Coulomb interaction-stabilized isolated narrow bands with Chern numbers $${{\mathcal{C}}} > 1$$ in twisted rhombohedral trilayer-bilayer graphene

Recently, fractional quantum anomalous Hall effects have been discovered in two-dimensional moiré materials when a topologically nontrivial band with Chern number $${{\mathcal{C}}}=1$$ is partially doped. 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 trilayer-bilayer graphene at θ ~ 1.2° as a field-tunable quantum anomalous Chern insulator that features spectrally-isolated, kinetically-quenched, and topologically-nontrivial bands with $${{\mathcal{C}}}=2,3$$ 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. Fractional Chern states with high Chern numbers could host exotic non Abelian phases but lack realistic zero field material platforms. Here, the authors propose that interactions in twisted rhombohedral trilayer-bilayer graphene generate narrow high Chern bands with near ideal quantum geometry, identifying regimes favorable for fractionalized states.