Higher-order topological insulators, providing a horizon beyond the conventional bulk-interface correspondence, have zero-dimensional topological corner states at different corners, such as a right-angled corner. Here, we numerically demonstrate a hierarchy of band topology in a two-dimensional square-lattice sonic crystal. In our system, the acoustic bulk bands mimic the quantum spin Hall effect, while gapped interface states emerge in the bulk gap due to symmetry reduction and carry quantized Zak phases, which result in zero-dimensional topological corner states in the interface gap. By direct acoustic measurement, we observe that zero-dimensional topological corner states are confined at not only the right-angled corner, but also the straight-angled corner. Our results present this type of topological shape-dependent corner state, which possibly possesses potential application in controlling and localizing acoustic waves.

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• Acoustics
• Symmetry protected topological states
• Topological phase transition
• Acoustic metamaterials