Valley Hall In-Plane Edge States as Building Blocks for Elastodynamic Logic Circuits

Ma, Jihong; Sun, Kai; Gonella, Stefano

doi:10.1103/physrevapplied.12.044015

Cited by 44 publications

(28 citation statements)

References 46 publications

(82 reference statements)

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“…The QVHE system only requires the formation of a single Dirac degeneracy in the dispersion relation. This Dirac point can be lifted by employing the passive method to form a new bandgap, which can develop the TPES for valley-dependent properties at high symmetry points in the Brillouin region [32][33][34]. Lu et al [29] proposed a bilayer sonic crystal consisting of two-layer rotatable regular triangle scatterers to realize the layer-mixed and layer-polarized topological valley Hall phases.…”

Section: Introductionmentioning

confidence: 99%

Valley Hall Elastic Edge States in Locally Resonant Metamaterials

et al. 2022

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This paper presents a locally resonant metamaterial periodically rearranged as a local resonator, that is hexagonal holes arranged in a thin plate replace the elastic local resonator to achieve the quantum valley Hall effect. Due to the C3v symmetry in the primitive hexagonal lattice, one Dirac point emerges at high symmetry points in the Brillouin zone in the sub-wavelength area. Rotating the beam element of the resonator can break the spatial inversion symmetry to lift the Dirac degeneracy and form a new bandgap. Thus, the band inversion is discovered by computing the relationship between the associated bandgap and the rotational parameter. We also confirmed this result by analyzing the vortex chirality and calculating the Chern number. We can discover two kinds of edge states in the projected band obtained by computing the supercell composed of different topological microstructures. Finally, the propagation behavior in various heterostructures at low frequencies was analyzed. It is shown that these valley Hall elastic insulators can guide elastic waves along sharp interfaces and are immune to backscattering from defects or disorder. By utilizing elastic resonators, a simple reconfigurable topological elastic metamaterial is realized in the sub-wavelength area.

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Section: Introductionmentioning

confidence: 99%

Valley Hall Elastic Edge States in Locally Resonant Metamaterials

et al. 2022

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“…Let n q ∈ Z + (q = 1, Q) collect the "nearby" dispersion branches ω nq (k) traversing the vicinity of (k s , λ1/2 n ), where we aim to pursue ansatz (32). With such setup in mind, we introduce the averaging operators • nq and • nq ρ and the "zero mean" Sobolev space H1 p0 (Y ) as…”

Section: Averaging Operators and Effective Solutionmentioning

confidence: 99%

“…Dynamic homogenization of periodic media such as composites, phononic crystals, and metamaterials serves to (i) deepen insight into the underpinning physical phenomena such as wave directivity, stop bands, and negative refraction [9,21,42], (ii) reduce the burden of multi-scale numerical simulations, and (iii) aid the "microstructural" design catering for applications such us cloaking [15], vibration control [11], logic circuits [32], or seismic shielding [1]. To survey the lay of the land in terms of homogenization strategies, it is generally convenient to distinguish between competing frequency and wavelength regimes.…”

Section: Introductionmentioning

confidence: 99%

On the spectral asymptotics of waves in periodic media with Dirichlet or Neumann exclusions

Oudghiri-Idrissi

Guzina

Meng

2020

Preprint

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We consider homogenization of the scalar wave equation in periodic media at finite wavenumbers and frequencies, with the focus on continua characterized by: (a) arbitrary Bravais lattice in R d , d 2, and (b) exclusions i.e. "voids" that are subject to homogenous (Neumann or Dirichlet) boundary conditions. Making use of the Bloch wave expansion, we pursue this goal via asymptotic ansatz featuring the "spectral distance" from a given wavenumbereigenfrequency pair (situated anywhere within the first Brillouin zone) as the perturbation parameter. We then introduce the effective wave motion via projection(s) of the scalar wavefield onto the Bloch eigenfunction(s) for the unit cell of periodicity, evaluated at the origin of a spectral neighborhood. For generality, we account for the presence of the source term in the wave equation and we consider -at a given wavenumber -generic cases of isolated, repeated, and nearby eigenvalues. In this way we obtain a palette of effective models, featuring both waveand Dirac-type behaviors, whose applicability is controlled by the local band structure and eigenfunction basis. In all spectral regimes, we pursue the homogenized description up to at least first order of expansion, featuring asymptotic corrections of the homogenized Bloch-wave operator and the homogenized source term. Inherently, such framework provides a convenient platform for the synthesis of a wide range of intriguing wave phenomena, including negative refraction and topologically protected states in metamaterials and phononic crystals. The proposed homogenization framework is illustrated by approximating asymptotically the dispersion relationships for (i) Kagome lattice featuring hexagonal Neumann exclusions, and (ii) "pinned" square lattice with circular Dirichlet exclusions. We complete the numerical portrayal of analytical developments by studying the response of a Kagome lattice due to a dipole-like source term acting near the edge of a band gap.

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“…Some of the most interesting phenomena arise at the boundaries of finite domains [17][18][19]. Certain edge properties are conceptually analogous to those observed in electrical or quantum systems, such as topological insulators [20][21][22][23]. Recently, a subclass of Maxwell lattices has been shown to exhibit topological behavior [2,24,25], whereby they posses the ability to localize deformation on one edge of the lattice (denoted as the floppy edge) in the form of zero-frequency floppy modes, while the opposite edge is rigid.…”

mentioning

confidence: 94%

Topological Flexural Modes in Polarized Bilayer Lattices

Charara,

Sun,

Mao

et al. 2021

Preprint

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Topological lattices have recently generated a great deal of interest based on the unique mechanical properties rooted in their topological polarization, including the ability to support localized modes at certain floppy edges. The study of these systems has been predominantly restricted to the realm of in-plane mechanics, to which many topological effects are germane. In this study, we stretch this paradigm by exploring the possibility to export certain topological attributes to the flexural wave behavior of thin lattice sheets. To couple the topological modes to the out-of-plane response, we assemble a bilayer lattice by stacking a thick topological kagome layer onto a thin twisted kagome lattice. The band diagram reveals the existence of modes whose out-of-plane character is controlled by the edge modes of the topological layer, a behavior elucidated via simulations and confirmed via laser vibrometer experiments on a bilayer prototype specimen. These results open a new direction for topological mechanics whereby flexural waves are controlled by the in-plane topology, leading to potential applications for flexural wave devices with engineered polarized response.

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Valley Hall In-Plane Edge States as Building Blocks for Elastodynamic Logic Circuits

Cited by 44 publications

References 46 publications

Valley Hall Elastic Edge States in Locally Resonant Metamaterials

Valley Hall Elastic Edge States in Locally Resonant Metamaterials

On the spectral asymptotics of waves in periodic media with Dirichlet or Neumann exclusions

Topological Flexural Modes in Polarized Bilayer Lattices

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