Experimental observation of non-Abelian topological charges and edge states

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).

Automated summary

Experimental observation of non-Abelian topological charges and edge states in a PT-symmetric transmission line network, along with the discovery of a non-Abelian quotient relation for the bulk-edge correspondence. This new topological property opens up possibilities for intriguing observable phenomena in the field of material science.