Realizing Topological Midgap States in Acoustic Metamaterials Using H-Resonator-Induced Negative Couplings

Classical wave systems, like acoustic metamaterials, provide a versatile platform for studying topological effects. Initially discovered in condensed matter, topological insulators have been adapted to acoustic systems.

This study investigates a new type of acoustic resonator, the H-resonator, which allows for the acoustic implementation of Hamiltonians with negative couplings. We discuss relevant principles for manufacturing and implementation, then validate the efficacy using a one-dimensional Su-Schrieffer-Heeger (SSH) model. We employ periodic boundary conditions and an interface to ensure the topological nature of the observed edge modes and to ensure their robustness and resistance to surface defects.

Next, we investigate an acoustic model of a quadrupole SSH system composed of H-resonators, inspired by the Kitaev superconducting chain to validate the negative coupling methods. By optimizing resonator geometry and coupling, we achieve topologically protected midgap states, analogous to Majorana-like bound states. The bulk states maintain a symmetric distribution around the midgap, ensuring their stability.