Special Quantum Matter Seminar

Recent experiments on rhombohedral pentalayer graphene with a substrate-induced moir\'e potential have identified both Chern insulators and fractional Quantum Hall states at zero magnetic field. Surprisingly, these states are observed in strong displacement fields where the effects of the moir\'e lattice are weak, and seem to be readily accessed without fine-tuning. To address these experimental puzzles, we study a model of interacting electrons in this geometry. Within self-consistent Hartree-Fock (SCHF), we find an isolated Chern band with small bandwidth and good quantum geometry. Exact diagonalization and density-matrix renormalization group calculations both confirm the band hosts fractional quantum Hall states without a magnetic field. Remarkably, the Chern band is stable at a wide range of angles, at four through six rhombohedral layers, at varying rhombohedral hopping parameters, and --- most strikingly --- survives in SCHF when the moir\'e potential vanishes. In this limit, the state spontaneously breaks time-reversal and translation symmetry simultaneously, giving a topological crystalline state that we term the ``anomalous Hall crystal'' (AHC). We argue this is a general mechanism to create stable Chern bands in rhombohedral multilayer graphene, opening the door to studying the interplay between electronic topology, fractionalization, and spontaneous translation symmetry breaking.