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Experimental observation of non-Abelian topological charges and edge states
Nature ( IF 42.778 ) Pub Date : 2021-06-09 , DOI: 10.1038/s41586-021-03521-3
Qinghua Guo, Tianshu Jiang, Ruo-Yang Zhang, Lei Zhang, Zhao-Qing Zhang, Biao Yang, Shuang Zhang, C. T. Chan

In the last few decades, topological phase1,2,3,4,5,6,7,8,9,10,11 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 charges12,13,14,15. Very recently, researchers proposed the notion of non-Abelian topological charges16,17,18,19, 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 systems16,17,20, admissible nodal line configurations in three dimensions16,19,20, and may provide insight into certain strongly correlated phases of twisted bilayer graphene21.



中文翻译:

非阿贝尔拓扑电荷和边缘态的实验观察

在过去的几十年里,拓扑相1,2,3,4,5,6,7,8,9,10,11已经成为超越 Ginzburg-Landau 对称破坏范式的一种新的物质状态分类。潜在的全局不变量通常由整数很好地表征,例如陈数或缠绕数——阿贝尔电荷12,13,14,15。最近,研究人员提出了非阿贝尔拓扑电荷的概念16,17,18,19,它具有非交换和富有成效的编织结构,多个(多个)带隙缠结在一起。在这里,我们通过实验观察了时间反转和反转对称传输线网络中的非阿贝尔拓扑电荷。四元数值的非阿贝尔拓扑电荷清楚地映射到本征态框架球体上。此外,我们发现了一个非阿贝尔商关系,它提供了关于边缘/畴壁状态分布的全局视角。我们的工作为非阿贝尔拓扑电荷的表征和操纵打开了大门,这可能会导致有趣的观察结果,例如二维系统中与轨迹相关的狄拉克/外尔节点碰撞16,17,20,三个维度中可接受的节点线配置16、19、20,并且可以深入了解扭曲双层石墨烯21 的某些强相关相。

更新日期:2021-06-09
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