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Second-order topological insulators possess unique boundary states beyond the conventional bulk-boundary correspondence, which provides opportunities for multidimensional wave manipulation in electronic and acoustic systems. This paper develops an acoustic second-order topological insulator by sonic crystals, hosting multiple corner states at different frequency ranges within one complete bandgap. The topologically protected multifrequency corner states provide robust control of acoustic waves with good immunity against defects. The one-dimensional sound propagation and zero-dimensional sound localization at different frequencies are experimentally observed. We also find these multifrequency corner states are susceptible to the bandgap size of sonic crystals, which could be systematically tunned through topology optimization. The reported results expand the boundaries of constructing second-order topological insulators and exploring multifrequency localized wave modes.
Li et al. (Wed,) studied this question.