Fractional Quantum Anomalous Hall Effect in Rhombohedral Multilayer Graphene in the Moiréless Limit

Abstract

The standard theoretical framework for fractional quantum anomalous Hall (FQAH) effect assumes an isolated flat Chern band in the single particle level. In this Letter, we challenge this paradigm for the FQAH effect recently observed in pentalayer rhombohedrally stacked graphene aligned with hexagonal boron nitride. We show that the external moiré superlattice potential is simply a perturbation in a model with continuous translation symmetry. Through Hartree-Fock calculations, we find that interaction opens a sizable remote-band gap, resulting in an isolated narrow C=1 Chern band at filling ν=1. From exact diagonalization we identify FQAH phases at various fillings. However, the FQAH states also exist in calculations without any external moiré potential. We suggest that the quantum anomalous Hall (QAH) insulator at ν=1 should be viewed as an interaction-driven topological Wigner crystal with QAH effect, which is subsequently pinned by a small moiré potential. The C=1 QAH crystal is robust with a crystal period around 10 nm in 4-layer, 5-layer, 6-layer, and 7-layer graphene systems. Our work suggests a new direction to explore the interplay between topology and FQAH with spontaneous crystal formation in the vanishing moiré potential limit. We also propose a new system to generate and control both honeycomb and triangular moiré superlattice potentials through Coulomb interaction from another control layer, which can stabilize or suppress the QAH crystal depending on the density of the control layer.