Robust Fano resonance between mechanical first- and second-order topological states

The Fano resonance, as a phenomenon of wave scattering, is based on the interaction between a "bright mode"and a "dark mode"giving rise to an asymmetric and ultrasharp spectral peak. However, the Fano resonant frequency is sensitive to structural imperfections such as defects or disorders, which will shift the resonant peak, or even damage the Fano line shape. Here, we harness the coupling between the first-order and the higher-order topological insulators to overcome this shortcoming. We construct a first-order topological edge state to serve as a bright mode, and a second-order topological corner state to be the dark mode using the same base configuration. As a result, a topological Fano resonance is expected to occur around the resonant frequency of the dark mode. The robustness of the Fano resonance is verified by deliberately introducing various types of imperfections into the system. Our findings may further enhance confidence in using the resonance such as acoustic switching, refractive index sensing, high quality factor filters, and accurate interferometers.