Realizing programmable topological states in quantum anomalous Hall (QAH) insulators requires the ability to design and dynamically tune their topological invariant, the Chern number C. Here, we report a designer QAH platform based on twisted rhombohedral graphene family, in which C becomes a programmable and electrically tunable degree of freedom. By engineering the layer configuration in twisted monolayer-rhombohedral N-layer graphene, denoted as (1+N)L, we realize QAH states with C=N at moire filling v=1, where the layer number N=3,4,5 directly sets the Chern number. Beyond such static layer programming, we demonstrate in-situ electrical control. In a twisted monolayer-trilayer device, the sign of C (chirality) can be switched by electrostatic doping or displacement field. Most strikingly, in twisted Bernal bilayer-rhombohedral tetralayer graphene denoted as (2+4)L, we drive a displacement-field-induced topological phase transition between two distinct QAH states with C=3 and C=4 in a single device. Our work establishes a layer-engineered and electrically tunable platform that transitions topological quantum matter from discovery to design, opening the way toward on-demand engineering of correlated topological states and reconfigurable topological electronics.
Spin-polarized Superconductivity and High-Chern Insulators in Twisted Rhombohedral Graphene Family
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；State Key Laboratory for Mesoscopic Physics, Frontiers Science Centre for Nano-optoelectronics, School of Physics, Peking University（北京大学物理学院介观物理国家重点实验室纳米光电子前沿科学中心）；Research Center for Electronic and Optical Materials, National Institute for Material Science（日本国立物质材料研究所电子与光学材料研究中心）；Research Center for Materials Nanoarchitectonics, National Institute for Material Science（日本国立物质材料研究所材料纳米结构研究中心）；Interdisciplinary Institute of Light-Element Quantum Materials and Research Centre for Light-Element Advanced Materials, Peking University（北京大学轻元素量子材料交叉研究院轻元素先进材料研究中心）
Fractional High-Chern Insulator in Twisted Rhombohedral Graphene
International Center for Quantum Materials, School of Physics, Peking University（北京大学物理学院量子材料国际中心）；State Key Laboratory for Mesoscopic Physics, Frontiers Science Centre for Nano-optoelectronics, School of Physics, Peking University（北京大学物理学院介观物理国家重点实验室纳米光电子前沿科学中心）；Research Center for Electronic and Optical Materials, National Institute of Material Sciences（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 of Material Sciences（物质材料研究机构材料纳米构造研究中心）；Interdisciplinary Center for Theoretical Physics and Information Sciences, Fudan University（复旦大学理论物理与信息科学交叉中心）；Hefei National Laboratory（合肥国家实验室）；Collaborative Innovation Center of Quantum Matter（量子物质协同创新中心）
Programmable Quantum Anomalous Hall Insulator in Twisted Crystalline Flatbands
Peking University（北京大学）；National Center for Nanoscience and Technology（国家纳米科学中心）；Shanghai Jiao Tong University（上海交通大学）；Fudan University（复旦大学）；Hefei National Laboratory（合肥国家实验室）；National Institute for Material Sciences（物质材料研究国际中心）
Moire-Engineered Excitonic Landscape and Phonon-Mediated Recombination in Twisted WSe2 Bilayers
Indian Institute of Technology Mandi（印度技术学院曼迪分校）；CSIR-National Physical Laboratory（印度科学工业研究理事会国家物理实验室）；Academy of Scientific and Innovative Research (AcSIR)（科学与创新研究学院）；Indian Institute of Science（印度科学学院）；National Institute of Material Science（国家物质科学研究所）
One-way electron mirrors from single-layer stacking shifts in rhombohedral graphite
Hungarian Research Network, HUN-REN Centre for Energy Research, Institute of Technical Physics and Materials Science（匈牙利研究网络，HUN-REN能源研究中心，技术物理与材料科学研究所）；Department of Physics, Institute of Physics, Budapest University of Technology and Economics（布达佩斯技术与经济大学，物理系，物理研究所）；MTA - HUN-REN EK Lendület “Momentum” Topology in Nanomaterials Research Group（匈牙利科学院-HUN-REN EK Lendület “Momentum”纳米材料拓扑研究组）；ELTE, Eötvös Loránd University（厄特沃什·罗兰大学）；Óbuda University（奥比杜斯大学）
Visualizing flat-band spatial renormalization in rhombohedral graphene superlattices
Key Laboratory for Micro/Nano Optoelectronic Devices of Ministry of Education & Hunan Provincial Key Laboratory of Low-Dimensional Structural Physics and Devices, School of Physics and Electronics, Hunan University（教育部微纳光电器件重点实验室与湖南省低维结构物理及器件重点实验室，湖南大学物理与电子学院）；Yuelushan Center for Industrial Innovation（岳麓山工业创新中心）；College of Semiconductors (College of Integrated Circuits), Hunan University（湖南大学半导体学院（集成电路学院））；College of Physics and Hebei Advanced Thin Films Laboratory, Hebei Normal University（河北师范大学物理学院与河北省先进薄膜材料实验室）
Quantum Phase Transitions and Fractional Quantized Anomalous Hall Insulators in Rhombohedral Graphene
Massachusetts Institute of Technology（麻省理工学院）；Weizmann Institute of Science（魏茨曼科学研究所）；Florida State University（佛罗里达州立大学）；National Institute for Materials Science（国立材料研究所）
Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers
University of Texas at Austin（德克萨斯大学奥斯汀分校）；The University of Hong Kong（香港大学）；National Yang Ming Chiao Tung University（阳明交通大学）；Pennsylvania State University（宾夕法尼亚州立大学）；National Institute for Materials Science（日本物质材料研究机构）
Observation of Kondo Effect in Rhombohedral Graphene Superlattices
State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics, Peking University（北京大学物理学院介观物理国家重点实验室和纳米光电前沿科学中心）；Centre for Quantum Physics, Key Laboratory of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), School of Physics, Beijing Institute of Technology（北京理工大学物理学院量子物理中心、先进光电子量子架构与测量教育部重点实验室）；Research Center for Electronic and Optical Materials, National Institute for Material Sciences（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 Material Sciences（物质材料研究机构材料纳米结构研究中心）；Hefei National Laboratory（合肥国家实验室）
Observation of Integer and Fractional Chern insulators in high Chern number flatbands
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）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；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构造研究中心）；Songshan Lake Materials Laboratory（松山湖材料实验室）
Moiré-induced lattice reconstruction at buried atomic interfaces
University of Manchester（曼彻斯特大学）；National Graphene Institute, University of Manchester（国家石墨烯研究所，曼彻斯特大学）；Diamond Light Source（英国钻石光源）；University of Oxford（牛津大学）；Henry Royce Institute for Advanced Materials（亨利·罗伊斯先进材料研究所）
Imaging topological polar structures in marginally twisted 2D semiconductors
Monash University（莫纳什大学）；John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）；Nanyang Technological University Singapore（新加坡南洋理工大学）；National University of Singapore（新加坡国立大学）；Flinders University（弗林德斯大学）；Melbourne Centre for Nanofabrication（墨尔本纳米制造中心）；Pennsylvania State University（宾夕法尼亚州立大学）；Swinburne University of Technology（斯威本科技大学）；National Institute for Materials Science（日本物质材料研究机构）
Incipient superconductivity and tunable Chern insulators in twisted bilayer-trilayer graphene
Department of Physics, University of Washington（华盛顿大学物理系）；Department of Materials Science and Engineering, University of Washington（华盛顿大学材料科学与工程系）；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（物质材料研究机构的材料纳米结构研究中心）
Locally resolved electronic textures of reconstruction domains in marginally twisted monolayer-bilayer graphene
University of Ottawa（渥太华大学）；University of Manchester（曼彻斯特大学）；National Graphene Institute, University of Manchester（曼彻斯特大学国家石墨烯研究所）；National Institute for Materials Science（国立材料研究所）
