Topological interface states in deep-subwavelength phononic beams with acoustic black hole configurations

We present deep-subwavelength phononic beams engineered with unit cells incorporating acoustic black hole (ABH) configurations. The ABH design enables the realization of topological interface states (TISs) within the first band gap at low frequencies, where the lattice constant (a) is far smaller than the wavelength (λ) of the controlled wave. Manipulating the ABH configuration and breaking the unit-cell symmetry allow us to control Zak phases for the topological beams. Two topologically distinct phononic beams are interconnected to produce the TIS within their low-frequency band gaps. Through numerical and experimental demonstrations, we confirm the existence of TISs at frequencies ranging from 4.3 to 8.5 Hz using the designed topological beams of which a/λ is less than 1/20. We also offer the potential to further reduce the value of a/λ by rearranging the ABH unit cells.