Hermitian and non-hermitian topological edge states in one-dimensional perturbative elastic metamaterials

Fan, Haiyan; Gao, He; An, Shuowei; Gu, Zhongming; Liang, Shanjun; Zheng, Yi Ning; Liu, Tuo

doi:10.1016/j.ymssp.2021.108774

Cited by 22 publications

(6 citation statements)

References 51 publications

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“…To examine the non-Hermiticity-controlled topological properties, we consider a finite-sized lattice with five nontrivial unit cells [Fig. 2(a)] fixed via partial plates at both ends [7,28,43]. The complex eigenfrequencies for the chain based on simulation are plotted in Figs.…”

Section: Non-hermitian Trimerized Elastic Lattice Modelmentioning

confidence: 99%

“…To our delight, it has been demonstrated that the non-Hermiticity, per se, other than simply a perturbation to the topological systems, can be a nontrivial parameter to drive the topological phase transition [13][14][15]. This has motivated a cascade of theoretical explorations based on tight-binding Hamiltonians [16][17][18][19][20][21] and experimental demonstrations in electrical circuit [22], optical lattices [23,24], acoustic crystals [25][26][27], and elastic perturbative metamaterials [28] with suitably arranged loss and/or gain, which significantly extended the topological notions to non-Hermitian systems as well as their practical applications. In the majority of non-Hermitian topological systems, the topological properties are considered to exist in the band gaps which separate the spatially localized modes from the bulk continuous spectra of propagating waves.…”

Section: Introductionmentioning

confidence: 99%

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Observation of non-Hermiticity-induced topological edge states in the continuum in a trimerized elastic lattice

Fan

Gao²,

An³

et al. 2022

Phys. Rev. B

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Topologically protected localized states are commonly existent inside bulk band gaps with topological features, which, however, can be shifted to coexist with a continuous spectrum under particular coupling modulations, forming the so-called topological bound states in the continuum (BICs). These embedded topological states have so far been derived under the Hermitian assumptions that neglect the influence of nonconservative characteristics of classical wave systems on the topological properties. In this study, with a one-dimensional trimerized elastic lattice, we report the experimental demonstration of topological edge states in the continuum produced solely by non-Hermiticity, without additional coupling modulation. The trimerized elastic lattice is a chain of plates connected through thin beams, with the non-Hermiticity introduced by attaching constrained damping layers to particular sites in the chain assembly. We prove that appropriately tailored non-Hermitian modulation can induce topological edge states that appear in the bulk spectrum rather than exist in the band gap. Besides, the existence of such topological edge states is observed to be closely linked to the configurations of the lattice boundaries. This study affirms that non-Hermiticity can play an important role in creating topological BICs, gaining insight into the non-Hermitian topological physics and offering interesting avenues for exploring sophisticated non-Hermitian topological phenomena including higher-order topology in the continuum.

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Section: Non-hermitian Trimerized Elastic Lattice Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observation of non-Hermiticity-induced topological edge states in the continuum in a trimerized elastic lattice

Fan

Gao²,

An³

et al. 2022

Phys. Rev. B

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“…Non-Hermiticity, arising from loss/gain or nonreciprocity, enables much richer topological phenomena, including the non-Hermitian skin effect with unconventional bulk-boundary correspondences [18][19][20], and non-Hermiticity-controlled topological phase transitions [21][22][23][24][25]. In addition, the non-Hermitian operators may give rise to the coalescence of two or more eigenvalues, known as exceptional points (EPs) [26,27], which leads to intriguing phenomena such as loss-induced lasing [28], unidirectional invisibility [29], and unidirectional sound focusing [30].…”

Section: Introductionmentioning

confidence: 99%

Reconfigurable topological modes in acoustic non-Hermitian crystals

et al. 2023

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Non-Hermiticity, usually represented in the context of gain and loss, gives rise to many exotic topological phenomena and offers more opportunities to steering topological functions. In modern acoustics, it has been widely perceived that the topological mode will be altered if topological phase changes. Our work shows otherwise in non-Hermitian acoustic crystals. We experimentally demonstrate an acoustic quadrupole topological insulator, whose topological corner, edge, and bulk modes could be arbitrarily engineered at any desired positions with its topological phase maintained. These non-Hermiticity-controlled topological modes bestow a bulk structure with unique features beyond the classical bulky state, offering a reconfigurable and versatile approach to manipulating topological phenomena. This non-Hermitian scheme can be readily generalized to other topological systems in various dimensions, such as the three-dimensional photonic/phononic lattices, which offer advanced and externally controllable recipes for manipulating topological phenomena.

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“…Non-Hermiticity is extensively accepted in describing nonequilibrium or open dynamic systems that exchange their energy with the environment (1,2). Experimental progress in optics markedly stimulates the development of non-Hermitian physics, whereby gain and loss are ubiquitous and dynamic evolution of the optical waves can be characterized by non-Hermitian Hamiltonians (3)(4)(5)(6), which has already been extended to other physical systems with controlled gain/loss effect (7)(8)(9)(10)(11)(12)(13). Reciprocity is a fundamental principle in many physical realms, such as the helical edge state in 2D topological insulators with time-reversal symmetry (TRS) protection (14) and Lorentz reciprocity in electromagnetism (15).…”

Section: Introductionmentioning

confidence: 99%

Non-Hermitian topology in static mechanical metamaterials

2023

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The combination of broken Hermiticity and band topology in physical systems unveils a novel bound state dubbed as the non-Hermitian skin effect (NHSE). Active control that breaks reciprocity is usually used to achieve NHSE, and gain and loss in energy are inevitably involved. Here, we demonstrate non-Hermitian topology in a mechanical metamaterial system by exploring its static deformation. Nonreciprocity is introduced via passive modulation of the lattice configuration without resorting to active control and energy gain/loss. Intriguing physics such as the reciprocal and higher-order skin effects can be tailored in the passive system. Our study provides an easy-to-implement platform for the exploration of non-Hermitian and nonreciprocal phenomena beyond conventional wave dynamics.

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Hermitian and non-hermitian topological edge states in one-dimensional perturbative elastic metamaterials

Cited by 22 publications

References 51 publications

Observation of non-Hermiticity-induced topological edge states in the continuum in a trimerized elastic lattice

Observation of non-Hermiticity-induced topological edge states in the continuum in a trimerized elastic lattice

Reconfigurable topological modes in acoustic non-Hermitian crystals

Non-Hermitian topology in static mechanical metamaterials

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