Moiré structures formed by twisting three layers of graphene with two independent twist angles present an ideal platform for studying correlated quantum phenomena, as an infinite set of angle pairs is predicted to exhibit flat bands. Moreover, the two mutually incommensurate moiré patterns among the twisted trilayer graphene (TTG) can form highly tunable moiré quasicrystals. This enables us to extend correlated physics in periodic moiré crystals to quasiperiodic systems. However, direct local characterization of the structure of the moiré quasicrystals and of the resulting flat bands are still lacking, which is crucial to fundamental understanding and control of the correlated moiré physics. Here, we demonstrate the existence of flat bands in a series of TTGs with various twist angle pairs and show that the TTGs with different magic angle pairs are strikingly dissimilar in their atomic and electronic structures. The lattice relaxation and the interference between moiré patterns are highly dependent on the twist angles. Our direct spatial mappings, supported by theoretical calculations, reveal that the localization of the flat bands exhibits distinct symmetries in different regions of the moiré quasicrystals.
Proximity Effects Between the Graphene Quasicrystal and Magic-Angle Twisted Bilayer Graphene
Catalan Institute of Nanoscience and Nanotechnology (ICN2), CSIC and BIST（加泰罗尼亚纳米科学技术研究所（ICN2），西班牙国家研究委员会和巴塞罗那高等研究院）；Department of Physics, Campus UAB（巴塞罗那自治大学物理系）；Institute of Condensed Matter and Nanosciences, Université catholique de Louvain (UCLouvain)（天主教鲁汶大学凝聚态与纳米科学研究所）；ICREA–Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚研究与高级研究所（ICREA））
Correlated interlayer quantum Hall state in large-angle twisted trilayer graphene
Daegu Gyeongbuk Institute of Science and Technology (DGIST)（大邱庆北科学技术院）；Ulsan National Institute of Science and Technology（蔚山科学技术院）；University of Seoul（首尔大学）；Pohang University of Science and Technology（浦项科技大学）；National Institute for Materials Science（物质材料研究机构）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute for Basic Science（基础科学研究所）
Electronic Reconstruction at the Quasicrystal-Moiré Crossover in Twisted Bilayer Graphene
National Cheng Kung University（国立成功大学）；Center for Quantum Frontiers of Research & Technology (QFort), National Cheng Kung University（国立成功大学量子前沿研究与技术中心）；National Taiwan University（国立台湾大学）；Center for Condensed Matter Sciences, National Taiwan University（国立台湾大学凝聚态科学中心）；Center of Atomic Initiative for New Materials, National Taiwan University（国立台湾大学原子级新材料创新中心）
Remote Moiré Modulation of Decoupled Dirac Subsystems in Twisted Trilayer Graphene
Daegu Gyeongbuk Institute of Science and Technology (DGIST)（大邱庆北科学技术院）；National Institute for Materials Science（国立材料研究所）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute for Basic Science（基础科学研究院）
Chern-Selective multi-valley Flat Bands in Twisted Mono-Bilayer and Mono-Trilayer MoTe$_2$
Beijing National Laboratory for Condensed Matter Physics and Institute of physics, Chinese academy of sciences（中国科学院物理研究所）；University of Chinese academy of sciences（中国科学院大学）；Center for Computational Quantum Physics, Flatiron Institute（平顿研究所计算量子物理中心）；Department of Physics, Princeton University（普林斯顿大学物理系）；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）
Heavy fermion phase diagram in magic-angle twisted trilayer graphene
Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）；University of Chinese Academy of Sciences（中国科学院大学）；IMDEA Nanociencia（IMDEA纳米科学中心）；National Institute for Materials Science（国立材料研究所）
Assessing quantitative phase reliability in electron ptychography using a twisted trilayer WS2 thickness staircase
University of Science and Technology of China（中国科学技术大学）；Yanshan University（燕山大学）；Zhejiang University of Technology（浙江工业大学）；University of Chinese Academy of Sciences（中国科学院大学）
Quasicrystalline 30° Twisted Bilayer Graphene as an Incommensurate Superlattice with Strong Interlayer Coupling
层间耦合可用于设计范德华异质结构（超晶格）的电子结构，以获得单一材料中不可能的特性。到目前为止，异质结构的研究一直集中在具有长程莫尔周期的公度超晶格上。具有旋转对称性但不具有平移对称性的无公度异质结构（类似于准晶）不仅在自然界中罕见，而且由于缺乏相位相干性，层间相互作用通常被认为是可以忽略的。本文报道了在Pt（111）衬底上成功生长的准晶态30°扭曲双层石墨烯（30°-tBLG），并揭示了其电子结构。低能电子衍射和1383 cm $^{-1}$处的谷间双共振喇曼模式证实了30°-tBLG。此外，每个石墨烯层的布里渊区内部镜像狄拉克锥的出现以及区边界处的间隙开口表明这两个石墨烯层经由广义Umklapp散射机制耦合，即一个石墨烯层中的狄拉克锥通过另一个石墨烯层的倒易晶格矢量的散射。我们的工作突出了层间耦合在无公度准晶超晶格中的重要作用，从而将能带结构工程扩展到无公度超结构。
Observation of square-like moire lattice and quasicrystalline order in twisted rock-salt nitrides
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家实验室）；Department of Physics & Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences（中国科学院大学物理科学与光电技术学院材料科学与光学电子工程中心）；School of information Science and Engineering, Shandong Agricultural University（山东农业大学信息科学与工程学院）；Department of Physics, Southern University of Science and Technology（南方科技大学物理系）
Moiré trapping of quadrupolar excitons in van der Waals trilayers
Newcastle University（纽卡斯尔大学）；Imperial College London（帝国理工学院）；Max Planck Institute for the Structure and Dynamics of Matter（马普物质结构与动力学研究所）；Flatiron Institute（平顿研究所）
