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Valleytronics is quickly emerging as an exciting field in fundamental and applied research. In this Letter, we study the acoustic version of valley states in sonic crystals and reveal a vortex nature of such states. In addition to the selection rules established for exciting valley polarized states, a mimicked valley Hall effect of sound is proposed further. The extraordinary chirality of valley vortex states, detectable in experiments, may open a new possibility in sound manipulations. This is appealing to scalar acoustics that lacks a spin degree of freedom inherently. In addition, the valley selection enables a handy way to create vortex matter in acoustics, in which the vortex chirality can be controlled flexibly. Potential applications can be anticipated with the exotic interaction of acoustic vortices with matter, such as to trigger the rotation of the trapped microparticles without contact.

Topological semimetals are materials whose band structure contains touching points that are topologically nontrivial and can host quasiparticle excitations that behave as Dirac or Weyl fermions [1][2][3][4][5][6][7] . These so-called Weyl points not only exist in electronic systems, but can also be found in artificial periodic structures with classical waves, such as electromagnetic waves in photonic crystals [8][9][10][11] and acoustic waves in phononic crystals 12,13 . Due to the lack of spin and a di culty in breaking time-reversal symmetry for sound, however, topological acoustic materials cannot be achieved in the same way as electronic or optical systems. And despite many theoretical predictions 12,13 , experimentally realizing Weyl points in phononic crystals remains challenging. Here, we experimentally realize Weyl points in a chiral phononic crystal system, and demonstrate surface states associated with the Weyl points that are topological in nature, and can host modes that propagate only in one direction. As with their photonic counterparts, chiral phononic crystals bring topological physics to the macroscopic scale.Recently, interest in Weyl semimetals has been growing 1-7 . Weyl semimetals are materials in which the electrons have linear dispersions in all directions while being doubly degenerate at a single point, called the Weyl point, near the Fermi surface in threedimensional (3D) momentum space. In other words, the electrons in Weyl semimetals obey the Weyl equation and thus behave like Weyl fermions. The Weyl point is a source or sink of the Berry curvature flux in momentum space; in other words, it is a magnetic monopole with a topological charge, defined as the Berry curvature flux threading a sphere enclosing the Weyl point with a value of either +1 or −1, corresponding to the chirality of the Weyl fermion. The Weyl point and the associated topological invariants enable Weyl semimetals to exhibit a variety of unusual properties, including robust surface waves (SWs) [14][15][16] and chiral anomaly 17,18 . In addition to the standard Weyl points possessing a point-like Fermi surface (referred to as type-I), another type of Weyl point was more recently recognized, which has a conical Fermi surface (referred to as type-II) 13,[19][20][21] . Since the Weyl point or Weyl cone in Weyl semimetals represents a special dispersion of electrons moving in periodic potentials, the question naturally arises as to whether a similar dispersion or the Weyl point for classical waves propagating in artificial periodic structures exists [8][9][10][11][12][13][22][23][24][25][26][27][28] . Lu et al. were the first to report the existence of Weyl points and the associated one-way SWs in photonic crystals based on double-gyroid structures 8,9 . Weyl points were also observed in photonic crystals fabricated using conventional planar fabrication technology 10,11 . Following the developments of the Weyl photonic crystals, Weyl phononic crystals (PCs) with Weyl points for acoustic waves have also been proposed in graph...

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Similar to their optic counterparts, acoustic components are anticipated to flexibly tailor the propagation of sound. However, the practical applications, e.g. for audible sound with large wavelengths, are frequently hampered by the issue of device thickness. Here we present an effective design of metasurface structures that can deflect the transmitted airborne sound in an anomalous way. This flat lens, made of spatially varied coiling-slit subunits, has a thickness of deep subwavelength. By elaborately optimizing its microstructures, the proposed lens exhibits high performance in steering sound wavefronts. Good agreement has been demonstrated experimentally by a sample around the frequency 2.55 kHz, incident with a Gaussian beam at normal or oblique incidence. This study may open new avenues for numerous daily life applications, such as controlling indoor sound effects by decorating rooms with light metasurface walls.

Recently, the topological physics in artificial crystals for classical waves has become an emerging research area. In this Letter, we propose a unique bilayer design of sonic crystals that are constructed by two layers of coupled hexagonal array of triangular scatterers. Assisted by the additional layer degree of freedom, a rich topological phase diagram is achieved by simply rotating scatterers in both layers. Under a unified theoretical framework, two kinds of valley-projected topological acoustic insulators are distinguished analytically, i.e., the layer-mixed and layer-polarized topological valley Hall phases, respectively. The theory is evidently confirmed by our numerical and experimental observations of the nontrivial edge states that propagate along the interfaces separating different topological phases. Various applications such as sound communications in integrated devices can be anticipated by the intriguing acoustic edge states enriched by the layer information.

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We report an experimental observation of the classical version of valley polarized states in a two-dimensional hexagonal sonic crystal, where the inversion-symmetry breaking of scatterers induces an omnidirectional frequency gap. The acoustic valley states, which carry specific linear momenta and orbital angular momenta, were selectively excited by external Gaussian beams and conveniently confirmed by the pressure distribution outside the crystal, according to the criterion of momentum conservation. The vortex nature of such intriguing crystal states was directly characterized by scanning the phase profile inside the crystal. In addition, we observed a peculiar beam splitting phenomenon, in which the separated beams are constructed by different valleys and locked to the opposite vortex chirality. The exceptional sound transport, encoded with valley-chirality locked information, may serve as the basis of designing conceptually novel acoustic devices with unconventional functions.