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 models (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 symmetry 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 accurate 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.