Nature volume 594, pages 195–200 (2021 )Cite this article
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.
The data and code that support the findings of this study are available in DataSpace@HKUST at https://doi.org/10.14711/dataset/5LXMUZ.