Design and experimental observation of valley-Hall edge states in diatomic-graphene-like elastic waveguides

We report on the design and experimental validation of a two-dimensional phononic elastic waveguide exhibiting topological valley-Hall edge states. The lattice structure of the waveguide is inspired by diatomic graphene, and it is imprinted in an initially flat plate by means of geometric indentations. The indentations are distributed according to a hexagonal lattice structure which guarantees the existence of Dirac dispersion at the boundary of the Brillouin zone. Starting from this basic material, domain walls capable of supporting edge states can be obtained by contrasting waveguides having broken space-inversion symmetry (SIS) achieved by using local resonant elements. Our theoretical study shows that such material maps into the acoustic analog of the quantum valley-Hall effect, while numerical and experimental results confirm the existence of protected edge states traveling along the walls of topologically distinct domains.