在石墨烯与过渡金属二硫族化合物的扭转异质结中观测到精细关联相，表明莫尔平带对某些类型的无序具有内在的鲁棒性。本文研究了 Bistrizer-MacDonald 模型手性极限下莫尔平带的稳健性——该模型在特定极限下适用于上述两种平台——并证明第一魔角与更高魔角在响应手性对称无序（例如由晶格弛豫引起的无序）时存在显著差异。利用一个隐藏的运动常数，我们将层间隧穿诱导的非阿贝尔规范场分解为两个解耦的阿贝尔规范场，其有效磁场分裂为反常贡献和涨落部分。反常场将莫尔平带映射到第零狄拉克朗道能级，由于拓扑指标定理，该能级的平带性能够抵御任意手性对称微扰——从而凸显了平带性的拓扑机制。只有第一魔角能够充分利用这种拓扑保护，因为其涨落磁场较弱。在更高魔角中，涨落幅度大大超过反常贡献，我们发现这导致对微观细节的极大敏感性。通过数值模拟，我们研究了各种类型的无序，并识别了在手性极限下被增强或抑制的过程。有趣的是，我们发现无序展宽的拓扑抑制在手性极限之外仍然存在，并且通过将单个子晶格极化的平带在能量上孤立出来而进一步得到增强。我们的分析表明，过渡金属二硫族化合物单层中 K 和 K' 价带顶部的贝里曲率热点对于其莫尔平带及其关联态的稳定性至关重要。
英文摘要：
The observation of delicate correlated phases in twisted heterostructures of graphene and transition metal dichalcogenides suggests that moiré flat bands are intrinsically resilient against certain types of disorder. Here, we investigate the robustness of moiré flat bands in the chiral limit of the Bistrizer-MacDonald model -- applicable to both platforms in certain limits -- and demonstrate drastic differences between the first magic angle and higher magic angles in response to chiral symmetric disorder that arise, for instance, from lattice relaxation. Using a hidden constant of motion, we decompose the non-abelian gauge field induced by interlayer tunnelings into two decoupled abelian ones, whose effective magnetic field splits into an anomalous contribution and a fluctuating part. The anomalous field maps the moiré flat bands onto a zeroth Dirac Landau level, whose flatness withstands any chiral symmetric perturbation due to a topological index theorem -- thereby underscoring a topological mechanism for band flatness. Only the first magic angle can fully harness this topological protection due to its weak fluctuating magnetic field. In higher magic angles, the amplitude of fluctuations largely exceeds the anomalous contribution, which we find results in an extremely large sensitivity to microscopic details. Through numerical simulations, we study various types of disorder and identify the processes that are enhanced or suppressed in the chiral limit. Interestingly, we find that the topological suppression of disorder broadening persists away from the chiral limit and is further accentuated by isolating a single sublattice polarized flat band in energy. Our analysis suggests the Berry curvature hotspot at the top of the $K$ and $K'$ valence band in the transition metal dichalcogenide monolayers is essential for the stability of its moiré flat bands and their correlated states.
Ideal Topological Flat Bands in Two-dimensional Moiré Heterostructures with Type-II Band Alignment
The Pennsylvania State University（宾夕法尼亚州立大学）；Northeastern University（东北大学）；University of Washington（华盛顿大学）；Princeton University（普林斯顿大学）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊克拉巴斯基克，巴斯克科学基金会）
$\mathbb Z_2$-Nontrivial Moiré Minibands and Interaction-Driven Quantum Anomalous Hall Insulators in Topological Insulator Based Moiré Heterostructures
The "Moiré Capacitor Effect" and Stabilization of Fractional Chern Insulators in Rhombohedral Graphene Superlattices
Center for Computational Quantum Physics, Flatiron Institute（Flatiron研究所计算量子物理中心）；Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité（巴黎高等师范学院物理实验室，ENS，PSL大学，CNRS，索邦大学，巴黎第七大学，索邦巴黎城）；Department of Physics, Princeton University（普林斯顿大学物理系）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；Princeton Center for Theoretical Science, Princeton University（普林斯顿大学理论科学中心）；Department of Physics, University of Texas at Dallas（德克萨斯大学达拉斯分校物理系）；IKERBASQUE, Basque Foundation for Science（伊卡巴斯基克，巴斯克科学基金会）；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）
Halperin States of Particles and Holes in Ideal Time Reversal Invariant Pairs of Chern Bands and The Fractional Quantum Spin Hall Effect in Moiré MoTe$_2$
Twist-angle-dependent quantum phase diagrams in twisted bilayer MoTe2
State Key Laboratory of Micro-nano Engineering Science, Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院微纳工程科学国家重点实验室人工结构量子控制教育部重点实验室）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交通大学李政道研究所）；Department of Physics, Hong Kong University of Science and Technology（香港科技大学物理系）；State Key Laboratory of Surface Physics and Department of Physics, Fudan University（复旦大学表面物理国家重点实验室物理系）；Department of Physics and Astronomy, University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校物理与天文学系）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（物质材料研究机构电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料研究机构材料纳米构造研究中心）；Hefei National Laboratory（合肥国家实验室）；Shanghai Research Center for Quantum Sciences（上海量子科学研究与交流中心）；Max Planck Institute for Chemical Physics of Solids（德国马克斯·普朗克固体化学物理研究所）；Min H. Kao Department of Electrical Engineering and Computer Science, University of Tennessee, Knoxville（田纳西大学诺克斯维尔分校明浩高电气工程和计算机科学系）；New Cornerstone Science Laboratory, Fudan University（复旦大学新基石科学实验室）
Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe$_2$
Beijing Institute of Technology（北京理工大学）；Beijing Key Laboratory of Quantum Matter State Control and Ultra-Precision Measurement Technology（北京量子物质态调控与超精密测量技术重点实验室）
Orientation-tunable correlated Chern insulating states in chiral twisted double bilayer graphene proximitized by WSe2
Nanjing University（南京大学）；Hefei National Laboratory（合肥国家实验室）；Yangtze Delta Region Academy of Beijing Institute of Technology (Jiaxing)（北京理工大学长三角研究院（嘉兴））；National Institute for Materials Science（国立材料研究所）；Beijing Institute of Technology（北京理工大学）；Nanjing University of Science and Technology（南京理工大学）；Jiangsu Physical Science Research Center（江苏物理科学研究中心）
