  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 the 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 (QVHE) while numerical and experimental results
confirm the existence of protected edge states traveling along the walls of
topologically distinct domains.
