Programmable elastic valley Hall insulator with tunable interface propagation routes

A challenge in the area of topologically protected edge waves in elastic media is how to tune the topological interface propagation route as needed. This paper proposes a tunable elastic valley Hall insulator, whose unit cell consists of two cavities and magnetic fluid with the same volume as the cavity. Interface route with arbitrary shape for propagating topologically protected edge waves can be achieved by controlling the distribution of magnetic fluid in each unit cell through a designed programmable magnet lifting array. As demonstrated through numerical simulations and experimental testing, the flexural wave is confined to propagate along the topological interface routes of different configurations. Finally, it is indicated that the proposed valley Hall insulator can be applied to achieve desired localized elastic energy which is robust to defects, sharp corners and so on.