Coulomb Interaction-Stabilized Integer and Fractional Chern Insulators in Twisted Rhombohedral M+N Multilayer Graphene

Recently, fractional quantum anomalous Hall effects have been discovered in two-dimensional moiré materials when a topologically nontrivial band with Chern number C = 1 is partially doped. Examples include rhombohedral graphene multilayers aligned with hexagonal boron nitride and twisted MoTe2 homobilayers. Remarkably, superlattice Bloch bands can carry higher Chern numbers that defy the Landau-level paradigm and may even host exotic fractionalized states with non-Abelian quasiparticles. Inspired by this exciting possibility, we propose twisted rhombohedral M+N graphene at small angles around 1 degree as a field-tunable quantum anomalous Chern insulator that features spectrally-isolated, kinetically-quenched, and topologically-nontrivial bands with C > 1 favorable for fractional phases once fractionally doped, as characterized by their quantum geometry. Based on extensive self-consistent mean-field calculations, we show that these phases are stabilized by Coulomb interactions and are robust against variations in dielectric environment, tight-binding hopping parameters, and lattice relaxation. We shall also discuss recent experimental observations that confirm our predictions and present progress updates on theoretical efforts to understand these fractional phases.