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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. 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 and acoustic waves in phononic crystals. Due to the lack of spin and a difficulty 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, 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.

Valleytronics — exploiting a system’s pseudospin degree of freedom — is being increasingly explored in sonic crystals. Now, valley transport of sound is reported for a macroscopic triangular-lattice array of rod-like scatterers in a 2D air waveguide. The concept of valley pseudospin, labelling quantum states of energy extrema in momentum space, is attracting attention 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 because of its potential as a new type of information carrier. Compared with the non-topological bulk valley transport, realized soon after predictions 1 , 2 , 3 , 4 , 5 , topological valley transport in domain walls 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 is extremely challenging owing to the inter-valley scattering inevitably induced by atomic-scale imperfections—but an electronic signature was recently observed in bilayer graphene 12 , 13 . Here, we report the experimental observation of topological valley transport of sound in sonic crystals. The macroscopic nature of sonic crystals permits a flexible and accurate design of domain walls. In addition to a direct visualization of the valley-selective edge modes through spatial scanning of the sound field, reflection immunity is observed in sharply curved interfaces. The topologically protected interface transport of sound, strikingly different from that in traditional sound waveguides 14 , 15 , may serve as the basis for designing devices with unconventional functions.

Exceptional points and skin effect, as the two distinct hallmark features unique to the non-Hermitian physics, have each attracted enormous interests. Recent theoretical works reveal that the topologically nontrivial exceptional points can guarantee the non-Hermitian skin effect, which is geometry-dependent, relating these two unique phenomena. However, such novel relation remains to be confirmed by experiments. Here, we realize a non-Hermitian phononic crystal with exceptional points, which exhibits the geometry-dependent skin effect. The exceptional points connected by the bulk Fermi arcs, and the skin effects with the geometry dependence, are evidenced in simulations and experiments. Our work, building an experimental bridge between the exceptional points and skin effect and uncovering the unconventional geometry-dependent skin effect, expands a horizon in non-Hermitian physics. Recent theoretical works reveal that the topologically nontrivial exceptional points can guarantee the geometry-dependent skin effect, but it remains to be confirmed by experiments. Here the authors realize a reciprocal non-Hermitian phononic crystal with exceptional points, and observe the geometry-dependent skin effect.

Reflection and refraction of waves occur at the interface between two different media. These two fundamental interfacial wave phenomena form the basis of fabricating various wave components, such as optical lenses. Classical refraction—now referred to as positive refraction—causes the transmitted wave to appear on the opposite side of the interface normal compared to the incident wave. By contrast, negative refraction results in the transmitted wave emerging on the same side of the interface normal. It has been observed in artificial materials 1 – 5 , following its theoretical prediction 6 , and has stimulated many applications including super-resolution imaging 7 . In general, reflection is inevitable during the refraction process, but this is often undesirable in designing wave functional devices. Here we report negative refraction of topological surface waves hosted by a Weyl phononic crystal—an acoustic analogue of the recently discovered Weyl semimetals 8 – 12 . The interfaces at which this topological negative refraction occurs are one-dimensional edges separating different facets of the crystal. By tailoring the surface terminations of the Weyl phononic crystal, constant-frequency contours of surface acoustic waves can be designed to produce negative refraction at certain interfaces, while positive refraction is realized at different interfaces within the same sample. In contrast to the more familiar behaviour of waves at interfaces, unwanted reflection can be prevented in our crystal, owing to the open nature of the constant-frequency contours, which is a hallmark of the topologically protected  surface states in Weyl crystals 8 – 12 . Sound waves in a specially designed crystal undergo ‘topologically protected’ negative refraction, whereby no reflection is allowed, at certain facets of the crystal and positive refraction at others.

Valley topological materials, in which electrons possess valley pseudospin, have attracted a growing interest recently. The additional valley degree of freedom offers a great potential for its use in information encoding and processing. The valley pseudospin and valley edge transport have been investigated in photonic and phononic crystals for electromagnetic and acoustic waves, respectively. In this work, by using a micromanufacturing technology, valley topological materials are fabricated on silicon chips, which allows the observation of gyral valley states and valley edge transport for elastic waves. The edge states protected by the valley topology are robust against the bending and weak randomness of the channel between distinct valley Hall phases. At the channel intersection, a counterintuitive partition of the valley edge states manifests for elastic waves, in which the partition ratio can be freely adjusted. These results may enable the creation of on-chip high-performance micro-ultrasonic materials and devices.

Valley pseudospin, labeling the pair of energy extrema in momentum space, has been attracting attention because of its potential as a new degree of freedom in manipulating electrons or classical waves. Recently, topological valley edge transport of sound, by virtue of the gapless valley-locked edge states, has been observed in the domain walls of sonic crystals. Here, by constructing a heterostructure with sonic crystals, a topological waveguide is realized. The waveguide states feature gapless dispersion, momentum-valley locking, immunity against defects, and a high capacity for energy transport. With a designable size, the heterostructures are more flexible for interfacing with the existing acoustic devices than the domain wall structures. Such heterostructures may serve as versatile new devices for acoustic wave manipulation, such as acoustic splitting, reflection-free guiding and converging. Here, by constructing a heterostructure with sonic crystals, a topological waveguide is realized by the authors. The waveguide states feature gapless dispersion, momentum-valley locking, immunity against defects, and a high capacity for energy transport.

The notion of higher-order topological insulators has endowed materials with topological states beyond the first order. Particularly, a three-dimensional (3D) higher-order topological insulator can host topologically protected 1D hinge states, referred to as the second-order topological insulator, or 0D corner states, referred to as the third-order topological insulator. Similarly, a 3D higher-order topological semimetal can be envisaged if it hosts states on the 1D hinges. Here we report the realization of a second-order topological Weyl semimetal in a 3D-printed acoustic crystal, which possesses Weyl points in 3D momentum space, 2D Fermi arc states on surfaces and 1D gapless states on hinges. Like the arc surface states, the hinge states also connect the projections of the Weyl points. Our experimental results evidence the existence of the higher-order topological semimetal, which may pave the way towards innovative acoustic devices. A second-order topological Weyl semimetal based on a 3D-printed acoustic crystal, exhibiting Weyl points, Fermi arc surface states, and hinge states, has been experimentally demonstrated.

Dislocations are ubiquitous in three-dimensional solid-state materials. The interplay of such real space topology with the emergent band topology defined in reciprocal space gives rise to gapless helical modes bound to the line defects. This is known as bulk-dislocation correspondence, in contrast to the conventional bulk-boundary correspondence featuring topological states at boundaries. However, to date rare compelling experimental evidences have been presented for this intriguing topological observable in solid-state systems, owing to the huge challenges in creating controllable dislocations and conclusively identifying topological signals. Here, using a three-dimensional acoustic weak topological insulator with precisely controllable dislocations, we report an unambiguous experimental evidence for the long-desired bulk-dislocation correspondence, through directly measuring the gapless dispersion of the one-dimensional topological dislocation modes. Remarkably, as revealed in our further experiments, the pseudospin-locked dislocation modes can be unidirectionally guided in an arbitrarily-shaped dislocation path. The peculiar topological dislocation transport, expected in a variety of classical wave systems, can provide unprecedented control over wave propagations. Flexible wave manipulations are crucial in the development of application for topological insulators. By stacking a 2D network of coupled acoustic resonators the authors demonstrate a 3D acoustic topological insulator with arbitrarily controllable dislocation paths.

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.