Topological helical edge states in water waves over a topographical bottom

Wu, Shiqiao; Wu, Ying; Mei, Jun

doi:10.1088/1367-2630/aa9cdb

Cited by 27 publications

(13 citation statements)

References 42 publications

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“…The derivation can be readily generalized to other mechanical TIs with discrete elements [17,52], possibly with dissipation [53] and forcing [30] included. Further extensions may include TIs in continuous media that can exhibit significant nonlinearity, such as recent proposals based on magnetic solitons [54] and water waves [55]. The existence of TPES in both photonic and phononic TIs may have significant impacts on practical applications such as optical and acoustic delay lines [56,57] and robust manipulation of light and sound [58,59] The Supplementary material here is organized into four sections and accompanying films for the bright and dark soliton simulations.…”

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confidence: 99%

Edge solitons in a nonlinear mechanical topological insulator

Snee

2019

Extreme Mechanics Letters

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We report localized and unidirectional nonlinear traveling edge waves discovered theoretically and numerically in a 2D mechanical (phononic) topological insulator. The lattice consists of a collection of pendula with weak Duffing nonlinearity connected by linear springs. We show that the classical 1D nonlinear Schrödinger equation governs the envelope of 2D edge modes, and study the propagation of traveling waves and rogue waves in 1D as edge solitons in 2D. As a result of topological protection, these edge solitons persist over long time intervals and through irregular boundaries.Topological insulators (TIs) are a unique state of matter with behavior that has significant ramifications in the fields of both condensed matter physics and optics. The importance of TIs has been established in the condensed matter community for almost a decade, with extensive literature on both one-dimensional and multidimensional systems [1][2][3]. The one stand out property of TIs which holds the ongoing interest in the topic is that a clear dichotomy exists between the edge (surface) and the bulk of the material as electrons are conducted only on the edge whilst the bulk is insulating. The existence of such edge states at the interface between two bulk materials with different topological invariants is guaranteed by the principle of bulk-edge correspondence [4,5]. More recently, the theoretical framework underlying quantum TIs has been generalized to photonic systems governed by classical electromagnetic fields [6][7][8]. In analogy to electrons in traditional TIs, electromagnetic waves in photonic TIs propagate along the edge with very little backscattering, even in the presence of disorders such as missing site(s) on the edge of a photonic lattice [9][10][11].The emerging field of topological mechanics utilizes such topological principles to reveal new collective excitations in classical mechanical (phononic) systems [12,13]. These topological acoustic metamaterials can be classified into two families depending on whether the topological edge modes appear at zero frequency or high frequencies. In the zero frequency case, these edge modes are identified as floppy modes and self-stress states in Maxwell frames [14]. Here we focus on the high frequency case, where topologically protected transport via phonons is enabled. Seminal work in this direction includes analogues of the quantum Hall effect using a lattice of hanging gyroscopes [15], and the quantum spin Hall effect (QSHE) using a lattice of coupled pendula [16] and bi-layered lattices of disks and springs [17].Over the last century, the theory of nonlinear waves in continuous systems has formed a cornerstone of nonlinear science [18]. A fundamental result is that in such systems, dispersion can balance with nonlinearity to produce robust localized nonlinear traveling waves known as solitons. The theory of nonlinear waves in discrete systems has flourished more recently, especially in the context of nonlinear optics and Bose-Einstein condensates [19]. In mechanical lattices, t...

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confidence: 99%

Edge solitons in a nonlinear mechanical topological insulator

Snee

2019

Extreme Mechanics Letters

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“…An alternative strategy to emulate acoustic pseudospin is to exploit the symmetry of a crystal lattice, in which case C is some sort of crystalline symmetry operation. Such a scheme, based on six-fold rotational symmetry, was initially proposed by Wu and Hu in 2015 in a triangular lattice of hexagonal resonators [191], and implemented in a variety of platforms including microwaves [192], photonics [193][194][195][196][197], elastic [198][199][200][201] and acoustics [202][203][204][205]. Figure 1k and 1l show an example [205] that employed this strategy to induce a deeply subwavelength acoustic topological edge mode in a subwavelength sonic crystal made of Helmholtz resonators (simple soda cans) arranged in a modified hexagonallike lattice.…”

Section: Z 2 Wave Insulatorsmentioning

confidence: 99%

Topological wave insulators: a review

Zangeneh-Nejad¹,

Alù²,

Fleury³

2020

Comptes Rendus. Physique

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Originally discovered in condensed matter systems, topological insulators (TIs) have been ubiquitously extended to various fields of classical wave physics including photonics, phononics, acoustics, mechanics, and microwaves. In the bulk, like any other insulator, electronic TIs exhibit an excessively high resistance to the flow of mobile charges, prohibiting metallic conduction. On their surface, however, they support one-way conductive states with inherent protection against certain types of disorder and defects, defying the common physical wisdom of electronic transport in presence of impurities. When transposed to classical waves, TIs open a wealth of exciting engineering-oriented applications, such as robust routing, lasing, signal processing, switching, etc., with unprecedented robustness against various classes of defects. In this article, we first review the basic concept of topological order applied to classical waves, starting from the simple onedimensional example of the Su-Schrieffer-Heeger (SSH) model. We then move on to two-dimensional wave TIs, discussing classical wave analogues of Chern, quantum Hall, spin-Hall, Valley-Hall, and Floquet TIs. Finally, we review the most recent developments in the field, including Weyl and nodal semimetals, higherorder topological insulators, and self-induced non-linear topological states.

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“…Soon, people realized that similar phenomena are not restricted to quantum systems, and nontrivial topology can also bring exciting phenomena and results in classical wave systems. Recently, classical analogs of QSH and QVH insulators were predicted and verified both theoretically and experimentally in electromagnetic [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18], acoustic [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], elastic [34][35][36][37][38][39][40][41][42][43], and even water surface wave systems [44]. Very recently, robust and high-capacity phononic communications were realized in the context of Lamb waves through topological edge states by multiplexing the pseudospin and valley indices [43].…”

Section: Introductionmentioning

confidence: 99%

Acoustic topological devices based on emulating and multiplexing of pseudospin and valley indices

Gao

Mei

2020

New J. Phys.

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We present a design paradigm for acoustic devices in which robust and controllable transport of wave signals can be realized. These devices are based on a simple acoustic platform, where different topological phases such as acoustic quantum spin Hall and quantum valley Hall insulators are emulated by engineering the spatial symmetries of the structure. Edge states along interfaces between different topological phases are shown to be promising information channels, where the multiplexing of pseudospin and/or valley degrees of freedom is unambiguously demonstrated in various devices including a multiport valve for acoustic power dividing and feeding. The information capacity in the input channel is substantially enhanced due to the creating of an extra dimension for the data carriers. The topological devices proposed here, when integrated with other state-of-the-art communication techniques, may suggest a significant step towards acoustic communication circuits with complex functionalities.

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Topological helical edge states in water waves over a topographical bottom

Cited by 27 publications

References 42 publications

Edge solitons in a nonlinear mechanical topological insulator

Edge solitons in a nonlinear mechanical topological insulator

Topological wave insulators: a review

Acoustic topological devices based on emulating and multiplexing of pseudospin and valley indices

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