Energetics of fractional anomalous Hall crystals in rhombohedral graphene

Abstract

Fractional anomalous Hall crystals (FAHCs) replicate the topological order of the fractional quantum Hall effect in the continuum without requiring any external magnetic field. They spontaneously break continuous translation symmetry like a Wigner crystal, but are distinguished by each unit cell holding a fixed fractional number of electrons. Until now, these states have been confined to theoretical speculation or engineered models, leaving open the question of whether they can plausibly emerge in actual physical systems. Here, we establish them as energetically competitive candidate states in a realistic material setting. We study rhombohedral pentalayer graphene (R5G) with variational wavefunctions that are exact zero modes of a recently proposed ideal model of R5G. We evaluate their energies using Monte Carlo, after reinstating realistic dispersion and screened Coulomb interactions. We find FAHCs to be energetically competitive with integer anomalous Hall crystals and Fermi liquids, and their stability follows a simple principle. Each crystal maps onto a parent quantum Hall liquid that fixes its interaction energy, while the kinetic energy favors crystal periods that match the finite-momentum minimum of R5G's Mexican-hat dispersion. A weak periodic potential can then selectively lower and pin the commensurate fractional crystals. This picture predicts how the integer and fractional quantum anomalous Hall stability windows evolve with twist angle and displacement field, which we compare to recent experiments. These results support a continuum-and-interactions-first route to fractional anomalous Hall states in rhombohedral graphene.