Achieving acoustic topological valley-Hall states by modulating the subwavelength honeycomb lattice.

Topological valley-contrasting physics is attracting increasing attention because of its potentials as a promising information carrier in electrics and classical systems. In this work, we reveal the valley-Hall effect and the valley projected edge states in two-dimensional sonic crystals with modulated acoustic honeycomb lattice. The sonic crystals are arranged by soft-material rods and thereby in a sub-wavelength scale, of which the lattice constant is only 0.267 times the wavelength and can be modulated to almost 0.1 times the wavelength. The degenerated valley states are lifted by breaking the inversion symmetry through introducing the refractive-index difference to the rods. The unidirectional excitation of valley chiral bulk state and the non-diffracting Bessel beams are realized by sources carrying orbital angular momentum with proper chirality. Furthermore, we demonstrate that the sub-wavelength valley creation can also be achieved by embedding modulated rubber rods with the mingled steel in a water background, which has significant potential in hydroacoustics, such as underwater communications, sound trapping and directional radiation.