishes the theoretical universality of both IQAH and FQAH in RnG.

7 pages, 6 figures. Comments are welcome

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• Correlated phases in rhombohedral multilayer graphene
• Ordering the topological order in the fractional quantum Hall effect
• Ideal quantum geometry of the surface states of rhombohedral graphite and its effects on the surface superconductivity
• Various electronic crystal phases in rhombohedral graphene multilayers
• Elastic Response and Instabilities of Anomalous Hall Crystals
• Time-dependent conserved operators for autonomous systems and quantization of resistance