标题： 库仑相互作用稳定的孤立狭窄能带与扭转菱方三层-双层石墨烯中的陈数$\mathcal{C} > 1$ 显示英文标题

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

摘要： 最近，在二维莫尔材料中，当陈数为 $\mathcal{C}=1$ 的拓扑非平凡能带被部分掺杂时，发现了分数量子反常霍尔效应。 值得注意的是，超晶格布洛赫能带可以承载更高的陈数，这违背了朗道能级范式，甚至可能包含具有非阿贝尔准粒子的奇异分数态。 受这一激动人心的可能性的启发，我们提出了一种扭转\textit{菱形}三层-双层石墨烯，其$\theta \sim 1.2^\circ$，可作为场可调的量子反常陈绝缘体。该绝缘体具有光谱隔离、动力学猝灭和拓扑非平凡能带的特征，$\mathcal{C} = 2,3$，一旦经过分数掺杂，就有利于分数相形成，其量子几何结构就是其特征。 基于广泛的自洽平均场计算，我们表明这些相由库仑相互作用稳定，并且对介电环境、紧密结合跳跃参数和晶格弛豫的变化具有鲁棒性。 显示英文摘要

摘要： 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.