Topological Interface States in the Low-Frequency Band Gap of One-Dimensional Phononic Crystals

Topological invariance has recently attracted rapidly growing attention, which can be characterized in a one-dimensional (1D) system by the Zak phase, a special kind of Berry phase. While acoustic systems are proven to be excellent platforms for exemplifying the diversity of topological properties, it remains challenging to downscale the device, since such interface states are usually attained at higher-frequency regimes. Here, we report both theoretically and experimentally the realization of interface states in the low-frequency band gap of a 1D chain of Helmholtz resonators. By numerically inspecting the Zak phase of the bulk band of the proposed system, we reveal the transition point of the band structure in a low -frequency range and elucidate the underlying mechanism of interface states at the lowest band gap in the spectrum. As a result, the lattice constant is reduced to the subwavelength scale, instead of being comparable to the wavelength. Our proposed mechanism is verified experimentally by measuring acoustic intensity for the interface state. The experimental results agree quite well with the theoretical predictions, showing the existence of interface states at the desired frequencies. We anticipate our mechanism to open up the possibility for the miniaturization and integration of acoustic functional devices and have far-reaching implications in diverse applications, such as enhanced sensing and biomedical imaging.