Non-Hermitian topological states in 2D line-graph lattices: Evolving triple exceptional points on reciprocal line graphs

Non-Hermitian (NH) topological states, such as the doubly-degenerate nodes dubbed as exceptional points (EPs) in Bloch band structure of 2D lattices driven by gain and loss, have attracted much recent interest. We demonstrate theoretically that in the three-site edge-centered lattices, i.e., the so-called line-graph lattices, such as Kagome lattice which is a line graph of hexagonal lattice, there exist three types of triply-degenerate EPs (TEPs) evolving intriguingly on another set of line graphs in the reciprocal space. A single TEP (STEP) with ±1/3 topological charge moves faithfully along the edges of reciprocal line graphs with varying gain and loss, while two STEPs merge distinctively into one unconventional orthogonal double TEP (DTEP) with ±2/3 charge at the vertices, which is characterized with two ordinary self-orthogonal eigenfunctions but one surprising “orthogonal” eigenfunction. Differently, in a modified line-graph lattice with an off-edge-center site, the ordinary coalesced state of DTEPs emerges with three identical self-orthogonal eigenfunctions. Such NH states and their evolution can be generally realized in various artificial systems, such as photonic and sonic crystals, where light and sonic vortex beams with different fractional twisting can be found. Our findings shed new light on fundamental understanding of gapless topological states in NH systems in terms of creation and evolution of high-order EPs, and open up new research directions to further link line graph and flow network theory coupled with topological physics, especially under non-equilibrium gain/loss conditions.

Square-root-like higher-order topological states in three-dimensional sonic crystals

The square-root descendants of higher-order topological insulators were proposed recently, whose topological property is inherited from the squared Hamiltonian. Here we present a three-dimensional (3D) square-root-like sonic crystal by stacking the 2D square-root lattice in the normal (z) direction. With the nontrivial intralayer couplings, the opened degeneracy at the K-H direction induces the emergence of multiple acoustic localized modes, i.e., the extended 2D surface states and 1D hinge states, which originate from the square-root nature of the system. The square-root-like higher order topological states can be tunable and designed by optionally removing the cavities at the boundaries. We further propose a third-order topological corner state in the 3D sonic crystal by introducing the staggered interlayer couplings on each square-root layer, which leads to a nontrivial bulk polarization in the z direction. Our work sheds light on the high-dimensional square-root topological materials, and have the potentials in designing advanced functional devices with sound trapping and acoustic sensing.

Acoustical Study of a Lossy Gradient-Based Sonic Crystal Using Acoustic Beamforming

Sonic crystals (SCs) are unique periodic structures designed to attenuate acoustic waves in tunable frequency bands known as bandgaps. Though previous works on conventional uniform SCs show good insertion loss (IL) inside the bandgaps, this work is focused on widening their bandgaps and achieving better IL inside the bandgaps by using a gradient-based sonic crystal (GBSC). The GBSC applies property gradient to the conventional SC array by varying its basic properties, i.e., the distance between the scatterers/resonators (lattice constant), and resonator dimensions between the columns and hence the name GBSC. The design of the GBSC is backed by the results of acoustic beamforming experiments conducted over the uniform SCs of hollow scatterers and Helmholtz resonators (HRs) having two-dimensional (2D) periodicity prepared by using Polyvinyl chloride (PVC) pipes without any property gradient and their respective 2D finite element (FE) studies. The experimental and FE simulation results of the uniform SCs were found to be in good agreement and therefore, the GBSC was modeled and analyzed using FE method considering the viscothermal losses inside the resonators. The results indicated that the property gradient improves both Bragg scattering and Helmholtz resonance compared to that of the uniform SCs and therefore, the GBSC exhibits wider attenuation gaps and higher attenuation levels. An array of 30 microphones was used to conduct acoustic beamforming experiments on the uniform SCs. Beamforming was found to be an advanced and fast method to perform quick measurements on the SCs.

Pseudospin-dependent Acoustic Topological Insulator by Sonic Crystals With Same Hexagonal Rods

We report the experimental and numerical realization of a pseudospin-dependent acoustic topological insulator based on two sonic crystals constructed by the same regular hexagonal rods. Based on the zone folding mechanism, we obtain double Dirac cones with a four-fold deterministic degeneracy in the sonic crystal, and realize a band inversion and topological phase transition by rotating the rods. We observe the topologically protected one-way sound propagation of pseudospin-dependent edge states in a designed topological insulator composed of two selected sonic crystals with different rotation angles of the rods. Furthermore, we experimentally demonstrate the robustness of topological sound propagation against two types of defects, in which the edge states are almost immune to backscattering, and remain pseudospin-dependent characteristics. Our work provides a diverse route for designing tunable topological functional sound devices.

Valley Vortex Assisted and Topological Protected Microparticles Manipulation with Complicated 2D Patterns in a Star-Like Sonic Crystal

Arranging microparticles into desired patterns, especially in a complicated pattern with a reliable and tunable manner, is challenging but highly desirable in the fields such as biomedicine and tissue engineering. To overcome these limitations, here, by using the concept of topology in acoustics, the valley vortex is utilized to manipulate particles on a large scale with complicated 2D patterns in the star-like sonic crystals at different frequencies. A topologically protected edge state is obtained at the interface of the crystals with different valley Hall phases, which shows the ability of reliable microparticles control along the sharp corner and the capability of robust particles cluster aggregation in a defective system. The results may provide intriguing resources for future microfluidic systems in a complicated and brittle environment.

Analysis of the interaction of helmholtz resonators in periodic acoustic metamaterials depending on its orientation with the acoustic source.

Acoustic screens based on sonic crystals constitute one of the most promising technological bets of recent years in the field of environmental acoustics. Sonic crystals are defined as new materials formed by arrays of acoustic scatterers embedded in air. The design of these screens is made using powerful simulation models that provide reliable results without the need of expensive experimental testing. This project applies the finite elements method in order to analise an acoustic barrier that includes (Helmholtz) resonators in its scatterers, and studies the interference of the sonic crystal with the effect of the Helmholtz resonator, depending on its orientation with the acoustic source.