Acoustic higher-order topological insulator on a Kagome lattice

Higher-order topological insulators are phases where the usual edge states are replaced by states localized at corners. In a 2D second-order TI, the key feature is topologically protected zero-dimensional corner states rather than gapless 1D edge modes. The abstract states that higher-order TIs had previously been demonstrated in classical mechanical and electromagnetic metamaterials. Here, the authors experimentally realize a second-order TI in an acoustic metamaterial using a breathing Kagome lattice. A central result is that this new acoustic higher-order TI has zero quadrupole polarization but still has nontrivial bulk topology, described by quantized Wannier centers. The corner states also depend on the corner geometry: they appear at acute-angled corners but not at obtuse-angled corners, enabling corner states to function as topologically protected but reconfigurable local resonances.