We investigate few- and many-body states in half-filled maximally symmetric topological insulator flat bands realized by two degenerate Landau levels which experience opposite magnetic fields. This serves as a toy model of flat bands in moiré materials in which valleys have Chern numbers $C= \pm 1$. We argue that although the spontaneously polarized Ising Chern magnet is a natural ground state for repulsive Coulomb interactions, it can be in reasonable energetic competition with correlated states which can be viewed as Laughlin states of excitons when short distance corrections to the interaction are included. This is because charge neutral excitons in these bands behave effectively as charged particles in ordinary Landau levels. In particular, the Ising Chern magnet is no longer the ground state once the strength of a short range intra-valley repulsion is about $30\%$ larger than the inter-valley repulsion. Remarkably, these excitonic Laughlin states feature valley number fractionalization but no charge fractionalization and a quantized charge Hall conductivity identical to the Ising magnet, $σ_{xy}= \pm e^2/h$, and thus cannot be distinguished from it by ordinary charge transport measurements. The most compact excitonic Laughlin state that can be constructed in these bands is an analogue of $ν=1/4$ bosonic Laughlin state and has no valley polarization even though it spontaneously breaks time reversal symmetry with a charge Hall conductivity $σ_{xy}= \pm e^2/h$.
我们认为，电子和空穴的相关流体可以表现出分数量子霍尔效应在零磁场类似的Laughlin状态填充$1/m$。我们介绍了一个变体的Laughlin波函数的电子和空穴，并表明，$m=1$它是一个自由费米子模型，描述$p_x + i p_y$激子配对的确切基态。对于$m>1$，我们开发了一个简单的复合费米子平均场理论，我们提出的证据表明，我们的波函数正确地描述了这个阶段。我们推导出一个相互作用的哈密顿量，我们的波函数是确切的基态，我们提出的物理参数，$m=3$状态可以实现在一个系统中的能带与角动量不同的$3$交叉的费米能量。这导致了一个无隙态与$(p_x + i p_y)^3$激子配对，我们认为这是有利于形成分数激子绝缘体中存在的相互作用。讨论了模型系统数值计算和能带结构工程在实际材料中实现这一阶段的前景。
Tunable Interlayer Charge-transfer States in MoSe$_2$/WS$_2$ Moiré Superlattices
University of California at Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；National Institute for Materials Science（物质材料研究机构）
University of Southern California（南加州大学）；Tamkang University（淡江大学）；The University of British Columbia（不列颠哥伦比亚大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Washington（华盛顿大学）；University of California at Berkeley（加利福尼亚大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）
Exciton-roton mode in moiré fractional Chern insulators
Tsinghua University（清华大学）；Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Frontier Science Center for Quantum Information, Beijing（北京量子前沿科学中心）
Valley polarization of moiré interlayer exciton complexes driven by many-body interactions
Technical University of Munich（慕尼黑工业大学）；Munich Center for Quantum Science and Technology (MCQST)（慕尼黑量子科学与技术中心）；National Institute for Materials Science（物质材料研究机构）；Research Center for Electronic and Optical Materials, National Institute for Materials Science（物质材料研究机构电子光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Materials Science（物质材料研究机构材料纳米架构研究中心）
Center for Computational Quantum Physics, Flatiron Institute（Flatiron Institute 计算量子物理中心）；Department of Physics, The University of Texas at Austin（德克萨斯大学奥斯汀分校物理系）；Materials Science Division, Argonne National Laboratory（阿贡国家实验室材料科学部）；Center for Quantum Phenomena, Department of Physics, New York University（纽约大学物理系量子现象中心）；Department of Physics, Columbia University（哥伦比亚大学物理系）；Department of Physics and Astronomy, Stony Brook University（石溪大学物理与天文系）
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$_2$
Fractional Chern Insulators Transition in Non-ideal Flat Bands of Twisted Mono-bilayer Graphene
State Key Laboratory of Semiconductor Physics and Chip Technologies, Institute of Semiconductors, Chinese Academy of Sciences（中国科学院半导体研究所半导体物理与芯片技术国家重点实验室）；Center for Quantum Matter, Zhejiang University（浙江大学量子物质中心）；College of Materials Science and Opto-electronic Technology, University of Chinese Academy of Sciences（中国科学院大学材料科学与光电技术学院）
