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

2021 ◽  
Author(s):  
Zhiguo Geng ◽  
Huanzhao Lv ◽  
Zhan Xiong ◽  
Yu-Gui Peng ◽  
Zhaojiang Chen ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Surface States ◽  
Higher Order ◽  
Square Root ◽  
Root Lattice ◽  
Third Order ◽  
Topological Materials ◽  
Topological States ◽  
Sonic Crystal ◽  
Sonic Crystals

Abstract 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.

scholarly journals Demonstration of a third-order hierarchy of topological states in a three-dimensional acoustic metamaterial

2020 ◽  
Vol 6 (13) ◽  
pp. eaay4166 ◽  
Author(s):  
Matthew Weiner ◽  
Xiang Ni ◽  
Mengyao Li ◽  
Andrea Alù ◽  
Alexander B. Khanikaev
Keyword(s):  
Three Dimensional ◽  
Surface States ◽  
Three Dimensions ◽  
Dimensional System ◽  
Edge States ◽  
Third Order ◽  
Acoustic Metamaterial ◽  
Boundary States ◽  
Topological States ◽  
Quantum Phenomena

Classical wave systems have constituted an excellent platform for emulating complex quantum phenomena, such as demonstrating topological phenomena in photonics and acoustics. Recently, a new class of topological states localized in more than one dimension of a D-dimensional system, referred to as higher-order topological (HOT) states, has been reported, offering an even more versatile platform to confine and control classical radiation and mechanical motion. Here, we design and experimentally study a 3D topological acoustic metamaterial supporting third-order (0D) topological corner states along with second-order (1D) edge states and first-order (2D) surface states within the same topological bandgap, thus establishing a full hierarchy of nontrivial bulk polarization–induced states in three dimensions. The assembled 3D topological metamaterial represents the acoustic analog of a pyrochlore lattice made of interconnected molecules, and is shown to exhibit topological bulk polarization, leading to the emergence of boundary states.

scholarly journals Dirac points and the transition towards Weyl points in three-dimensional sonic crystals

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Boyang Xie ◽  
Hui Liu ◽  
Hua Cheng ◽  
Zhengyou Liu ◽  
Jianguo Tian ◽  
...  
Keyword(s):  
Dirac Point ◽  
Three Dimensional ◽  
Surface States ◽  
Interface States ◽  
Band Inversion ◽  
Sonic Crystal ◽  
Topological Semimetals ◽  
Sonic Crystals ◽  
Physical Phenomena ◽  
Topological Matter

AbstractA four-fold-degenerate three-dimensional (3D) Dirac point, represents a degenerate pair of Weyl points carrying opposite chiralities. Moreover, 3D Dirac crystals have shown many exotic features different from those of Weyl crystals. How these features evolve from 3D Dirac to Weyl crystals is important in research on 3D topological matter. Here, we realized a pair of 3D acoustic Dirac points from band inversion in a hexagonal sonic crystal and observed the surface states and helical interface states connecting the Dirac points. Furthermore, each Dirac point can transition into a pair of Weyl points with the introduction of chiral hopping. The exotic features of the surface states and interface states are inherited by the resulting Weyl crystal. Our work may serve as an ideal platform for exploring exotic physical phenomena in 3D topological semimetals.

scholarly journals Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
Xiujuan Zhang ◽  
Bi-Ye Xie ◽  
Hong-Fei Wang ◽  
Xiangyuan Xu ◽  
Yuan Tian ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Surface States ◽  
Higher Order ◽  
Order Topology ◽  
Wave Trapping ◽  
One Dimensional ◽  
Wave Dynamics ◽  
Future Technology ◽  
Integration Density ◽  
Sonic Crystals

AbstractWave trapping and manipulation are at the heart of modern integrated photonics and acoustics. Grand challenges emerge on increasing the integration density and reducing the wave leakage/noises due to fabrication imperfections, especially for waveguides and cavities at subwavelength scales. The rising of robust wave dynamics based on topological mechanisms offers possible solutions. Ideally, in a three-dimensional (3D) topological integrated chip, there are coexisting robust two-dimensional (2D) interfaces, one-dimensional (1D) waveguides and zero-dimensional (0D) cavities. Here, we report the experimental discovery of such a dimensional hierarchy of the topologically-protected 2D surface states, 1D hinge states and 0D corner states in a single 3D system. Such an unprecedented phenomenon is triggered by the higher-order topology in simple-cubic sonic crystals and protected by the space group $${P}_{m\bar{3}m}$$Pm3 ¯m. Our study opens up a new regime for multidimensional wave trapping and manipulation at subwavelength scales, which may inspire future technology for integrated acoustics and photonics.

Vibroacoustic Comparisons and Acoustic Power Insulation Mechanisms of Multidirectional Stiffened Laminated Plates

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Xiongtao Cao ◽  
Hongxing Hua
Keyword(s):  
Fourier Transform ◽  
High Efficiency ◽  
Three Dimensional ◽  
Acoustic Power ◽  
Higher Order ◽  
Laminated Plates ◽  
Transverse Displacement ◽  
Third Order ◽  
First Order ◽  
Implicit Equations

Vibroacoustic characteristics of multidirectional stiffened laminated plates with or without compliant layers are explored in the wavenumber and spatial domains with the help of the two-dimensional continuous Fourier transform and discrete inverse fast Fourier transform. Implicit equations of motion for the arbitrary angle ply laminated plates are derived from the three-dimensional higher order and Reddy third order shear deformation plate theories. The expressions of acoustic power of the stiffened laminated plates with or without complaint layers are formulated in the wavenumber domain, which is a significant method to calculate acoustic power of the stiffened plates with multiple sets of cross stiffeners. Vibroacoustic comparisons of the stiffened laminated plates are made in terms of the transverse displacement spectra, forced responses, acoustic power, and input power according to the first order, Reddy third order, and three-dimensional higher order plate theories. Sound reduction profiles of compliant layers are further examined by the theoretical deductions. This study shows the feasibility and high efficiency of the first order and Reddy third order plate theories in the broad frequency range and allows a better understanding the principal mechanisms of acoustic power radiated from multidirectional stiffened laminated composite plates with compliant layers, which has not been adequately addressed in its companion paper. (Cao and Hua, 2012, “Sound Radiation From Shear Deformable Stiffened Laminated Plates With Multiple Compliant Layers,” ASME J. Vib. Acoust., 134(5), p. 051001.)

scholarly journals Three-Dimensional Topological States of Phonons with Tunable Pseudospin Physics

Research ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-8 ◽  
Author(s):  
Yizhou Liu ◽  
Yong Xu ◽  
Wenhui Duan
Keyword(s):  
Degrees Of Freedom ◽  
Three Dimensional ◽  
Surface States ◽  
Phonon Transport ◽  
Efficient Control ◽  
Topological States ◽  
Topological Surface ◽  
Symmetry Protected ◽  
Energy Information ◽  
Crystalline Symmetry

Efficient control of phonons is crucial to energy-information technology, but limited by the lacking of tunable degrees of freedom like charge or spin. Here we suggest to utilize crystalline symmetry-protected pseudospins as new quantum degrees of freedom to manipulate phonons. Remarkably, we reveal a duality between phonon pseudospins and electron spins by presenting Kramers-like degeneracy and pseudospin counterparts of spin-orbit coupling, which lays the foundation for “pseudospin phononics”. Furthermore, we report two types of three-dimensional phononic topological insulators, which give topologically protected, gapless surface states with linear and quadratic band degeneracies, respectively. These topological surface states display unconventional phonon transport behaviors attributed to the unique pseudospin-momentum locking, which are useful for phononic circuits, transistors, antennas, etc. The emerging pseudospin physics offers new opportunities to develop future phononics.

scholarly journals Time-periodic corner states from Floquet higher-order topology

2022 ◽  
Vol 13 (1) ◽  
Author(s):  
Weiwei Zhu ◽  
Haoran Xue ◽  
Jiangbin Gong ◽  
Yidong Chong ◽  
Baile Zhang
Keyword(s):  
Three Dimensional ◽  
Higher Order ◽  
Topological Phases ◽  
Time Dynamics ◽  
Topological States ◽  
Acoustic Lattice ◽  
Static Systems ◽  
Time Invariant ◽  
Time Periodic ◽  
Spatial Axis

AbstractThe 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.

scholarly journals Three-dimensional higher-order topological acoustic system with multidimensional topological states

2020 ◽  
Vol 102 (10) ◽  
Author(s):  
Shengjie Zheng ◽  
Baizhan Xia ◽  
Xianfeng Man ◽  
Liang Tong ◽  
Junrui Jiao ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Higher Order ◽  
Acoustic System ◽  
Topological States

scholarly journals Three-dimensional acetylenic modified graphene for high-performance optoelectronics and topological materials

2021 ◽  
Vol 7 (1) ◽  
Author(s):  
Yan Gao ◽  
Chengyong Zhong ◽  
Shengyuan A. Yang ◽  
Kai Liu ◽  
Zhong-Yi Lu
Keyword(s):  
High Performance ◽  
Materials Science ◽  
Three Dimensional ◽  
3D Graphene ◽  
Graphene Layers ◽  
Carbon Allotropes ◽  
Topological Materials ◽  
Topological States ◽  
Direct Band ◽  
Modified Graphene

AbstractSeeking carbon phases with versatile properties is one of the fundamental goals in physics, chemistry, and materials science. Here, based on the first-principles calculations, a family of three-dimensional (3D) graphene networks with abundant and fabulous electronic properties, including rarely reported dipole-allowed truly direct band gap semiconductors with suitable band gaps (1.07–1.87 eV) as optoelectronic/photovoltaic materials and topological nodal-ring semimetals, are proposed through stitching different graphene layers with acetylenic linkages. Remarkably, the optical absorption coefficients in some of those semiconducting carbon allotropes express possibly the highest performance among all of the semiconducting carbon phases known to date. On the other hand, the topological states in those topological nodal-ring semimetals are protected by the time-reversal and spatial symmetry and present nodal rings and nodal helical loops topological patterns. Those newly revealed carbon phases possess low formation energies and excellent thermodynamic stabilities; thus, they not only host a great potential in the application of optoelectronics, photovoltaics, and quantum topological materials etc., but also can be utilized as catalysis, molecule sieves or Li-ion anode materials and so on. Moreover, the approach used here to design novel carbon allotropes may also give more enlightenments to create various carbon phases with different applications.

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