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

Abstract

Nodal lines are symmetry-protected one-dimensional band degeneracies in momentum space, which can appear in numerous topological configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian topological physics has been proposed in space-time inversion (PT) symmetric systems, and attract widespread attention. One of the most special configurations in non-Abelian system is the earring nodal link, composing of a nodal chain linking with an isolated nodal line, is signature of non-Abelian topology and cannot be elucidated using Abelian topological classifications. However, the earring nodal links have not been yet observed in real system. Here we design the phononic crystals with earring nodal links, and verify its non-Abelian topologicial charge in full-wave simulations. Moreover, we experimentally observed two different kinds of earring nodal links by measuring the band structures for two phononic crystals. Specifically, we found that the order of the nodal chain and line can switch after band inversion but their link cannot be severed. Our work provides experimental evidence for phenomena unique to non-Abelian band topology and our simple acoustic system provides a convenient platform for studying non-Abelian charges.

arXiv comment14 pages, 3 figures

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• Topological acoustics
• Topological Non-Hermitian skin effect
• Minimal non-abelian nodal braiding in ideal metamaterials
• Observation of Dirac hierarchy in three-dimensional acoustic topological insulators
• Spinful topological phases in acoustic crystals with projective PT symmetry
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• Phase transitions of non-Abelian charged nodal links in a spring-mass system
• Experimental demonstration of non-adjacent band topology connecting multiple nodal links
• Demonstration of non-Abelian frame charge flow in photonic crystals
• Direct measurement of topological invariants through temporal adiabatic evolution of bulk states in the synthetic Brillouin zone
• Observing the nodal-line conversion determined by the relative homotopy
• Fractal Nodal Band Structures
• Morse theory study on the evolution of nodal lines in $\mathcal{P}\mathcal{T}$-symmetric nodal-line semimetals
• Euler band topology in superfluids and superconductors
• Hinge modes of three-dimensional Euler insulators