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Experimental observation of non-Abelian topological charges and edge states

机译：非雅典拓扑收费和边缘状态的实验观察

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摘要

Non-Abelian topological charges and edge states in a PT-symmetric transmission line network are experimentally observed, and a non-Abelian quotient relation for the bulk-edge correspondence is found.In the last few decades, topological phase(1-11) has emerged as a new classification of matter states beyond the Ginzburg-Landau symmetry-breaking paradigm. The underlying global invariant is usually well characterized by integers, such as Chern numbers or winding numbers-the Abelian charges(12-15). Very recently, researchers proposed the notion of non-Abelian topological charges(16-19), which possess non-commutative and fruitful braiding structures with multiple (more than one) bandgaps tangled together. Here we experimentally observe the non-Abelian topological charges in a time-reversal and inversion-symmetric transmission line network. The quaternion-valued non-Abelian topological charges are clearly mapped onto an eigenstate-frame sphere. Moreover, we find a non-Abelian quotient relation that provides a global perspective on the distribution of edge/domain-wall states. Our work opens the door towards characterization and manipulation of non-Abelian topological charges, which may lead to interesting observables such as trajectory-dependent Dirac/Weyl node collisions in two-dimensional systems(16,17,20), admissible nodal line configurations in three dimensions(16,19,20), and may provide insight into certain strongly correlated phases of twisted bilayer graphene(21).
机译：在实验观察到PT对称传输线网络中的非雅典拓扑电荷和边缘状态，并且发现了对散装边缘对应的非雅中商值。在过去几十年中，拓扑阶段（1-11）已经存在由于林茨堡 - Landau对称范式之外，作为新的物质国家的新分类。底层的全局不变通常很好地具有整数，例如Chern Number或绕组编号 - 雅中费用（12-15）。最近，研究人员提出了非雅思拓扑费用（16-19）的概念，它具有非换向和富有成效的编织结构，其中多个（多于一个）带缠结在一起。在这里，我们在实验中观察在时间 - 反转和反转对称传输线网络中的非雅典拓扑电荷。四元值值有价值的非雅典拓扑电荷清楚地映射到特征框架球体上。此外，我们找到了一个非雅中商态，提供了关于边缘/域墙状态分布的全局视角。我们的作品开辟了对非雅中拓扑电荷的表征和操纵的门，这可能导致有趣的观察，例如二维系统（16,17,20）中的轨迹依赖的DIRAC / Weyl节点碰撞，可允许的节点线配置三维（16,19,20），并且可以深入了解扭曲双层石墨烯（21）的某些强相关的相。

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  • 来源
    《Nature》 |2021年第7862期|195-200|共6页
  • 作者

    Guo Qinghua; Jiang Tianshu; Zhang Ruo-Yang; Zhang Lei; Zhang Zhao-Qing; Yang Biao; Zhang Shuang; Chan C. T.;

  • 作者单位

    Hong Kong Univ Sci & Technol Dept Phys Hong Kong Peoples R China|Hong Kong Univ Sci & Technol Inst Adv Study Hong Kong Peoples R China;

    Hong Kong Univ Sci & Technol Dept Phys Hong Kong Peoples R China|Hong Kong Univ Sci & Technol Inst Adv Study Hong Kong Peoples R China;

    Hong Kong Univ Sci & Technol Dept Phys Hong Kong Peoples R China|Hong Kong Univ Sci & Technol Inst Adv Study Hong Kong Peoples R China;

    Hong Kong Univ Sci & Technol Dept Phys Hong Kong Peoples R China|Hong Kong Univ Sci & Technol Inst Adv Study Hong Kong Peoples R China|Shanxi Univ Inst Laser Spect State Key Lab Quantum Opt & Quantum Opt Devices Taiyuan Peoples R China|Shanxi Univ Collaborat Innovat Ctr Extreme Opt Taiyuan Peoples R China;

    Hong Kong Univ Sci & Technol Dept Phys Hong Kong Peoples R China|Hong Kong Univ Sci & Technol Inst Adv Study Hong Kong Peoples R China;

    Hong Kong Univ Sci & Technol Dept Phys Hong Kong Peoples R China|Hong Kong Univ Sci & Technol Inst Adv Study Hong Kong Peoples R China|Natl Univ Def Technol Coll Adv Interdisciplinary Studies Changsha Peoples R China|Natl Univ Def Technol Hunan Prov Key Lab Novel Nanooptoelect Inform Mat Changsha Peoples R China;

    Univ Birmingham Sch Phys & Astron Birmingham W Midlands England|Univ Hong Kong Dept Phys Hong Kong Peoples R China|Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China;

    Hong Kong Univ Sci & Technol Dept Phys Hong Kong Peoples R China|Hong Kong Univ Sci & Technol Inst Adv Study Hong Kong Peoples R China;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
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