Experimental observation of non-Abelian topological charges and edge states

Qinghua Guo, Tianshu Jiang, Ruo-Yang Zhang, Lei Zhang, Zhao-Qing Zhang, Biao Yang (), Shuang Zhang () and C. T. Chan ()
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Qinghua Guo: The Hong Kong University of Science and Technology
Tianshu Jiang: The Hong Kong University of Science and Technology
Ruo-Yang Zhang: The Hong Kong University of Science and Technology
Lei Zhang: The Hong Kong University of Science and Technology
Zhao-Qing Zhang: The Hong Kong University of Science and Technology
Biao Yang: The Hong Kong University of Science and Technology
Shuang Zhang: University of Birmingham
C. T. Chan: The Hong Kong University of Science and Technology

Nature, 2021, vol. 594, issue 7862, 195-200

Abstract: Abstract In the last few decades, topological phase1–11 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 charges12–15. Very recently, researchers proposed the notion of non-Abelian topological charges16–19, 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.

Date: 2021
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DOI: 10.1038/s41586-021-03521-3

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