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.