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Despite extensive exploration of acoustic vortices carrying orbital angular momentum (OAM), the generation of acoustic vortices with OAM orientations beyond the conventional longitudinal direction remains largely unexplored. Spatiotemporal (ST) vortices, featuring spiral phase twisting in the ST domain and carrying transverse OAM, have recently attracted considerable interest in optics and acoustics. Here, we report the generation of three-dimensional (3D) ST acoustic vortices with arbitrarily oriented OAM, thereby opening up a new dimension in acoustic OAM control. By utilizing a two-dimensional (2D) acoustic phased array, we introduce two approaches to manipulate the orientation of OAM: through the direct rotation of vortices in 3D space and the intersection of vortices carrying distinct types of OAM. These methods enable unprecedented control over the orientation of acoustic OAM, providing a new degree of freedom in the manipulation of acoustic waves. The arbitrarily oriented OAM holds promise for enhancing acoustic communication by broadening capacity and enabling more complex particle manipulation techniques. Our work establishes a foundation for future explorations into the complex dynamics of novel structured acoustic fields in the ST domain.

Spin and orbital angular momenta are fundamental physical characteristics described by polarization and spatial degrees of freedom, respectively. Polarization is a feature of vector fields while spatial phase gradient determines the orbital angular momentum ubiquitous to any scalar field. Common wisdom treats these two degrees of freedom as distinct and independent principles to manipulate wave propagations. Here, we demonstrate their synergy. This is achieved by introducing two orthogonal $p$-orbitals as eigenbases, whose spatial modal features are exploited to generate orbital angular momenta and the associated orbital orientations provide means to simultaneously manipulate polarizations. Through periodic modulation and directional coupling, we realize a full cyclic evolution of the synchronized and synergized spin-orbital angular momenta. Remarkably, this evolution acquires a nontrivial geometric phase, leading to its representation on a M\"obius strip. Experimentally, an acoustic cavity array is designed, whose dipole resonances precisely mimic the $p$-orbitals. The acoustic waves, uniquely, see the pressure (scalar) field as a spatial feature and carry an intrinsic polarization defined by the velocity (vector) field, serving as an ideal platform to observe the synergy of spin and orbital angular momenta. Based on such a property, we further showcase a spin-orbital-Hall effect, highlighting the intricate locking of handedness, directionality, spin density and spatial mode profile. Our study unveils a fundamental connection between spin and orbital angular momenta, promising avenues for novel applications in information coding and high-capacity communications.

Topological corner states are exotic topological boundary states that are bounded to zero-dimensional geometry even the dimension of systems is large than one. As an elegant physical correspondence, their numbers are dictated by the bulk topological invariants. So far, all previous realizations of HOTIs are hallmarked by $\mathbb{Z}_2$ topological invariants and therefore have only one corner state at each corner. Here we report an experimental demonstration of $\mathbb{Z}$-class HOTI phases in electric circuits, hosting $N$ corner modes at each single corner structure. By measuring the impedance spectra and distributions, we clearly demonstrate the $\mathbb{Z}$-class HOTI phases, including the zero-energy corner modes and their density distributions. Moreover, we reveal that the local density of states (LDOS) at each corner for $N=4$ are equally distributed at four corner unit cells, prominently differing from $\mathbb{Z}_2$-class case where the LDOS only dominates over one corner unit cell. Our results extend the observation of HOTIs from $\mathbb{Z}_2$ class to $\mathbb{Z}$ class and the coexistence of spatially overlapped large number of corner modes which may enable exotic topological devices that require high degeneracy boundary states., Comment: 8 pages, 4 figures

Local density-of-states (LDOS) is a fundamental spectral property that plays a central role in various physical phenomena such as wave-matter interactions. Here, we report on the direct measurement of the LDOS of acoustic systems and derive from which the fractional topological number in an acoustic Su-Schrieffer-Heeger system. The acoustic LDOS is quantified here with a state-of-the-art technique through the measurement of the volume flow rate and the acoustic pressure with a local excitation-probe configuration. Based on this method, we study the acoustic Purcell effect and establish experimentally the important relation between the near-field LDOS and the far-field acoustic emission power. Moreover, we detect the LDOS in the one-dimensional acoustic Su-Schrieffer-Heeger model and observe the fractional topological number of the system. Our work unveils the important role of the LDOS in acoustic phenomena and paves the way toward characterizing and tailoring the LDOS in topological systems.

The past decades have witnessed the flourishing of non-Hermitian physics in non-conservative systems, leading to unprecedented phenomena of unidirectional invisibility, enhanced sensitivity and more recently the novel topological features such as bulk Fermi arcs. Among them, growing efforts have been invested to an intriguing phenomenon, known as the non-Hermitian skin effect (NHSE). Here, we review the recent progress in this emerging field. By starting from the one-dimensional (1D) case, the fundamental concepts of NHSE, its minimal model, the physical meanings and consequences are elaborated in details. In particular, we discuss the NHSE enriched by lattice symmetries, which gives rise to unique non-Hermitian topological properties with revised bulk-boundary correspondence (BBC) and new definitions of topological invariants. Then we extend the discussions to two and higher dimensions, where dimensional surprises enable even more versatile NHSE phenomena. Extensions of NHSE assisted with extra degrees of freedom such as long-range coupling, pseudospins, magnetism, non-linearity and crystal defects are also reviewed. This is followed by the contemporary experimental progress for NHSE. Finally, we provide the outlooks to possible future directions and developments.

Defects play a crucial role in the physical properties of crystals, whether for classical or quantum systems. For example, in photonic/phononic crystals, defects can serve as precise guidance and localization of classical electromagnetic or mechanical waves. Rainbow concentrating, a recently proposed exotic wave localization [Phys. Rev. Lett. 126, 113902 (2021)] exploits defects to enable the collection and frequency routing of weak signals in real space. In this paper, using a solid-state phononic crystal (PnC) plate, we experimentally verify this phenomenon by deliberately infusing a homogeneous graded dislocation, i.e., a line defect, into the PnC. Two PnCs separated by the defect will breed deterministic interface states along with the defect, offering rainbow trapping and concentrating for elastic waves. Our PnC-based rainbow trappers and concentrators are scalable and configurable, promising for advancing applications like energy harvesting, information processing, and acoustofluidic manipulating., Comment: 10 Page, 7 figures

Hermitian theories play a major role in understanding the physics of most phenomena. It has been found only in the past decade that non-Hermiticity enables unprecedented effects such as exceptional points, spectral singularities and bulk Fermi arcs. Recent studies further show that non-Hermiticity can fundamentally change the topological band theory, leading to the non-Hermitian band topology and non-Hermitian skin effect, as confirmed in one-dimensional (1D) systems. However, in higher dimensions, these non-Hermitian effects remain unexplored in experiments. Here, we demonstrate the spin-polarized, higher-order non-Hermitian skin effect in two-dimensional (2D) acoustic metamaterials. Using a lattice of coupled whisper-gallery acoustic resonators, we realize a spinful 2D higher-order topological insulator (HOTI) where the spin-up and spin-down states are emulated by the anti-clockwise and clockwise modes, respectively. We find that the non-Hermiticity drives wave localizations toward opposite edge boundaries depending on the spin polarizations. More interestingly, for finite systems with both edge and corner boundaries, the higher-order non-Hermitian skin effect leads to wave localizations toward two corner boundaries for the bulk, edge and corner states in a spin-dependent manner. We further show that such a non-Hermitian skin effect enables rich wave manipulation through the loss configuration in each unit-cell. The reported spin-dependent, higher-order non-Hermitian skin effect reveals the interplay between higher-order topology and non-Hermiticity, which is further enriched by the spin degrees of freedom. This unveils a new horizon in the study of non-Hermitian physics and the design of non-Hermitian metamaterials.

Waveguides and resonators are core components in the large-scale integration of electronics, photonics, and phononics, both in existing and future scenarios. In certain situations, there is critical coupling of the two components; i.e., no energy passes through the waveguide after the incoming wave couples into the resonator. The transmission spectral characteristics resulting from this phenomenon are highly advantageous for signal filtering, switching, multiplexing, and sensing. In the present study, adopting an elastic-wave platform, we introduce topological insulator (TI), a remarkable achievement in condensed matter physics over the past decade, into a classical waveguide-ring-resonator configuration. Along with basic similarities with classical systems, a TI system has important differences and advantages, mostly owing to the spin-momentum locked transmission states at the TI boundaries. As an example, a two-port TI waveguide resonator can fundamentally eliminate upstream reflections while completely retaining useful transmission spectral characteristics, and maximize the energy in the resonator, with possible applications being novel signal processing, gyro/sensing, lasering, energy harvesting, and intense wave-matter interactions, using phonons, photons, or even electrons. The present work further enhances the confidence of using topological protection for practical device performance and functionalities, especially considering the crucial advantage of introducing (pseudo)spins to existing conventional configurations. More in-depth research on advancing phononics/photonics, especially on-chip, is foreseen.

Higher-order topological insulator, as a newly found non-trivial material and structure, possesses a topological phase beyond the bulk-boundary correspondence. Here, we present an experimental observation of photonic higher-order topological crystalline insulator and its topological protection to quantum superposition and entanglement in a two-dimensional lattice. By freely writing the insulator structure with femtosecond laser and directly measuring evolution dynamics with single-photon imaging techniques, we are able to observe the distinct features of the topological corner states in C_4 and C_2 photonic lattice symmetry. Especially, we propose and experimentally identify the topological corner states by exciting the photonic lattice with single-photon superposition state, and we examine the protection impact of topology on quantum entanglement for entangled photon states. The single-photon dynamics and the protected entanglement reveal an intrinsic topological protection mechanism isolating multi-partite quantum states from diffusion-induced decoherence. The higher-order topological crystalline insulator, built-in superposition state generation, heralded single-photon imaging and quantum entanglement demonstrated here link topology, material, and quantum physics, opening the door to wide investigations of higher-order topology and applications of topological enhancement in genuine quantum regime., Comment: 46 pages, 6 figures in main text, 16 figures in Supplementary Materials

Macroscopic two-dimensional sonic crystals with inversion symmetry are studied to reveal higher-order topological physics in classical wave systems. By tuning a single geometry parameter, the band topology of the bulk and the edges can be controlled simultaneously. The bulk band gap forms an acoustic analog of topological crystalline insulators with edge states which are gapped due to symmetry reduction on the edges. In the presence of mirror symmetry, the band topology of the edge states can be characterized by the Zak phase, illustrating the band topology in a hierarchy of dimensions, which is at the heart of higher-order topology. Moreover, the edge band gap can be closed without closing the bulk band gap, revealing an independent topological transition on the edges. The rich topological transitions in both bulk and edges can be well-described by the symmetry eigenvalues at the high-symmetry points in the bulk and surface Brillouin zones. We further analyze the higher-order topology in the shrunken sonic crystals where slightly different physics but richer corner and edge phenomena are revealed. In these systems, the rich, multidimensional topological transitions can be exploited for topological transfer among zero-, one- and two- dimensional acoustic modes by controlling the geometry.

Band topology and related spin (or pseudo-spin) physics of photons provide us with a new dimension for manipulating light, which is potentially useful for information communication and data storage. Especially, the quantum spin Hall effect of light, where electromagnetic waves propagate along surfaces of samples with strong spin-momentum locking, paves the way for achieving topologically protected photonic spin transport. Recently, the conventional bulk-edge correspondence of the band topology has been extended to higher-order cases that enables the explorations of topological states with codimensions larger than 1 such as hinge and corner states. Here, for the first time, we demonstrate a higherorder quantum spin Hall effect of light by utilizing an all-dielectric C6v-symmetric photonic crystal. We observe corner states with opposite pseudospin polarizations at different corners owing to nontrivial higher-order topology and finite spin-spin coupling. By applying the spin-polarized excitation sources, we can selectively excite the corner states at different spatial positions through spin-momentum-locked decaying edge states, resembling the quantum spin Hall effect in a higher-order manner. Our work which breaks the barriers between the spin photonics and higher-order topology opens the frontiers for studying lower-dimensional spinful classical surface waves and supports explorations in robust communications., Comment: 24 pages, 4 figures

Bound states in the continuum (BICs) in photonic crystals represent the unique solutions of wave equations possessing an infinite quality-factor. We design a type of bilayer photonic crystal and study the influence of symmetry and coupling between TE and TM polarizations on BICs. The BIC modes possess $C_{3v}$ symmetry in the x-y plane while the mirror-flip symmetry in the z-direction is broken, and they provide selective coupling into different layers by varying frequency. The enhanced TE-TM coupling due to broken mirror-flip symmetry in the z-direction gives rise to high-Q factor BIC states with unique spatial characteristics. We show the emergence of such BIC states even in the presence of coupling between the TE- and TM-like modes, which is different from the existing single polarization BIC models. We propose to study BICs in multilayer systems, and the results may be helpful in designing photonic settings to observe and manipulate BICs with various symmetries and polarizations for practical applications., Comment: 15 pages, 6 figures

Exploring new topological materials with large topological nontrivial bandgaps and simple composition is attractive for both theoretical investigation and experimental realization. Recently alpha tin ({\alpha}-Sn) has been predicted to be such a candidate and it can be tuned to be either a topological insulator or a Dirac semimetal by applying appropriate strain. However, free-standing {\alpha}-Sn is only stable below 13.2 {\deg}C. In this study, a series of high-quality {\alpha}-Sn films with different thicknesses have been successfully grown on InSb substrates by molecular beam epitaxy (MBE). Confirmed by both X-ray diffraction (XRD) and reciprocal space mapping (RSM), all the films remained fully strained up to 4000 {\AA}, proving the strain effect from the substrate. Remarkably, the single-crystalline {\alpha} phase can persist up to 170 {\deg}C for the 200 {\AA} thick sample. The critical temperature where the {\alpha} phase disappears decreases as the film thickness increases, showing the thermal stabilization can be engineered by varying the {\alpha}-Sn thickness. A plastic flow model taking the work hardening into account is introduced to explain this dependence, assuming the strain relaxation and the phase transition occur successively. This enhanced thermal stability is prerequisite for above room-temperature characterization and application of this material system., Comment: 21 pages, 4 figures, 1 table

Topological phases of matter have been extensively studied for their intriguing bulk and edge properties. Recently, higher-order topological insulators with boundary states that are two or more dimensions lower than the bulk states, have been proposed and investigated as novel states of matter. Previous implementations of higher-order topological insulators were based on two-dimensional (2D) systems in which 1D gapped edge states and 0D localized corner states were observed. Here we theoretically design and experimentally realize a 3D higher-order topological insulator in a sonic crystal with a large topological band gap. We observe the coexistence of third-, second- and first-order topological boundary states with codimension three, two and one, respectively, indicating a dimensional hierarchy of higher-order topological phenomena in 3D crystals. Our acoustic metamaterial goes beyond the descriptions of tight-binding model and possesses a band structure which automatically breaks the chiral symmetry, leading to the separation of bulk, surface, hinge and corner states. Our study opens a new route toward higher-order topological phenomena in three-dimensions and paves the way for topological wave trapping and manipulation in a hierarchy of dimensions in a single system., Comment: 29 pages, 4 figures

The discovery of quadrupole topology opens a new horizon in the study of topological phenomena. However, the existing experimental realizations of quadrupole topological insulators in symmorphic lattices with $\pi$-fluxes often break the protective mirror symmetry. Here, we present a theory for anomalous quadrupole topological insulators in nonsymmorphic crystals without flux, using 2D sonic crystals with $p4gm$ and $p2gg$ symmetry groups as concrete examples. We reveal that the anomalous quadrupole topology is protected by two orthogonal glide symmetries in square or rectangular lattices. The distinctive features of the anomalous quadrupole topological insulators include: (i) minimal four bands below the topological band gap, (ii) nondegenerate, gapped Wannier bands and special Wannier sectors with gapped composite Wannier bands, (iii) quantized Wannier band polarizations in these Wannier sectors. Remarkably, the protective glide symmetries are well-preserved in the sonic-crystal realizations where higher-order topological transitions can be triggered by symmetry or geometry engineering., Comment: 5+ pages 4 figures

The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been investigated as a novel topological phase of matter beyond the conventional bulk-boundary correspondence. Previous studies of HOTIs have been mainly focused on the topological multipole systems with negative coupling between lattice sites. Here we experimentally demonstrate that second-order topological insulating phases without negative coupling can be realized in two-dimensional dielectric photonic crystals (PCs). We visualize both one-dimensional topological edge states and zero-dimensional topological corner states by using near-field scanning technique. To characterize the topological properties of PCs, we define a novel topological invariant based on the bulk polarizations. Our findings open new research frontiers for searching HOTIs in dielectric PCs and provide a new mechanism for light-manipulating in a hierarchical way., Comment: 23 pages, 4 figures

Symmetry and topology are two fundamental aspects of many quantum states of matter. Recently, new topological materials, higher-order topological insulators, were discovered, featuring, e.g., bulk-edge-corner correspondence that goes beyond the conventional topological paradigms. Here, we discover experimentally that the nonsymmorphic $p4g$ acoustic metacrystals host a symmetry-protected hierarchy of topological multipoles: the lowest band gap has a quantized Wannier dipole and can mimic the quantum spin Hall effect, while the second band gap exhibits quadrupole topology with anomalous Wannier bands. Such a topological hierarchy allows us to observe experimentally distinct, multiplexing topological phenomena and to reveal a topological transition triggered by the geometry-transition from the $p4g$ group to the $C_{4v}$ group which demonstrates elegantly the fundamental interplay between symmetry and topology. Our study demonstrates an instance that classical systems with controllable geometry can serve as powerful simulators for the discovery of novel topological states of matter and their phase transitions., Comment: 5 figures. Accepted by Nature Communications

Recently, the concept of valley pseudospin, labeling quantum states of energy extrema in momentum space, has attracted enormous attention because of its potential as a new type of information carrier. Here, we present surface acoustic wave (SAW) waveguides, which utilize and transport valley pseudospins in two-dimensional SAW phononic crystals (PnCs). In addition to a direct visualization of the valley-dependent states excited from the corresponding chiral sources, the backscattering suppression of SAW valley-dependent edge states transport is observed in sharply curved interfaces. By means of band structure engineering, elastic wave energy in the SAW waveguides can be transported with remarkable robustness, which is very promising for new generations of integrated solid-state phononic circuits with great versatility.

Recently, we witnessed a tremendous effort to conquer the realm of acoustics as a possible playground to test with sound waves topologically protected wave propagation. Acoustics differ substantially from photonic and electronic systems since longitudinal sound waves lack intrinsic spin polarization and breaking the time-reversal symmetry requires additional complexities that both are essential in mimicking the quantum effects leading to topologically robust sound propagation. In this article, we review the latest efforts to explore with sound waves topological states of quantum matter in two- and three-dimensional systems where we discuss how spin and valley degrees of freedom appear as highly novel ingredients to tailor the flow of sound in the form of one-way edge modes and defect-immune protected acoustic waves. Both from a theoretical stand point and based on contemporary experimental verifications, we summarize the latest advancements of the flourishing research frontier on topological sound., Comment: 33 pages, 8 figures

Topological insulators with unique gapless edge states have revolutionized the understanding of electronic properties in solid materials. These gapless edge states are dictated by the topological invariants associated with the quantization of generalized Berry phases of the bulk energy bands through the bulk-edge correspondence, a paradigm that can also be extended to acoustic and photonic systems. Recently, high-order topological insulators (HOTIs) are proposed and observed, where the bulk topological invariants result in gapped edge states and in-gap corner or hinge states, going beyond the conventional bulk-edge correspondence. However, the existing studies on HOTIs are restricted to tight-binding models which cannot describe the energy bands of conventional sonic/photonic crystals that are due to multiple Bragg scatterings. Here, we report theoretical prediction and experimental observation of acoustic second-order topological insulators (SOTI) in two-dimensional (2D) sonic crystals (SCs) beyond the tight-binding picture. We observe gapped edge states and degenerate in-gap corner states which manifest bulk-edge correspondence in a hierarchy of dimensions. Moreover, topological transitions in both the bulk and edge states can be realized by tuning the angle of the meta-atoms in each unit-cell, leading to various conversion among bulk, edge and corner states. The emergent properties of the acoustic SOTIs open up a new route for topological designs of robust localized acoustic modes as well as topological transfer of acoustic energy between 2D, 1D and 0D modes., Comment: 19 pages, 4 figures

Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have not been found in photonic systems yet. In this article, we propose a type of two-dimensional second-order photonic crystals with zero-dimensional corner states and one-dimensional boundary states for optical frequencies. All of these states are topologically non-trivial and can be understood based on the theory of topological polarization. Moreover, by tuning the easily-fabricated structure of the photonic crystals, we can realize different topological phases with unique topological boundary states straightforwardly. Our result can be generalized to higher dimensions and provides unprecedented venues for higher-order photonic topological insulators and semimetals., Comment: 6 pages, 6 figures, Phys. Rev. B 2018

Weyl points emerge as topological monopoles of Berry flux in the three-dimensional (3D) momentum space and have been extensively studied in topological semimetals. As the underlying topological principles apply to any type of waves under periodic boundary conditions, Weyl points can also be realized in classical wave systems, which are easier to engineer compared to condensed matter materials. Here, we made an acoustic Weyl phononic crystal by breaking space inversion (P) symmetry using a combination of slanted acoustic waveguides. We conducted angle-resolved transmission measurements to characterize the acoustic Weyl points. We also experimentally confirmed the existence of acoustic "Fermi arcs" and demonstrated robust one-way acoustic transport, where the surface waves can overcome a step barrier without reflection. This work lays a solid foundation for the basic research in 3D topological acoustic effects., Comment: 17 pages, 5 figures

The explorations of the quantum-inspired symmetries in optical and photonic systems have witnessed immense research interests both fundamentally and technologically in a wide range of subjects of physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory, recently ramified into diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant applications prospects and engineering of novel materials. In addition, it has observed increasing research interests in many emerging directions beyond optics and photonics. This Review paper attempts to bring together the state of the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings along with elucidating key concepts and background and a detailed perspective on new emerging directions. It can be anticipated that this trendy field of interest can be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, opto-electronics and beyond, and offer distinctive applications prospects in novel functional materials., Comment: 88 Pages, 18 Figures

Two-dimensional (2D) coupled resonant optical waveguide (CROW), exhibiting topological edge states, provides an efficient platform for designing integrated topological photonic devices. In this paper, we propose an experimentally feasible design of 2D honeycomb CROW photonic structure. The characteristic optical system possesses two-fold and three-fold Dirac points at different positions in the Brillouin zone. The effective gauge fields implemented by the intrinsic pseudo-spin-orbit interaction open up topologically nontrivial bandgaps through the Dirac points. Spatial lattice geometries allow destructive wave interference, leading to a dispersionless, nearly-flat energy band in the vicinity of the three-fold Dirac point in the telecommunication frequency regime. This nontrivial nearly-flat band yields topologically protected edge states. The pertinent physical effects brought about due to non-Hermitian gain/loss medium into the honeycomb CROW device are discussed. The generalized gain-loss lattice with parity-time symmetry decouples the gain and the loss at opposite zigzag edges, leading to purely gain or loss edge channels. Meanwhile, the gain and loss effects on the armchair boundary cancel each other, giving rise to dissipationless edge states in non-Hermitian optical systems. These characteristics underpin the fundamental importance as well as the potential applications in various optical devices such as polarizers, optical couplers, beam splitters and slow light delay lines., Comment: 16 pages, 4 figures

Topological acoustic and elastic waves have recently emerged as an exciting interdisciplinary field which is still mainly focused on low-dimensional structures and model systems. Here we demonstrate numerically an elastic-wave analogue of topological node-lines in three-dimensional mechanical metacrystals with ribbon- or drumhead-like surface states. These two-dimensional topological surface states offer unprecedented, robust subwavelength confinement of elastic waves. Design principles for topological mechanical metamaterials, from both material and symmetry aspects, are unveiled and connected to fundamental conservation laws and nonsymmorphic space group. Our study paves the way toward the synergy between three-dimensional mechanical metamaterials and topological wave dynamics.

Precise control of elastic waves in modes and coherences is of great use in reinforcing nowadays elastic energy harvesting/storage, nondestructive testing, wave-mater interaction, high sensitivity sensing and information processing, etc. All these implementations are expected to have elastic transmission with lower transmission losses and higher degree of freedom in transmission path. Inspired by topological states of quantum matters, especially quantum spin Hall effects (QSHEs) providing passive solutions of unique disorder-immune surface states protected by underlying nontrivial topological invariants of the bulk, thus solving severe performance trade-offs in experimentally realizable topologically ordered states. Here, we demonstrate experimentally the first elastic analogue of QSHE, by a concise phononic crystal plate with only perforated holes. Strong elastic spin-orbit coupling is realized accompanied by the first topologically-protected phononic circuits with both robustness and negligible propagation loss overcoming many circuit- and system-level performance limits induced by scattering. This elegant approach in a monolithic substrate opens up the possibility of realizing topological materials for phonons in both static and time-dependent regimes, can be immediately applied to multifarious chip-scale devices with both topological protection and massive integration, such as on-chip elastic wave-guiding, elastic splitter, elastic resonator with high quality factor, and even (pseudo-)spin filter.

The asymmetric electron dispersion in type-II Weyl semimetal theoretically hosts anisotropic transport properties. Here we observe the significant anisotropic Adler-Bell-Jackiw (ABJ) anomaly in the Fermi-level delicately adjusted WTe$_{1.98}$ crystals. Quantitatively, $C_w$ , a coefficient representing intensity of ABJ anomaly, along a- and b-axis of WTe$_{1.98}$ are 0.030 and 0.051 T$^{-2}$ at 2 K, respectively. We found that temperature-sensitive ABJ anomaly is attributed to topological phase transition from type-II Weyl semimetal to trivial semimetal, which is verified by first-principles calculation using experimentally determined lattice parameters at different temperatures. Theoretical electrical transport study reveals that observation of ansotropic ABJ both along a- and b-axis in WTe$_{1.98}$ is attributed to electrical transport in the quasi-classical regime. Our work may suggest that electron-doped WTe$_2$ is an ideal playground to explore the novel properties in type-II Weyl semimetals., Comment: 20 pages, 5 figures, 1 table

Recently, the extremely large magnetoresistance observed in transition metal telluride, like WTe$_2$, attracted much attention because of the potential applications in magnetic sensor. Here we report the observation of extremely large magnetoresistance as 3.0$\times$10$^4$ % measured at 2 K and 9 T magnetic field aligned along [001]-ZrSiS. The significant magnetoresistance change (~1.4$\times$10$^4$ %) can be obtained when the magnetic field is titled from [001] to [011]-ZrSiS. These abnormal magnetoresistance behaviors in ZrSiS can be understood by electron-hole compensation and the open orbital of Fermi surface. Because of these superior MR properties, ZrSiS may be used in the novel magnetic sensors., Comment: 18 pages, 5 figures, 21 references

We report an atomic-scale characterization of ZrTe$_5$ by using scanning tunneling microscopy. We observe a bulk bandgap of ~80 meV with topological edge states at the step edge, and thus demonstrate ZrTe$_5$ is a two dimensional topological insulator. It is also found that an applied magnetic field induces energetic splitting and spatial separation of the topological edge states, which can be attributed to a strong link between the topological edge states and bulk topology. The perfect surface steps and relatively large bandgap make ZrTe$_5$ be a potential candidate for future fundamental studies and device applications., Comment: 11 pages, 3 figures

Discovery of novel topological orders of condensed matters is of a significant interest in both fundamental and applied physics due to the associated quantum conductance behaviors and unique symmetry-protected backscattering-immune propagation against defects, which inspired similar fantastic effects in classical waves system, leading to the revolution of the manipulation of wave propagation. To date, however, only few theoretical models were proposed to realize acoustic topological states. Here, we theoretically and experimentally demonstrate a two dimensional acoustic topological insulators with acoustic analogue of quantum spin Hall Effect. Due to the band inversion mechanism near the double Dirac cones, acoustic one-way pseudospin dependent propagating edge states, corresponding to spin-plus and spin-minus, can be observed at the interface between two graphene-like acoustic crystals. We have also experimentally verified the associated topological immunity of such one-way edge states against the different lattice defects and disorders, which can always lead to inherent propagation loss and noise. We show that this unique acoustic topological phenomenon can offer a new promising application platform for the design of novel acoustic devices, such as one-way sound isolators, acoustic mode switchers, splitters, filters etc., Comment: 13 pages, 3 figures

Symmetry-protected photonic topological insulator exhibiting robust pseudo-spin-dependent transportation, analogous to quantum spin Hall (QSH) phases and topological insulators, are of great importance in fundamental physics. Such transportation robustness is protected by time-reversal symmetry. Since electrons (fermion) and photons (boson) obey different statistics rules and associate with different time-reversal operators (i.e., Tf and Tb, respectively), whether photonic counterpart of Kramers degeneracy is topologically protected by bosonic Tb remains unidentified. Here, we construct the degenerate gapless edge states of two photonic pseudo-spins (left/right circular polarizations) in the band gap of a two-dimensional photonic crystal with strong magneto-electric coupling. We further demonstrated that the topological edge states are in fact protected by Tf rather than commonly believed Tb and their pseudo-spin dependent transportation is robust against Tf invariant impurities, discovering for the first time the topological nature of photons. Our results will pave a way towards novel photonic topological insulators and revolutionize our understandings in topological physics of fundamental particles., Comment: 20 pages, 4 figures

Artificial honeycomb lattices with Dirac cone dispersion provide a macroscopic platform to study the massless Dirac quasiparticles and their novel geometric phases. In this paper, a quadruple-degenerate state is achieved at the center of Brillouin zone (BZ) in a two-dimensional honeycomb lattice phononic crystal, which is a result of accidental degeneracy of two double-degenerate states. In the vicinity of the quadruple-degenerate state, the dispersion relation is linear. Such quadruple degeneracy is analyzed by rigorous representation theory of groups. Using method, a reduced Hamiltonian is obtained to describe the linear Dirac dispersion relations of such quadruple-degenerate state, which is well consistent with the simulation results. Near such accidental degeneracy, we observe some unique wave propagating properties, such as defect insensitive propagating character and Talbot effect., Comment: 24 pages, 7 figures and 1 table

We propose an optical counterpart of the quantum spin Hall (QSH) effect in a two-dimensional photonic crystal composed of a gyrotropic medium exhibiting both gyroelectric and gyromagnetic properties simultaneously. Such QSH effect shows unidirectional polarization-dependent transportation of photonic topological edged states, which is robust against certain disorders and impurities. More importantly, we find that such unique property is not protected by conventional time-reversal symmetry of photons obeying the Bosonic statistics but rather by the same symmetry, as electron's time-reversal symmetry. Based on the tight-binding approximation approach, we construct an effective Hamiltonian for this photonic structure, which is shown to have a similar form to that of an electronic QSH system. Furthermore, the invariant of such model is calculated in order to unify its topological non-trivial character. Our finding provides a viable way to exploit the optical topological property, and also can be leveraged to develop a photonic platform to mimic the spin properties of electrons., Comment: 20 pages, 5 figures

We report the design of nonreciprocal resonant transmission/reflection using a one-dimensional photonic crystal (1DPC) adjacent to the magneto-optical (MO) metal film. The nonreciprocal surface modes are found at the interface between the PC and MO metal within the forbidden band of native PC structure. Breaking time-reversal symmetry using external magnetic field gives rise of such unique nonreciprocal properties. Quantitatively understanding of nonreciprocal resonant optical transmission/reflection behavior is performed using an effective admittance-matching theory. With excitation of the nonreciprocal surface modes, light can transmit and be reflected in one-way. Such design offers promising potential in realizing the optical diode.