Acoustic Lattice Research Articles

Topological edge states on the acoustic Mobius band

Mobius molecules, such as Mobius annulenes and cyclacenes, are commonly existed in nature, which are usually classified and assembled by different twist numbers, and display discrepant Mobius topology and rich configurations. However, the Mobius geometries in acoustic crystals have rarely been investigated, as well as their topological effects. Here, we propose acoustic lattices on Mobius band with different configurations, where the topological edge states propagating in three-dimensional (3D) trajectories are clearly observed. These Mobius geometries can exhibit one or two integrated channels and display great robustness for guiding sound waves. The mapping between Mobius topology and lattice symmetries are also given for studying the in-gapped edge states by band dispersions. Our results provide a route to flexibly mimic the Mobius molecules by curved lattices and may inspire further research on, e.g., topological phenomena for classical waves in Mobius or other curved geometries.

Defect-controlled topological edge states in the curved acoustic lattices

The concept of disclinations and dislocations, which are related to the real-space topology, have been widely studied in crystal materials. In two-dimensional (2D) materials, disclinations lead to the warping and deformation of the hosting material, yielding non-Euclidean geometries. However, such geometries have not been linked to the effects of topological edge states. Here we construct the curved waveguide paths by disclinations in the C 3 symmetric valley acoustic crystals with the non-Euclidean geometries. We then discuss the topological edge states as well as the curved waveguide modes in different defect-constructed structures. Simulation results show that the topological waveguide modes can be controlled not only by the alignment of topologically different valley acoustic crystals, but also by the edge dislocation. Our work may provide a route to study new exotic phenomena related to topological defects in non-Euclidean geometries and metamaterials.

Padé-Based Strain Gradient Modeling of Bandgaps in Two-Dimensional Acoustic Lattice Metamaterials

A strain gradient (SG) continuum theory of two-dimensional (2D) lattice metamaterials based on Padé approximation has been proposed, called PSGM hereafter, to predict their acoustic dispersion characteristics. Square and triangular elastic lattices have been investigated for a demonstrating purpose. By applying Padé approximation to the Taylor expansion of displacement field, the fourth- and eighth-order SG continuum models are established. The dispersion relations obtained by the proposed model are examined by comparing with the results by discrete analyses as well as existing SG theories. It is confirmed that the proposed theory is always more accurate than the existing SG counterpart with the same SG order. Furthermore, the present formulation is free of any unrealistic instability issue in dispersion, which has challenged the existing SG theories. The results also show that the accuracy of PSGM will be enhanced with increasing SG orders. Within the present parameter settings, it can be found that the eighth-order PSGM can successfully capture the dispersive properties of both lattices throughout the first irreducible Brillouin zone.

Generation of 2D and 3D acoustic lattices in midair using polygonal active diffraction gratings

This paper presents a method to generate two- and three-dimensional periodic or quasi-periodic acoustic lattices in air using polygonal active diffraction gratings. The radiated field depends on design parameters and is well predictable in terms of a superposition of oblique plane waves, with very good agreement with simulations and experiments. Our device represents a simple and efficient approach for producing acoustic lattices with attractive advantages, such as planar single-sided geometry, simple electronics, axial steering, and broadband operation. The design is scalable and compatible with other scientific applications, such as microfluidic platforms.

Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice

We present a one-dimensional coupled ring resonator lattice exhibiting a variant of the non- Hermitian skin effect (NHSE) that we call the anomalous Floquet NHSE. Unlike existing approaches to achieving the NHSE by engineering gain and loss on different ring segments, our design uses fixed on-site gain or loss in each ring. The anomalous Floquet NHSE is marked by the existence of skin modes at every value of the Floquet quasienergy, allowing for broadband asymmetric transmission. Varying the gain/loss induces a non-Hermitian topological phase transition, reversing the localization direction of the skin modes. An experimental implementation in an acoustic lattice yields good agreement with theoretical predictions, with a very broad relative bandwidth of around 40%.

Synthetic Pseudo-Spin-Hall effect in acoustic metamaterials

While vector fields naturally offer additional degrees of freedom for emulating spin, acoustic pressure field is scalar in nature, and it requires engineering of synthetic degrees of freedom by material design. Here we experimentally demonstrate the control of sound waves by using two types of engineered acoustic systems, where synthetic pseudo-spin emerges either as a consequence of the evanescent nature of the field or due to lattice symmetry. First, we show that evanescent sound waves in perforated films possess transverse angular momentum locked to their propagation direction which enables their directional excitation. Second, we demonstrate that lattice symmetries of an acoustic kagome lattice also enable a synthetic transverse pseudo-spin locked to the linear momentum, enabling control of the propagation of modes both in the bulk and along the edges. Our results open a new degree of control of radiation and propagation of acoustic waves thus offering new design approaches for acoustic devices.

High frequency homogenization for a one-dimensional acoustic black hole lattice

A hybrid theoretical framework was developed to understand the wave propagation properties of acoustic black hole (ABH) lattices, based on a combination of WKB theory and the high-frequency homogenization method. Explicit approximate expressions were obtained for the associated dispersion curves. Firstly, a matrix formulation to model wave propagation in a one-dimensional lattice was developed, where the wave components of the flexural displacement were described as WKB solutions of the flexural wave equation. The standing wave frequencies and the corresponding wave shape functions required by the high-frequency homogenization analysis were obtained accordingly. Secondly, the effective dispersion relation of the ABH lattice was obtained analytically by utilizing high-frequency homogenization. Based on the dispersion results obtained from the hybrid framework, the group velocity and hence the modal density of the ABH lattice were obtained analytically. Finally, the proposed technique was validated through several numerical examples.

Higher-order topological phase in an acoustic fractal lattice

We introduce fractality into a square lattice, and uncovered a squeezed higher-order phase diagram featuring abundant corner states, which include zero-dimensional outer corner states and 1.89 dimensional inner corner states. The calculated fractional charges at the outer/inner corners indicates that all corner states in the fractional system are indeed topological nontrivial. Finally, in a fabricated fractal lattice, we experimentally observe the outer/inner corner states with local acoustic measurements.

Reversible topological non-reciprocity by positive–negative Poisson's ratio switch in chiral metamaterials

Topological non-reciprocity provides a robust approach to control the wave field. To realize reversible topological non-reciprocity in chiral metamaterials, researchers usually rely on reversing angular momentum bias of the circulation flow, time reversing the spatiotemporal modulation, and so on. Here, we demonstrate that switching Poisson's ratio from positive to negative can reverse the topological non-reciprocity by mechanically stretching and compressing a chiral acoustic metamaterial. We find that the positive–negative switch of Poisson's ratio is associated with the topological phase transition of the acoustic lattice, which is manifested as the reversed propagation of topological edge modes. The reversed topological non-reciprocity of metamaterials is attributed to the transmission switch of the three-port chiral unit. Finally, we propose a design of topological wave splitters, in which transmission directions are adjusted by the Poisson's ratio of the device. Our results indicate that the Poisson's ratio of metamaterials can introduce peculiar topological properties and bring potential applications for wave isolators, modulators, and circulators.

Higher-order topological phases on fractal lattices

Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well characterized by now, their presence in fractional dimensions remains vastly unexplored. Here, we theoretically show that a special class of crystalline phases, namely, higher-order topological phases that via an extended bulk-boundary correspondence feature robust gapless modes on lower dimensional boundaries, such as corners and hinges, can be found on a representative family of fractional materials: \emph{quantum fractals}. To anchor this general proposal, we demonstrate realizations of second-order topological insulators and superconductors, supporting charged and neutral Majorana corner modes, on planar Sierpi\'{n}ski carpet and triangle fractals, respectively. These predictions can be experimentally tested on designer electronic fractal materials, as well as on various highly tunable metamaterial platforms, such as photonic and acoustic lattices.

Observation of Degenerate Zero-Energy Topological States at Disclinations in an Acoustic Lattice.

Building upon the bulk-boundary correspondence in topological phases of matter, disclinations have recently been harnessed to trap fractionally quantized density of states (DOS) in classical wave systems. While these fractional DOS have associated states localized to the disclination's core, such states are not protected from deconfinement due to the breaking of chiral symmetry, generally leading to resonances which, even in principle, have finite lifetimes and suboptimal confinement. Here, we devise and experimentally validate in acoustic lattices a paradigm by which topological states bind to disclinations without a fractional DOS but which preserve chiral symmetry. The preservation of chiral symmetry pins the states at the midgap, resulting in their protected maximal confinement. The integer DOS at the defect results in twofold degenerate states that, due to symmetry constraints, do not gap out. Our study provides a fresh perspective about the interplay between symmetry protection in topological phases and topological defects, with possible applications in classical and quantum systems alike.

Multi-stable acoustic metamaterials with re-configurable mass distribution

This article proposes a design strategy for acoustic metamaterial lattices which leverages the characteristic multi-stability and kinematic amplification of the internal architecture to realize a re-configurable effective mass distribution, enabling a corresponding frequency band structure of extreme tunability. The approach builds metamaterial lattices from bi-stable elastic elements featuring the typical two-bar inertial amplification mechanism, whose deformation axis is uniquely misaligned with that of its elastic support such that the realized amplification is configuration-specific. Conveniently, a change in the configuration does not simultaneously alter the element dimensions and, therefore, the size/shape of the finite metamaterial structure remains constant. Moreover, as the multi-stability and kinematic amplification are each based on geometry, scaling the resulting metamaterial structure is expected to be straightforward. The dynamic performance of 1D/2D metamaterial architectures exhibiting the proposed design strategy is analytically determined via Bloch wave analysis and supported by numerical demonstration of the corresponding finite structures.

Exact strain gradient modelling of prestressed nonlocal diatomic lattice metamaterials

In this article, an exact strain gradient (SG) continuum model to capture the broadband bandgap characteristics of the prestressed diatomic lattice (PDL) with local/nonlocal interactions has been proposed. By considering the periodicity of wave motion, the wavelength-dependent Taylor expansion is established, leading to a desirable prediction when the wavelength is close to the lattice scale. For PDL, the dispersion curves of the proposed continuum model are always consistent with those of discrete model in the first Brillouin zone. The proposed SG continuum model is used to investigate the effects of structural parameters, orders of SG continua and various nonlocal interactions on bandgap properties of PDL. Highlights Continuum modelling of prestressed acoustic diatomic lattices. Perfect agreements achieved between dispersion diagrams by discrete and proposed continuum models. Effects of prestress, nonlocal interactions, mass and stiffness ratios on band gap structures analyzed. Proper strain gradient (SG) orders determined to guarantee a satisfactory accuracy.

Harmonic acoustics for dynamic and selective particle manipulation.

Precise and selective manipulation of colloids and biological cells has long been motivated by applications in materials science, physics and the life sciences. Here we introduce our harmonic acoustics for a non-contact, dynamic, selective (HANDS) particle manipulation platform, which enables the reversible assembly of colloidal crystals or cells via the modulation of acoustic trapping positions with subwavelength resolution. We compose Fourier-synthesized harmonic waves to create soft acoustic lattices and colloidal crystals without using surface treatment or modifying their material properties. We have achieved active control of the lattice constant to dynamically modulate the interparticle distance in a high-throughput (>100 pairs), precise, selective and reversible manner. Furthermore, we apply this HANDS platform to quantify the intercellular adhesion forces among various cancer cell lines. Our biocompatible HANDS platform provides a highly versatile particle manipulation method that can handle soft matter and measure the interaction forces between living cells with high sensitivity.

Projectively Enriched Symmetry and Topology in Acoustic Crystals.

Symmetry plays a key role in modern physics, as manifested in the revolutionary topological classification of matter in the past decade. So far, we seem to have a complete theory of topological phases from internal symmetries as well as crystallographic symmetry groups. However, an intrinsic element, i.e., the gauge symmetry in physical systems, has been overlooked in the current framework. Here, we show that the algebraic structure of crystal symmetries can be projectively enriched due to the gauge symmetry, which subsequently gives rise to new topological physics never witnessed under ordinary symmetries. We demonstrate the idea by theoretical analysis, numerical simulation, and experimental realization of a topological acoustic lattice with projective translation symmetries under a Z_{2} gauge field, which exhibits unique features of rich topologies, including a single Dirac point, Möbius topological insulator, and graphenelike semimetal phases on a rectangular lattice. Our work reveals the impact when gauge and crystal symmetries meet together with topology and opens the door to a vast unexplored land of topological states by projective symmetries.

Observing localization and delocalization of the flat-band states in an acoustic cubic lattice

Over the past decades, wave localization and a wide variety of related phenomena have come to the forefront of research. Here, we theoretically and experimentally investigate the localization and delocalization of the flat-band states in an acoustic cubic lattice. Under evanescent couplings, the band structure of the designed cubic lattice has two dispersive bands and two degenerate flat bands. According to the analyses, we find that the constructions of flat-band states only depend on the excitation pressures and the coupling coefficients, which are frequency independent. With the flat-band state excitation, the acoustic wave can be either localized or delocalized in the lattice, which is determined by the excitation frequency. When the excitation frequency is close to the flat-band frequency of the lattice, the flat-band state can spread into the whole cubic lattice due to the resonance energy transfer among primitive cells. On the other hand, when the excitation frequency deviates from the flat-band frequency, the flat-band state can be localized in any primitive cell of the designed lattice. This work lays the groundwork for exploring the high-dimensional bound states in acoustic systems and has potential impacts on the applications of acoustic sensing and sound energy harvesting.

Type-II Weyl points in a synthetic three-dimensional acoustic lattice

We propose to realize type-II Weyl points in a one-dimensional Aubry–Andre–Harper model with cosine modulation in both hopping and on-site terms, which together form a synthetic three-dimensional parameter space. By constructing a one-dimensional acoustic lattice comprising multiple coupled cavities with two adjustable structural parameters, we implement the acoustical analogue of the type-II Weyl semimetal. Good agreement is observed between the theoretical predictions and numerical simulations, with both displaying the tilted dispersion and Fermi arc. Our study enables the exploration of high-dimensional topological physics by constructing a low-dimensional physical system and may open up possibilities for the design of novel acoustic devices.

Time-periodic corner states from Floquet higher-order topology

The recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, previously limited to topological states at boundaries of materials, to include topological states at boundaries of boundaries, such as corners. So far, all HOTI realisations have been based on static systems described by time-invariant Hamiltonians, without considering the time-variant situation. There is growing interest in Floquet systems, in which time-periodic driving can induce unconventional phenomena such as Floquet topological phases and time crystals. Recent theories have attempted to combine Floquet engineering and HOTIs, but there has been no experimental realisation so far. Here we report on the experimental demonstration of a two-dimensional (2D) Floquet HOTI in a three-dimensional (3D) acoustic lattice, with modulation along a spatial axis serving as an effective time-dependent drive. Acoustic measurements reveal Floquet corner states with double the period of the underlying drive; these oscillations are robust, like time crystal modes, except that the robustness arises from topological protection. This shows that space-time dynamics can induce anomalous higher-order topological phases unique to Floquet systems.

On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model

We have proposed an “exact” strain gradient (SG) continuum model to properly predict the dispersive characteristics of diatomic lattice metamaterials with local and nonlocal interactions. The key enhancement is proposing a wavelength-dependent Taylor expansion to obtain a satisfactory accuracy when the wavelength gets close to the lattice spacing. Such a wavelength-dependent Taylor expansion is applied to the displacement field of the diatomic lattice, resulting in a novel SG model. For various kinds of diatomic lattices, the dispersion diagrams given by the proposed SG model always agree well with those given by the discrete model throughout the first Brillouin zone, manifesting the robustness of the present model. Based on this SG model, we have conducted the following discussions. (I) Both mass and stiffness ratios affect the band gap structures of diatomic lattice metamaterials, which is very helpful for the design of metamaterials. (II) The increase in the SG order can enhance the model performance if the modified Taylor expansion is adopted. Without doing so, the higher-order continuum model can suffer from a stronger instability issue and does not necessarily have a better accuracy. The proposed SG continuum model with the eighth-order truncation is found to be enough to capture the dispersion behaviors all over the first Brillouin zone. (III) The effects of the nonlocal interactions are analyzed. The nonlocal interactions reduce the workable range of the well-known long-wave approximation, causing more local extrema in the dispersive diagrams. The present model can serve as a satisfactory continuum theory when the wavelength gets close to the lattice spacing, i.e., when the long-wave approximation is no longer valid. For the convenience of band gap designs, we have also provided the design space from which one can easily obtain the proper mass and stiffness ratios corresponding to a requested band gap width.

Diagrammatic quantum Monte Carlo study of an acoustic lattice polaron

We present a diagrammatic Monte Carlo study of a lattice polaron interacting with an acoustic phonon branch through the deformation potential. Weak and strong coupling regimes are separated by a self-trapping region where quantum resonance between various possible lattice deformations is seen in the ground-state properties, spectral function, and optical conductivity. This study shows that the acoustic lattice polaron represents a distinct quantum object with unique features, markedly different from any previously considered polaron model. In particular, the acoustic lattice polaron exhibits an interplay between long- and short wavelength acoustic vibrations, resulting in a composite phonon cloud which leads to the formation of multiple competing polaron states with a complex spectral response.