Acoustic square-root topological states

Yan, Mou; Huang, Xueqin; Luo, Lingaï; Lu, Jiuyang; Deng, Weiyin; Liu, Zhengyou

doi:10.1103/physrevb.102.180102

Cited by 53 publications

(29 citation statements)

References 49 publications

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“…Crucially, however, the cylinders were not closely spaced and the authors did not consider any topological aspects of the array; it is likely that the quality of the edge states in this system would be reduced by longerranged coupling between voids and their next-nearest-neighbours. On the other hand, Yan et al [44] studied a honeycomb-kagome array of acoustic resonators connected by narrow channels and considered the symmetry protected topology. However, in their work the width of the channels were alternated to produce a square-root topological insulator where the topology was inherited from the breathing kagome sector of the squared Hamiltonian, whereas we study the lattice with equal channel widths, which is akin to the mass-spring/tight-binding models of Mizoguchi et al [40], where the nontrivial topology is inherited from the honeycomb sector of the squared Hamiltonian.…”

Section: Mass-spring and Void-channel Modelsmentioning

confidence: 99%

Asymptotically exact photonic analogues of chiral symmetric topological tight-binding models

Palmer,

Ignatov,

Craster

et al. 2021

Preprint

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Topological photonic edge states, protected by chiral symmetry, are attractive for guiding wave energy as they can allow for more robust guiding and greater control of light than alternatives; however, for photonics, chiral symmetry is often broken by long-range interactions. We look to overcome this difficulty by exploiting the topology of networks, consisting of voids and narrow connecting channels, formed by the spaces between closely spaced perfect conductors. In the limit of low frequencies and narrow channels, these void-channel systems have a direct mapping to analogous discrete mass-spring systems in an asymptotically rigorous manner and therefore only have short-range interactions. We demonstrate that the photonic analogues of topological tight-binding models that are protected by chiral symmetries, such as the SSH model and square-root semimetals, are reproduced for these void-channel networks with appropriate boundary conditions. We anticipate, moving forward, that this paper provides a basis from which to explore continuum photonic topological systems, in an asymptotically exact manner, through the lens of a simplified tight-binding model.

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Section: Mass-spring and Void-channel Modelsmentioning

confidence: 99%

Asymptotically exact photonic analogues of chiral symmetric topological tight-binding models

Palmer,

Ignatov,

Craster

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…After this proposal, analysis of square-root topological insulators in higher dimensions has been addressed [25][26][27][28][29][30][31][32] , which has elucidated ubiquity of the squareroot topological phases. For instance, a square-root counterpart of higher-order topological phases are reported by both theoretical 25 and experimental works 33,34 . In addition, Refs.…”

Section: Introductionmentioning

confidence: 98%

Square-root topological phase with time-reversal and particle-hole symmetry

et al. 2021

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Square-root topological phases have been discussed mainly for systems with chiral symmetry. In this paper, we analyze the topology of the squared Hamiltonian for systems preserving the timereversal and particle-hole symmetry. Our analysis elucidates that two-dimensional systems of class CII host helical edge states due to the nontrivial topology of the squared Hamiltonian in contrast to the absence of ordinary topological phases. The emergence of the helical edge modes is demonstrated by analyzing a toy model. We also show the emergence of surface states induced by the non-trivial topology of the squared Hamiltonian in three dimensions.

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“…The very appealing property of a localized mode with a locked disorder-insensitive frequency has generated a lot of interest in reproducing the behavior of the SSH model using acoustic wave systems. Most of the approaches to date are based on coupled resonator systems [8][9][10][11][12][13]. There, to mimic the SSH model, the resonating acoustic cavities play the role of the atoms and the hoppings are realized by connecting tubes.…”

Section: Introductionmentioning

confidence: 99%

Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to the Su-Schrieffer-Heeger model

et al. 2021

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Topological band theory strongly relies on prototypical lattice models with particular symmetries. We report here on a theoretical and experimental work on acoustic waveguides that are directly mapped to the onedimensional Su-Schrieffer-Heeger model. Starting from the continuous two-dimensional wave equation, we use a combination of monomode approximation and the condition of equal-length tube segments to arrive at the wanted chiral symmetric discrete equations. It is shown that open or closed boundary conditions lead automatically to the existence of topological edge modes. We illustrate by graphical construction how the edge modes appear naturally owing to a quarter-wavelength condition and the conservation of flux. Furthermore, the transparent chirality of our system, which is ensured by simple geometrical constraints allows us to study chiral disorder numerically and experimentally. Our experimental results in the audible regime demonstrate the predicted robustness of the topological edge modes.

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Acoustic square-root topological states

Cited by 53 publications

References 49 publications

Asymptotically exact photonic analogues of chiral symmetric topological tight-binding models

Asymptotically exact photonic analogues of chiral symmetric topological tight-binding models

Square-root topological phase with time-reversal and particle-hole symmetry

Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to the Su-Schrieffer-Heeger model

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