Experimental realization of non-Abelian higher-order topological insulators in two-dimensional phononic crystals

Non-Abelian multiband topology, characterized by frame charges, has garnered significant attention in the past few years. The non-Abelian frame charge evolution can be deduced from the rotation of the multiband in momentum space, which can promise potential applications based on the dynamic non-Abelian topological effects. In this work, based on two-dimensional phononic crystals, we directly observe the eigenstate frame rotation to verify non-Abelian band topology, which further predicts the location of the corner modes in this multigap system. These one-dimensional edge states of band gaps or bulk band continuum that induce zero-dimensional corner states are also confirmed experimentally. The corresponding higher-order topology is examined by detecting the acoustic responses in a finite phononic crystal sample. Our work provides experimental evidence for the unique non-Abelian band topology and a convenient platform for studying novel higher-order topological matter phases.