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Non-Hermitian topological phases, which exhibit unique features such as skin effect and exceptional points originated from nontrivial band topologies in complex plane, have attracted enormous attention in condensed-matter physics and metamaterials. Here we report the realization of an exceptional line semimetal in a three-dimensional non-Hermitian phononic crystal. A pair of exceptional rings with opposite topologies are connected by the drumhead bulk states in the first Brillouin zone. The exceptional rings not only possess wave-function topology and thus result in the drumhead surface states, but also host spectral topology and thereby give rise to the hybrid-order geometry-dependent skin effect in three dimensions. Our experimental results evidence the complete non-Hermitian bulk-boundary correspondence of the three-dimensional exceptional line semimetal, and may pave the way for designing non-Hermitian acoustic devices., Comment: 5 figures

Band crossing points, such as Weyl and Dirac points, play a crucial role in the topological classification of materials and guide the exploration of exotic topological phases. The Berry dipole, a three-dimensional band crossing point beyond the Chern class, hosts a dipolar Berry curvature field and gives rise to numerous nontrivial quantum geometric effects. It has been proposed that the Berry dipole exhibits oriented Landau levels, whose spectrum critically relies on the orientation of the applied magnetic field. However, experimental demonstration of this phenomenon has remained elusive. Here we experimentally demonstrate oriented Landau levels by carefully engineering an inhomogeneous acoustic lattice. We observe distinct Landau level spectra and different propagation properties when the orientation of the pseudomagnetic field is reversed. Notably, we discover a new type of helical zero modes whose existence critically depends on the magnetic field's orientation. Our work paves the way for studying band crossings beyond Chern-class crossing points, including Berry multipoles and even-dimensional monopoles. Furthermore, it offers new insight for exploring topological devices.

Bound states in the continuum (BICs) are spatially localized states with energy embedded in the continuum spectrum of extended states. The combination of BICs physics and nontrivial band topology theory giving rise to topological BICs, which are robust against disorders and meanwhile of the merit of conventional BICs, is attracting wide attention recently. Here, we report valley edge states as topological BICs, which appear at domain wall between two distinct valley topological phases. The robustness of such BICs is demonstrated. The simulations and experiments show great agreement. Our findings of valley related topological BICs shed light on both BICs and valley physics, and may foster innovative applications of topological acoustic devices., Comment: A revised version has been accepted by Science Bulletin

Higher-order topological insulators and semimetals, which generalize the conventional bulk-boundary correspondence, have attracted extensive research interest. Among them, higher-order Weyl semimetals feature two-fold linear crossing points in three-dimensional (3D) momentum space, 2D Fermi-arc surface states, and 1D hinge states. Higher-order nodal-point semimetals possessing Weyl points or Dirac points have been implemented. However, higher-order nodal-line or nodal-surface semimetals remain to be further explored in experiments in spite of many previous theoretical efforts. In this work, we realize a second-order nodal-line semimetal in 3D phononic crystals. The bulk nodal lines, 2D drumhead surface states guaranteed by Zak phases, and 1D flat hinge states attributed to kz-dependent quadrupole moments, are observed in simulations and experiments. Our findings of nondispersive surface and hinge states may promote applications in acoustic sensing and energy harvesting., Comment: accepted for publication in PRL

As a distinctive feature unique to non-Hermitian systems, non-Hermitian skin effect displays fruitful exotic phenomena in one or higher dimensions, especially when conventional topological phases are involved. Among them, hybrid skin-topological effect is theoretically proposed recently, which exhibits anomalous localization of topological boundary states at lower-dimensional boundaries accompanied by extended bulk states. Here we experimentally realize the hybrid skin-topological effect in a non-Hermitian phononic crystal. The phononic crystal, before tuning to be non-Hermitian, is an ideal acoustic realization of the Kane-Mele model, which hosts gapless helical edge states at the boundaries. By introducing a staggered distribution of loss, the spin-dependent edge modes pile up to opposite corners, leading to a direct observation of the spin-dependent hybrid skin-topological effect. Our work highlights the interplay between topology and non-Hermiticity and opens new routes to non-Hermitian wave manipulations.

The Bloch band theory and Brillouin zone (BZ) that characterize wave behaviors in periodic mediums are two cornerstones of contemporary physics ranging from condensed matter to topological physics. Recent theoretical breakthrough revealed that, under the projective symmetry algebra enforced by artificial gauge fields, the usual two-dimensional (2D) BZ (orientable Brillouin two-torus) can be fundamentally modified to a non-orientable Brillouin Klein bottle with radically distinct topology and novel topological phases. However, the physical consequence of artificial gauge fields on the more general three-dimensional (3D) BZ (orientable Brillouin three-torus) was so far missing. Here, we report the first theoretical discovery and experimental observation of non-orientable Brillouin Klein space and orientable Brillouin half-turn space in a 3D acoustic crystal with artificial gauge fields. We experimentally identify peculiar 3D momentum-space non-symmorphic screw rotation and glide reflection symmetries in the measured band structures. Moreover, we demonstrate a novel 3D Klein bottle insulator featuring a nonzero Z_2 topological invariant and self-collimated topological surface states at two opposite surfaces related by a nonlocal twist, radically distinct from all previous topological insulators. Our discovery not only fundamentally modifies the 3D Bloch band theory and 3D BZ, but also opens the door towards a wealth of previously overlooked momentum-space topologies and unexplored topological physics with gauge symmetry beyond the existing paradigms.

Higher-order topological phases have raised widespread interest in recent years with the occurrence of the topological boundary states of dimension two or more less than that of the system bulk. The higher-order topological states have been verified in gapped phases, in a wide variety of systems, such as photonic and acoustic systems, and recently also observed in gapless semimetal phase, such as Weyl and Dirac phases, in systems alike. The higher-order topology is signaled by the hinge states emerging in the common bandgaps of the bulk states and the surface states. In this Letter, we report our first prediction and observation of a new type of hinge states, the bound hinge states in the continuum (BHICs) bulk band, in a higher-order Weyl semimetal implemented in phononic crystal. In contrast to the hinge state in gap, which is characterized by the bulk polarization, the BHIC is identified by the nontrivial surface polarization. The finding of the topological BHICs broadens our insight to the topological states, and may stimulate similar researches in other systems such as electronic, photonic, and cold atoms systems. Our work may pave the way toward high-Q acoustic devices in application.

The concept of topological energy bands and their manifestations have been demonstrated in condensed matter systems as a fantastic paradigm toward unprecedented physical phenomena and properties that are robust against disorders. Recent years, this paradigm was extended to phononic metamaterials (including mechanical and acoustic metamaterials), giving rise to the discovery of remarkable phenomena that were not observed elsewhere thanks to the extraordinary controllability and tunability of phononic metamaterials as well as versatile measuring techniques. These phenomena include, but not limited to, topological negative refraction, topological 'sasers' (i.e., the phonon analog of lasers), higher-order topological insulating states, non-Abelian topological phases, higher-order Weyl semimetal phases, Majorana-like modes in Dirac vortex structures and fragile topological phases with spectral flows. Here we review the developments in the field of topological phononic metamaterials from both theoretical and experimental perspectives with emphasis on the underlying physics principles. To give a broad view of topological phononics, we also discuss the synergy with non-Hermitian effects and cover topics including synthetic dimensions, artificial gauge fields, Floquet topological acoustics, bulk topological transport, topological pumping, and topological active matters as well as potential applications, materials fabrications and measurements of topological phononic metamaterials. Finally, we discuss the challenges, opportunities and future developments in this intriguing field and its potential impact on physics and materials science., Comment: Under review at Rep. Prog. Phys. (invited by the editor in 2021)

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 give rise to the non-Hermitian skin effect, which is geometry-dependent. However, this kind of novel correspondence between the exceptional points and skin effect remains to be confirmed by experiments. Here, we corroborate the correspondence in a non-Hermitian phononic crystal. 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.

The discovery of Weyl semimetals opens the door for searching topological semimetals in physical science. The Weyl points are generally recognized as conventional, quadratic, spin-1, and those of high topological charges. Here we report the observation of the quadruple Weyl point of charge 4, the highest topological charge a twofold degenerate node can carry. Besides the quadruple Weyl point, the phononic semimetal also hosts conventional, quadratic, and spin-1 Weyl points, which stands as a system with yet the richest types of Weyl points. The quadruple-helicoid surface states, specific to the quadruple Weyl point, are demonstrated. The finding of the high-charge Weyl point enriches the knowledge of Weyl semimetals and may stimulate related researches in other systems, such as photonic, mechanical and cold atom systems., Comment: 15 pages, 3 figures, and 1 table

The robust transport of edge modes is perhaps the most useful property of topological materials. The existence of edge modes is guaranteed by the bulk-edge correspondence, which states that the number of topological edge modes is determined by the bulk topological invariants. To obtain robust transport on the edge, we need to make volumetric changes to many bulk atoms to control the properties of a few edge atoms in a lower dimension. We suggest here that we can do the reverse in some cases: the properties of the edge can guarantee chiral transport phenomena in some bulk modes, achieving phenomena that are essentially the same as those observed in topological valley-Hall systems. Specifically, we show that a topologically trivial 2D hexagonal phononic crystal slab (waveguide) bounded by hardwall boundaries guarantees the existence of bulk modes with chiral anomaly inside a pseudogap. We experimentally observed robust valley-selected transport, complete valley state conversion, and valley focusing of the chiral anomaly bulk states (CABSs) in such phononic crystal waveguides., Comment: 17 pages, 5 figures

Elastic wave manipulation is important in a wide variety of scales in applications including information processing in tiny elastic devices and noise control in big solid structures. The recent emergence of topological materials opens a new avenue toward modulating elastic waves in solids. However, because of the full-vector feature, and the complicated couplings of the longitudinal and transverse components of elastic waves, manipulating elastic waves is generally difficult, compared with manipulating acoustic waves (scalar waves) and electromagnetic waves (vectorial waves but transverse only). Up to date, topological materials, including insulators and semimetals, have been realized for acoustic and electromagnetic waves. Although topological materials of elastic waves have also been reported, the topological edge modes observed all lie on the domain wall. A natural question can be asked: whether there exists an elastic metamaterial with the topological edge modes on its own boundary only? Here, we report a 3D metal-printed bilayer metamaterial, insulating topologically the elastic waves. By introducing the chiral interlayer couplings, the spin-orbit couplings for elastic waves are induced, which give rise to nontrivial topological properties. The helical edge states with the vortex feature are demonstrated on the boundary of the single topological phase. We further show a heterostructure of the metamaterial, which exhibits tunable edge transport. Our work may have potential in devices based on elastic waves in solids.

Recent breakthrough on topological Anderson insulators revealed the breakdown of the traditional perception that sufficiently strong disorder may induce the appearance of topological protected transport states instead of destruction. Although topological Anderson insulators have been observed in various time-reversal symmetry breaking systems, the observation of topological Anderson insulators protected by time-reversal symmetry remains scarce, which are considered to be more promising in applications such as the integrated devices. Here, we report the experimental observation of topological Anderson insulator in a two-dimensional bilayer phononic crystal. The robust spin-dependent edge states, as evidence of topological Anderson insulating phase, are observed by introducing on-site disorder. In addition, spin Bott index was computed to identify the topological invariants of the system with disorder, which confirmed the occurrence of disorder-induced topological state. Our results reveal that the impurities and defects introduced in the processing of integrated devices may induce the formation of topological transport states, which are promising for the exploration of new routes for the integration devices design.

The discovery of topologically protected boundary states in topological insulators opens a new avenue toward exploring novel transport phenomena. The one-way feature of boundary states against disorders and impurities prospects great potential in applications of electronic and classical wave devices. Particularly, for the 3D higher-order topological insulators, it can host hinge states, which allow the energy to transport along the hinge channels. However, the hinge states haveonly been observed along a single hinge, and a natural question arises: whether the hinge states can exist simultaneously on all the three independent directions of one sample? Here we theoretically predict and experimentally observe the hinge states on three different directions of a higher-order topological phononic crystal, and demonstrate their robust one-way transport from hinge to hinge. Therefore, 3D topological hinge transport is successfully achieved. The novel sound transport may serve as the basis for acoustic devices of unconventional functions.

Nodal lines are symmetry-protected one-dimensional band degeneracies in momentum space, which can appear in numerous topological configurations such as nodal rings, chains, links, and knots. Very recently, non-Abelian topological physics has been proposed in space-time inversion (PT) symmetric systems, and attract widespread attention. One of the most special configurations in non-Abelian system is the earring nodal link, composing of a nodal chain linking with an isolated nodal line, is signature of non-Abelian topology and cannot be elucidated using Abelian topological classifications. However, the earring nodal links have not been yet observed in real system. Here we design the phononic crystals with earring nodal links, and verify its non-Abelian topologicial charge in full-wave simulations. Moreover, we experimentally observed two different kinds of earring nodal links by measuring the band structures for two phononic crystals. Specifically, we found that the order of the nodal chain and line can switch after band inversion but their link cannot be severed. Our work provides experimental evidence for phenomena unique to non-Abelian band topology and our simple acoustic system provides a convenient platform for studying non-Abelian charges., Comment: 14 pages, 3 figures

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 are presented for this intriguing topological observable, owing to the presence of various challenges in solid-state systems. Here, using a three-dimensional acoustic 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 controllability over wave propagations.

Topological phases, including the conventional first-order and higher-order topological insulators and semimetals, have emerged as a thriving topic in the fields of condensed-matter physics and material science. Usually, a topological insulator is characterized by a fixed order topological invariant and exhibits associated bulk-boundary correspondence. Here, we realize a new type of topological insulator in a bilayer phononic crystal, which hosts simultaneously the first-order and second-order topologies, referred here as the hybrid-order topological insulator. The one-dimensional gapless helical edge states, and zero-dimensional corner states coexist in the same system. The new hybrid-order topological phase may produce novel applications in topological acoustic devices., Comment: 4 figures

A quadrupole topological insulator, being one higher-order topological insulator with nontrivial quadrupole quantization, has been intensely investigated very recently. However, the tight-binding model proposed for such emergent topological insulators demands both positive and negative hopping coefficients, which imposes an obstacle in practical realizations. Here we introduce a feasible approach to design the sign of hopping in acoustics, and construct the first acoustic quadrupole topological insulator that stringently emulates the tight-binding model. The inherent hierarchy quadrupole topology has been experimentally confirmed by detecting the acoustic responses at the bulk, edge and corner of the sample. Potential applications can be anticipated for the topologically robust in-gap states, such as acoustic sensing and energy trapping., Comment: This paper was published in PRL: Phys. Rev. Lett. 124, 206601 (2020)

The higher-order topological insulators (HOTIs), with such as the topological corner states, emerge as a thriving topic in the field of topological physics. But few connections have been found for the HOTIs with the well explored first-order topological insulators described by the Z_2 index. However, most recently, a proposal asserts that a significant bridge can be established between the HOTIs and the Z_2 topological insulators. When subject to an in-plane Zeeman field, the corner states, the signature of the HOTIs, can be induced in a Z_2 topological insulator. Such Zeeman field can be produced, for example, by the ferromagnetic proximity effect or magnetic atom doping, which obviously involves the drastically experimental complexity. Here we show that, a phononic crystal, designed as a bilayer of coupled acoustic cavities, hosts exactly the Kane-Mele model with built-in in-plane Zeeman fields. We observe that the helical edge states along the zigzag edges are gapped, and the corner states, localized spatially at the corners of the samples, appear in the gap, confirming the effect induced by the Zeeman field. We further demonstrate the intriguing contrast properties of the corner states at the outer and inner corners in a hexagonal ring-shaped sample.

Square-root topological states are new topological phases, whose topological property is inherited from the square of the Hamiltonian. We realize the first-order and second-order square-root topological insulators in phononic crystals, by putting additional cavities on connecting tubes in the acoustic Su-Schrieffer-Heeger model and the honeycomb lattice, respectively. Because of the square-root procedure, the bulk gap of the squared Hamiltonian is doubled. In both two bulk gaps, the square-root topological insulators possess multiple localized modes, i.e., the end and corner states, which are evidently confirmed by our calculations and experimental observations. We further propose a second-order square-root topological semimetal by stacking the decorated honeycomb lattice to three dimensions., Comment: 3 figures

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., Comment: 4 figures in the Main Text. Nature Materials (2021)

Topological semimetal, hosting spin-1 Weyl point beyond Dirac and Weyl points, has attracted a great deal of attention. However, the spin-1 Weyl semimetal, which possesses exclusively the spin-1 Weyl points in a clean frequency window, without shadowed by any other nodal points, is yet to be discovered. Here, we report for the first time a spin-1 Weyl semimetal in a phononic crystal. Its spin-1 Weyl points, touched by two linear dispersions and an additional flat band, carry monopole charges (-2,0,2) or (2,0,-2) for the three bands from bottom to top, and result in double Fermi arcs existing both between the 1st and 2nd bands, as well as between the 2nd and 3rd bands. We further observe robust propagation against the multiple joints and topological negative refraction of acoustic surface arc wave. Our results pave the way to explore on the macroscopic scale the exotic properties of the spin-1 Weyl physics.

Dirac semimetals, the materials featured with discrete linearly crossing points (called Dirac points) between four bands, are critical states of topologically distinct phases. Such gapless topological states have been accomplished by a band-inversion mechanism, in which the Dirac points can be annihilated pairwise by perturbations without changing the symmetry of the system. Here, we report an experimental observation of Dirac points that are enforced completely by the crystal symmetry, using a nonsymmorphic three-dimensional phononic crystal. Intriguingly, our Dirac phononic crystal hosts four spiral topological surface states, in which the surface states of opposite helicities intersect gaplessly along certain momentum lines, as confirmed by our further surface measurements. The novel Dirac system may release new opportunities for studying the elusive (pseudo)relativistic physics, and also offer a unique prototype platform for acoustic applications.

Very recently, novel quasiparticles beyond those mimicking the elementary high-energy particles such as Dirac and Weyl fermions have attracted great interest in condensed matter physics and materials science1-9. Here we report the first experimental observation of the long-desired quadratic Weyl points10 by using a three-dimensional chiral metacrystal of sound waves. Markedly different from the newly observed unconventional quasiparticles5-9, such as the spin-1 Weyl points and the charge-2 Dirac points that are featured respectively with threefold and fourfold band crossings, the charge-2 Weyl points identified here are simply twofold degenerate, and the dispersions around them are quadratic in two directions and linear in the third one10. Besides the essential nonlinear bulk dispersions, we further unveil the exotic double-helicoid surface arcs that emanate from a projected quadratic Weyl point and terminate at two projected conventional Weyl points through Fourier transformation of the scanned surface fields. This unique global surface connectivity provides conclusive evidence for the double topological charges of such unconventional topological nodes., Comment: 4 figures

Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. The integer quantum Hall effect has delivered on that promise in the electronic realm through high-precision metrology devices. However, both the route of implementing an analogue of the quantum Hall effect as well as the quantum spin Hall effect are obstructed for acoustics by the requirement of a magnetic field, or the presence of fermionic quantum statistics, respectively. Here, we use a two-dimensional acoustic crystal with two layers to mimic spin-orbit coupling, a crucial ingredient of topological insulators. In particular, our setup allows us to free ourselves of symmetry constraints as we rely on the concept of a non-vanishing "spin" Chern number. We experimentally characterize the emerging boundary states which we show to be gapless and helical. Moreover, in an H-shaped device we demonstrate how the transport path can be selected by tuning the geometry, enabling the construction of complex networks.

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can stabilize fragile Bloch bands that challenge our very notion of topology: while answering to the most basic definition of topology, one can trivialize these bands through the addition of trivial Bloch bands. Here, we fully characterize the symmetry properties of the response of an acoustic metamaterial to establish the fragile nature of the low-lying Bloch bands. Additionally, we present a spectral signature in the form of spectral flow under twisted boundary conditions., Comment: 4 pages, 3 figures + supplementary information (21 pages, 13 figures, 7 tables). Note the accompanying paper by Zhi-Da Song et al. "Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology"' posted on the same day on the arXiv

Ideal Weyl points, which are related by symmetry and thus reside at the same frequency, could promote the deep development and utilization of the Weyl physics. Although the ideal type-I Weyl points have been achieved in photonic crystals, the ideal type-II Weyl points with tilted cone-like band dispersions, are still beyond discovery. Here we realize ideal type-II Weyl points of minimal number in three-dimensional layer-stacked phononic crystals, and demonstrate topological phase transition from Weyl semimetal to valley insulators of two distinct types. The Fermi-arc surface states exist on the interface of the Weyl and valley phases, while the Fermi-circle ones occur on that of the two distinct valley phases. We show the interesting wave partition of Fermi-circle surface states on the interfaces formed by distinct valley phases.

Recently, intense efforts have been devoted to realizing classical analogues of various topological phases of matter. In this Letter, we explore the intriguing Weyl physics by a simple one-dimensional sonic crystal, in which two extra structural parameters are combined to construct a synthetic three-dimensional space. Based on our underwater ultrasonic experiments, we have not only observed the synthetic Weyl points directly, but also probed the novel reflection phase singularity that connects inherently with the topological robustness of Weyl points. As a smoking gun evidence of the topological states of matter, the presence of nontrivial interface modes has been demonstrated further. All experimental data agree well with our full-wave simulations. As the first realization of topological acoustics in synthetic space, our study exhibits great potential of probing high-dimensional topological phenomena by such easily-fabricated and -detected low-dimension acoustic systems., Comment: Accepted by PRL

Reflection and refraction occur at interface between two different media. These two fundamental phenomena form the basis of fabricating various wave components. Specifically, refraction, dubbed positive refraction nowadays, appears in the opposite side of the interface normal with respect to the incidence. Negative refraction, emerging in the same side by contrast, has been observed in artificial materials1-5 following a prediction by Veslago6, which has stimulated many fascinating applications such as super-resolution imaging7. Here we report the first discovery of negative refraction of the topological surface arc states of Weyl crystals, realized for airborne sound in a novel woodpile phononic crystal. The interfaces are one-dimensional edges that separate different crystal facets. By tailoring the surface terminations of such a Weyl phononic crystal, open equifrequency contours of surface acoustic waves can be delicately designed to produce the negative refraction, to contrast the positive counterpart realized in the same sample. Strikingly different from the conventional interfacial phenomena, the unwanted reflection can be made forbidden by exploiting the open nature of the surface equifrequency contours, which is a topologically protected surface hallmark of Weyl crystals8-12., Comment: An updated version has been published in Nature

Recently, the topological physics in acoustics has been attracting much attention. However, all the studies are aimed to elastic or airborne sound systems. Realizing topological insulators for underwater sound is of great importance, since water is another crucial sound medium in addition to solid and air. Here we report an experimental study on the valley-projected edge states for underwater sound. The edge states are directly observed in our ultrasound scanning experiments, together with a solid evidence for the valley-selective excitation. The experimental data agree well with our numerical results. Prospective applications can be anticipated, such as for underwater sound signal processing and ocean noise control., Comment: 5 figures

Many intriguing phenomena occur for electrons under strong magnetic fields. Recently, it was proposed that an appropriate strain texture in graphene can induce a synthetic gauge field, in which the electrons behave like in a real magnetic field. This opened the door to control quantum transport by mechanical means and to explore unprecedented physics in high-field regime. Such studies have been achieved in molecular and photonic lattices. Here we report the first experimental realization of giant uniform pseudomagnetic field in acoustics by introducing a simple uniaxial deformation to acoustic graphene. Benefited from the controllability of our macroscopic platform, we observe the acoustic Landau levels in frequency-resolved spectroscopy and their spatial localization in pressure-field distributions. We further visualize the quantum-Hall-like edge states (connected to the zeroth Landau level), which have been elusive before owing to the challenge in creating large-area uniform pseudomagnetic fields. These results, highly consistent with our full-wave simulations, establish a complete framework for artificial structures under constant pseudomagnetic fields. Our findings, conceptually novel in acoustics, may offer new opportunities to manipulate sound., Comment: 3 figures

The effect of the dipole polarization on the quantum dipole dipole interaction near an Ag nanosphere (ANS) is investigated. A theoretical formalism in terms of classical Green function is developed for the transfer rate and the potential energy of the dipole dipole interaction (DDI) between two polarized dipoles. It is found that a linear transition dipole can couple to a left circularly polarized transition dipole much stronger than to a right circularly polarized transition dipole. This polarization selectivity exists over a wide frequency range and is robust against the variation of the dipoles' position or the radius of the ANS. In contrast, a right circularly polarized transition dipole, can change sharply from coupling strongly to another right circularly polarized dipole to coupling strongly to a left circularly polarized dipole with varying frequency. However, if the two dipoles are placed in the same radial direction of the sphere, the right circularly polarized transition dipole can only couple to the dipole with the same polarization while not to the left circularly polarized transition dipole. These findings may be used in solid-state quantum-information processing based on the DDI., Comment: 7 pages, 5 figures

Acoustics-based techniques are investigated to focus and bunch nanoparticle beams. This allows to overcome the prominent problem of the longitudinal and transverse mismatch of particle stream and x-ray beam in single-particle/single molecule imaging at x-ray free-electron lasers (XFEL). It will also enable synchronised injection of particle streams at kHz repetition rates. Transverse focusing concentrates the particle flux to the (sub)micrometer x-ray focus. In the longitudinal direction, focused acoustic waves can be used to bunch the particle to the same repetition rate as the x-ray pulses. The acoustic manipulation is based on simple mechanical recoil effects and could be advantageous over light-pressure-based methods, which rely on absorption. The acoustic equipment is easy to implement and can be conveniently inserted into current XFEL endstations. With the proposed method, data collection times could be reduced by a factor of $10^4$. This work does not just provide an efficient method for acoustic manipulation of streams of arbitrary gas phase particles, but also opens up wide avenues for acoustics-based particle optics.

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., Comment: This work has been accepted by PRL

The artificial crystals for classical waves provide a good platform to explore the topological physics proposed originally in condensed matter systems. In this paper, acoustic Dirac degeneracy is realized by simply rotating the scatterers in sonic crystals, where the degeneracy is induced accidentally by modulating the scattering strength among the scatterers during the rotation process. This gives a flexible way to create topological phase transition in acoustic systems. Edge states are further observed along the interface separating two topologically distinct gapped sonic crystals., Comment: 4 figures

Here we present an experimental observation of the self-organization effect of the polystyrene particles formed by acoustically-induced interaction forces. Two types of stable configurations are observed experimentally: one is mechanically equilibrium and featured by nonzero inter-particle separations, and the other corresponds to a close-packed assembly, which is formed by strong attractions among the aggregated particles. For the former case involving two or three particles, the most probable inter-particle separations (counted for numerous independent initial arrangements) agree well with the theoretical predictions. For the latter case, the number of the final stable configurations grows with the particle number, and the occurrence probability of each configuration is interpreted by a simple geometric model., Comment: 14 pages, 5 figures

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. Besides the selection rules established for exciting valley polarized states, a mimicked spin Hall effect of sound is proposed further. The extraordinary chirality of valley vortex states, detectable in experiments, may open new possibility in sound manipulations. This is appealing to scalar acoustics that lacks spin degree of freedom inherently. Besides, 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.

Valley pseudospin, labeling quantum states of energy extrema in momentum space, is attracting tremendous attention1-13 because of its potential in constructing new carrier of information. Compared with the non-topological bulk valley transport realized soon after predictions1-5, the topological valley transport in domain walls6-13 is extremely challenging owing to the inter-valley scattering inevitably induced by atomic scale imperfectness, until the recent electronic signature observed in bilayer graphene12,13. Here we report the first experimental observation of topological valley transport of sound in sonic crystals. The macroscopic nature of sonic crystals permits the flexible and accurate design of domain walls. In addition to a direct visualization of the valley-selective edge modes through spatial scanning of sound field, reflection immunity is observed in sharply curved interfaces. The topologically protected interface transport of sound, strikingly different from that in traditional sound waveguides14,15, may serve as the basis of designing devices with unconventional functions.

The Letter reports 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., Comment: 12 pages and 4 figures, experimental study