Coulomb Interaction-Stabilized Isolated Narrow Bands with Chern Numbers C > 1 in Twisted Rhombohedral Trilayer-Bilayer Graphene

Abstract Recently, fractional quantum anomalous Hall effects have been discovered in two-dimensional moir\'{e} materials when a topologically nontrivial band with Chern number 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 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.