Routing Edge States in an Anisotropic Elastic Topological Insulator

Topological insulators, protected by nontrivial band topology, exhibit backscattering-immune edge states, conducive to robust waveguiding with high efficiency. However, routing such robust edge states has been restricted by the isotropy in conventional unit cells respecting crystalline symmetries, such as $C_{4v}$ symmetry in a square lattice or $C_3$ symmetry in a hexagonal lattice. We effectively tackle this issue by introducing anisotropic coupling into a square lattice. With theoretical prediction from the discrete mechanical model, we experimentally demonstrate that such anisotropy can enable distinctive topological phases along different directions, giving rise to directional edge states. In addition, when the bands along the two directions are topologically identical and untrivial, the coexisting edge states have distinctive frequency ranges, giving rise to the frequency-routed properties. Our work offers an effective strategy for the robust steering, filtering, detection, and transmission of elastic waves through tactical edge state routing.