Topological edge state analysis of hexagonal phononic crystals

In this study, we propose valley phononic crystals that consist of a hexagonal aluminum plate with six chiral arrangements of ligaments. Valley phononic crystals were introduced into a topological insulator (TI) system to produce topologically protected edge waves (TPEWs) along the topological interfaces. The implementation of chiral topological edge states is different from the implementation of topological edge states of systems with symmetry. Unlike the conventional breaking of mirror symmetry, a new complete band with topological edge modes gap was opened up at the Dirac point by tuning the difference in lengths of the ligaments in the chiral unit cells. We investigated the dispersion properties in chiral systems and applied the dispersion properties to waveguides on the interfaces to achieve designable route systems. Furthermore, we simulated the robust propagation of TPEWs in different routes and demonstrated their immunity to backscattering at defects. Finally, the existence of the valley Hall effect in chiral systems was demonstrated. The study findings may lead to the further study of the topological states of chiral materials.