Coulomb Interaction-Stabilized Isolated Narrow Bands with Chern Numbers $\mathcal{C} > 1$ in Twisted Rhombohedral Trilayer-Bilayer Graphene

TL;DR

This paper proposes twisted rhombohedral trilayer-bilayer graphene as a tunable platform hosting isolated narrow bands with high Chern numbers, stabilized by Coulomb interactions, potentially enabling fractional quantum anomalous Hall effects with non-Abelian quasiparticles.

Contribution

It introduces a new material system with high Chern number bands and demonstrates their stability and topological properties through self-consistent mean-field calculations.

Findings

Bands with Chern numbers 2 and 3 are spectrally isolated and topologically nontrivial.

Coulomb interactions stabilize these high Chern number phases.

The phases are robust against environmental and structural variations.

Abstract

Recently, fractional quantum anomalous Hall effects have been discovered in two-dimensional moir\'{e} 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 \textit{rhombohedral} trilayer-bilayer graphene at $\theta \sim 1.2^\circ$ 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.