Subwavelength quantum Hall spin effects in spatially elliptical coiled phononic crystals based on the local resonance principle

Abstract Aiming to obtain a spatial helical square lattice with a subwavelength structure and quantum spin Hall effect, we have designed a spatially coiled square lattice with a subwavelength structure and quantum Hall effect. By adjusting the angle θ to break its nonpoint group symmetry, the quantum spin Hall effect is obtained by inducing the inversion of the energy bands. This serves as a basis for investigating its edge states. Through this study, we obtain a second-order topological insulator with a one-dimensional edge and a two-dimensional corner state. Finally, we use the topological properties to study its energy loss in transmitting different paths. This demonstrates that paths of different topological phases have high energy transfer efficiency.