biostudies-literaturePeng BEngineering and Physical Sciences Research Council423https://www.ebi.ac.uk/biostudies/studies/S-EPMC8776786biostudies-literatureUnknown13(1)Topological phases of matter have revolutionised the fundamental understanding of band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies have been extensively explored, and a large number of materials have been theoretically proposed and experimentally observed. These ideas have recently been extended to multi-gap topologies with band nodes that carry non-Abelian charges, characterised by invariants that arise by the momentum space braiding of such nodes. However, the constraints placed by the Fermi-Dirac distribution to electronic systems have so far prevented the experimental observation of multi-gap topologies in real materials. Here, we show that multi-gap topologies and the accompanying phase transiNature communicationsPhonons as a platform for non-Abelian braiding and its manifestation in layered silicates.PMC8776786EP/P020259/1Monserrat BBouhon APeng BSlager RJfalsePhonons as a platform for non-Abelian braiding and its manifestation in layered silicates.Topological phases of matter have revolutionised the fundamental understanding of band theory and hold great promise for next-generation technologies such as low-power electronics or quantum computers. Single-gap topologies have been extensively explored, and a large number of materials have been theoretically proposed and experimentally observed. These ideas have recently been extended to multi-gap topologies with band nodes that carry non-Abelian charges, characterised by invariants that arise by the momentum space braiding of such nodes. However, the constraints placed by the Fermi-Dirac distribution to electronic systems have so far prevented the experimental observation of multi-gap topologies in real materials. Here, we show that multi-gap topologies and the accompanying phase transi2022-01-01T00:00:00Z2022 Jan2025-04-22T08:34:27.579Z2025-04-05T22:35:11.176ZS-EPMC87767863505847310.1038/s41467-022-28046-9