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Nodal lines are symmetry-protected one-dimensional band degeneracies inmomentum space, which can appear in numerous topological configurations such asnodal rings, chains, links, and knots. Very recently, non-Abelian topologicalphysics has been proposed in space-time inversion (PT) symmetric systems, andattract widespread attention. One of the most special configurations innon-Abelian system is the earring nodal link, composing of a nodal chainlinking with an isolated nodal line, is signature of non-Abelian topology andcannot be elucidated using Abelian topological classifications. However, theearring nodal links have not been yet observed in real system. Here we designthe phononic crystals with earring nodal links, and verify its non-Abeliantopologicial charge in full-wave simulations. Moreover, we experimentallyobserved two different kinds of earring nodal links by measuring the bandstructures for two phononic crystals. Specifically, we found that the order ofthe nodal chain and line can switch after band inversion but their link cannotbe severed. Our work provides experimental evidence for phenomena unique tonon-Abelian band topology and our simple acoustic system provides a convenientplatform for studying non-Abelian charges.

Experimental observation of non-Abelian earring nodal links in phononic crystals