Chiral Symmetry Breaking of Tight-Binding Models in Coupled Acoustic-Cavity Systems

A finite one-dimensional Su-Schrieffer-Heeger (SSH) chain exhibits zero-energy boundary-mode solutions that are protected by chiral symmetry. The breaking of chiral symmetry leads to several important consequences, including a shift of the boundary mode energies. Here, we systematically study the coupled acoustic-cavity system (CACS), which is an important acoustic platform for realizing tight-binding mod-els (TBMs). We find that the length and number of coupling waveguides not only affect hopping, but also induce a perturbation to the onsite eigenfrequency, which can be attributed to the breaking of chiral sym-metry in the TBM. The acoustic origin of these phenomena is discussed, and the conditions of the exact realization of TBMs are identified. Meanwhile, we build an acoustic second-order topological insulator by extending the SSH model to two dimensions and show that the frequency of the topological corner modes is tunable by the same chiral-symmetry-breaking term. This finding is experimentally validated through the demonstration of in-gap and in-band topological corner modes. Our study provides a detailed and accu-rate understanding of the CACS and clarifies several important nuances for realizing tight-binding systems in acoustics. These results solidify CACS as a foundation for future studies of topological acoustics and non-Hermitian acoustics.