Subwavelength multiple topological interface states in one-dimensional labyrinthine acoustic metamaterials

Acoustic analogies of topological insulators reside at the frontier of ongoing metamaterials research. Of particular interest are the topological interface states that are determined by the Zak phase, which is the geometric phase characterizing the topological property of the bands in one-dimensional systems. Here we design double-channel Mie resonators based on the so-called labyrinth acoustic metamaterials, which can be considered equivalent to a ultraslow medium of large refractive index, inevitably containing structural features on a subwavelength scale. The metamolecule containing two cells is engineered to host the degenerated states through a zone-folding mechanism, whereupon the Zak phase transition takes place when the interval between two cells changes from shrunk to expanded. Furthermore, the topological interface state displays strong robustness against randomly introduced perturbations whose acoustic intensity is enhanced by nearly a factor 1600 in comparison to an ordinary waveguide.