Displacement Field-Controlled Fractional Chern Insulators and Charge Density Waves in a Graphene/hBN Moire Superlattice

The fractional quantum Hall effect is arguably the most well-studied manifestation of the interplay between electronic correlations and non-trivial topology in condensed matter physics. Recent experiments on bilayer MoTe2 and rhombohedral multilayer graphene realized the long-sought fractional quantum anomalous Hall effect (FQAHE) at zero magnetic field. The past year has seen a flurry of experimental and theoretical efforts towards understanding this exotic phenomenon. In bilayer MoTe2, the prerequisite flat Chern bands can be understood at the single-particle level. However, in rhombohedral graphene, electronic correlations themselves produce the topological minibands required for the FQAHE, making this a challenging system to address theoretically. The aim of this work is to explore previously unexplored parameter regimes to pin down the conditions for the observation of topological states as well as to look for new many-body electronic phases.

We focus on five-layer rhombohedral graphene aligned to a layer of hexagonal boron nitride. Due to the lattice mismatch between the two materials, the rhombohedral graphene develops a long-period moiré superlattice potential. The FQAHE appears when electrons are pushed away from the superlattice by an electric field; the majority of studies so far have focused on this moiré-distant limit. In contrast, our work examines the opposite limit, in which the moiré potential is significantly stronger. By tuning the electric and magnetic fields, we can modify the topology and charge order of the correlated phases, revealing a rich phase diagram of delicate symmetry-broken states. Crucially, we observe fractional Chern insulators extending to nearly zero magnetic field with topology that is qualitatively different than in the moiré-distant case, along with a Wigner solid and a series of charge density waves. These are phases that, while seen individually in other moiré platforms, now all occur within close proximity to each other in a single system. Consequently, our work opens the door to further studies of topological phases and their competition via tuning of moiré potential strength in rhombohedral graphene multilayers.