Coulomb interaction-stabilized isolated narrow bands with Chern numbers <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>></mo><mn>1</mn></math> in twisted rhombohedral trilayer-bilayer graphene.

Abstract

Recently, fractional quantum anomalous Hall effects have been discovered in two-dimensional moiré materials when a topologically nontrivial band with Chern number <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>1</mn></math> 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 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>2</mn><mo>,</mo><mn>3</mn></math> 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.