Observation of acoustic hybrid-order topological insulator induced by non-Hermiticity and anisotropy

The discovery of hybrid-order topological insulators (TIs), where the first- and second-order topologies are obtained independently in different complete band gaps, further refines the classification of topological phases. In the electronic system, simultaneous measurements of the edge and corner states in two complete bulk gaps are difficult due to the fermionic band filling. In this paper, we demonstrate a non-Hermiticity-induced acoustic hybrid-order TI, incorporating on-site losses within the two-dimensional anisotropic Su-Schrieffer-Heeger (SSH) model. The robust one-dimensional edge states and zero-dimensional corner states are observed independently in different bulk band gaps. Interestingly, by taking advantage of the mutual effect between on-site non-Hermiticity and coupling anisotropy, the corner states are always captured in the middle bulk bandgap, and the directions of edge states are controllable in multiband. Our work provides a route to design the acoustic devices with multifrequency and multidirectional sound transport, and paves the way to explore various exotic non-Hermiticity-induced topological phases.