Negative Refraction and Partition in Acoustic Valley Materials of a Square Lattice

The transport behaviors of valley kink states with potential applications have become a research hotspot for acoustic waves in phononic crystals, which are usually constructed in hexagonal lattices, such as graphene and kagome lattices. We realize an acoustic valley material of a square lattice by stacking the dimerized chains of resonators in which topological phase transition is implemented by tuning the height ratio of nonequivalent resonators. The topological transports of the acoustic kink waves with reflection immunity are observed along the interface between distinct valley phases. The topological negative refraction of kink states outcoupling into free space is experimentally visualized with a tunable refraction angle. In particular, an abnormal partition transport of the acoustic kink states at the channel intersection is demonstrated in phononic crystals. These findings may have potential applications in directional vocalization, noise reduction, and beam splitting.