Magic-angle twisted bilayer graphene is the best-studied physical platform featuring moiré potential-induced narrow bands with nontrivial topology and strong electronic correlations. Despite their significance, the Chern insulating states observed at a finite magnetic field—and extrapolating to a band filling $s$ at zero field—remain poorly understood. Unraveling their nature is among the most important open problems in the province of moiré materials. Here, we present the first comprehensive study of interacting electrons in finite magnetic field while varying the electron density, twist angle, and heterostrain. Within a panoply of correlated Chern phases emerging at a range of twist angles, we uncover a unified description for the ubiquitous sequence of states with the Chern number $t$ for $(s,t)=\pm (0,4)$, $\pm (1,3)$, $\pm (2,2)$, and $\pm (3,1)$. We also find correlated Chern insulators at unconventional sequences with $s+t\ne \pm 4$, as well as with fractional $s$, and elucidate their nature.

中文翻译：

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扭曲双层石墨烯中相关陈绝缘子理论


魔角扭曲双层石墨烯是研究最深入的物理平台，具有莫尔势引起的窄带、不平凡的拓扑结构和强电子相关性。尽管它们很重要，但在有限磁场下观察到的陈绝缘态——并推断出零场下填充 $s$ 的能带——仍然知之甚少。揭开它们的本质是莫尔条纹材料领域最重要的开放性问题之一。在这里，我们首次全面研究了有限磁场中电子相互作用，同时改变电子密度、扭转角和异应变。在一系列以一系列扭转角出现的相关陈相中，我们发现了对普遍存在的状态序列的统一描述，陈数 $t$ 为 $(s,t)=\pm (0,4)$ 、 $\pm (1,3)$ 和 $\pm (3,1)$ 。我们还在非常规序列上发现了与 $s+t\ne \pm 4$ 以及分数 $s$ 相关的陈绝缘子，并阐明了它们的性质。