Edge States and Topological Pumping in Spatially Modulated Elastic Lattices

Rosa, Matheus I. N.; Pal, Raj Kumar; Arruda, José Roberto de França; Ruzzene, Massimo

doi:10.1103/physrevlett.123.034301

Cited by 134 publications

(92 citation statements)

References 34 publications

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“…The topology of the Hermitian lattice is trivial, since its dispersion does not form a closed loop in the complex plane. Indeed, in Hermitian systems, edge states can only be found for frequencies inside a band-gap [18,22,29], with the localization of bulk modes at the boundaries due to NHSE is a feature unique to non-Hermitian systems.…”

Section: Bulk Topology and Non-hermitian Skin Effectmentioning

confidence: 99%

“…Topological states have been successfully observed in several platforms [13][14][15][16][17][18][19][20][21], and have been pursued to achieve robust, diffraction-free wave motion. Additional functionalities have been explored in the context of topological pumping [22][23][24][25][26], quasi-periodicity [27][28][29], and non-reciprocal wave propagation in active [30][31][32][33][34][35][36] or passive non-linear [37][38][39][40] systems. These works and the references therein illustrate a wealth of strategies for the manipulation of elastic and acoustic waves, and suggest intriguing possibilities for technological applications in acoustic devices, sensing, energy harvesting, among others.…”

Section: Introductionmentioning

confidence: 99%

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Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Rosa

Ruzzene

2020

New J. Phys.

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We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems.

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Section: Bulk Topology and Non-hermitian Skin Effectmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Rosa

Ruzzene

2020

New J. Phys.

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“…A topological pump is known to generate robust energy transfer across a finite structure when its system parameters are adiabatically and cyclically varied, as has been shown in recent exciting wave‐based experiments. [ 30–32 ] These implemented topologial pumps typically incorporate adiabatic modulation of the geometrical parameters, which leads to a smooth crossing of propagating edge states from one boundary to the opposite. Moreover, since corner states can be understood through the vectorial Zak phase, it is not surprising that a 2D pumping process can push a corner state excitation into the opposite corner through bulk‐mode hybridization.…”

Section: Figurementioning

confidence: 99%

Topological Sound Pumping of Zero‐Dimensional Bound States

Gao

Christensen

2020

Adv Quantum Tech

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Topological phases have spurred unprecedented abilities for sound, light, and matter engineering and recent progress has shown how waves not only confine at the interfaces between topologically distinct insulators, but in the form of zero‐dimensional non‐propagating states bound to defects or corners. Majorana‐like bound states have recently been observed in man‐made Kekulé textured lattices. It is shown here how the acoustic version of the associated Jackiw–Rossi vortex embodies a topological pumping process, in which the spectral flow of corner states adiabatically merge with the said Majorana‐like state. Moreover, it is argued how the chirality of the Kekulé vortex additionally maps into a 2D quantum‐Hall system comprising spatially separated sonic hotspots. It is foreseen that the findings should provide novel exotic tools to enable contemporary control over sound.

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“…For some modes, like the one displayed in figure 9(a), this transition occurs while maintaining the mode shape essentially unaltered, in a manner that is vaguely reminiscent of solitons [35]. These transitions may be exploited to produce novel physical behavior like adiabatic pumping through a continuous translation of the localized mode, in contrast to the topological pumps realized so far that rely on egde-bulk-edge transitions like the one shown in figure 9(d) along a second spatial [22,36] or temporal [37][38][39][40][41] dimension. Naturally, this implies the ability to modify the arrangement of the springs, or the strength of the interaction through active means or adaptive materials.…”

Section: Mode Transitions Driven By Phase Modulationsmentioning

confidence: 99%

Topological bands and localized vibration modes in quasiperiodic beams

2019

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We investigate a family of quasiperiodic continuous elastic beams, the topological properties of their vibrational spectra, and their relation to the existence of localized modes. We specifically consider beams featuring arrays of ground springs at locations determined by projecting from a circle onto an underlying periodic system. A family of periodic and quasiperiodic structures is obtained by smoothly varying a parameter defining such projection. Numerical simulations show the existence of vibration modes that first localize at a boundary, and then migrate into the bulk as the projection parameter is varied. Explicit expressions predicting the change in the density of states of the bulk define topological invariants that quantify the number of modes spanning a gap of a finite structure. We further demonstrate how modulating the phase of the ground springs distribution causes the topological states to undergo an edge-to-edge transition. The considered configurations and topological studies provide a framework for inducing localized modes in continuous elastic structural components through globally spanning, deterministic perturbations of periodic patterns defined by the considered projection operations. systems [19] by exploiting the notion that QP lattices are projections of higher dimensional manifolds onto lower dimensional lattices [20,21]. Notable examples include the investigations in [22,23], where photonic waveguides are used to achieve adiabatic pumping of waves between opposite ends of one-dimensional (1D) QP lattices. With further studies, a dynamically generated four-dimensional (4D) quantum Hall system was experimentally demonstrated using two-dimensional (2D) periodic lattices [24]. In the classic mechanics realm, localized modes at the boundary of a QP chain of magnetic spinners were shown in [25], while topological boundary and interface modes were experimentally demonstrated in acoustic waveguides with QP patterning of the walls [26]. Although open questions still remain regarding how eigenmodes may localize in any region of the domain, these studies provide insight into modes that are localized at edges or interfaces, and suggest new methodologies for wave localization and transport based on higher dimensional topological properties.Motivated by these contributions, we here investigate how localized modes arise in continuous elastic media with QP stiffness modulations. Such modulations are introduced through arrays of ground springs embedded in structural beams undergoing transverse vibrations (figure 1). The locations of the springs are determined by projecting from periodic array of circles. This pattern-generating procedure identifies families of structures ranging from periodic to QP, that are obtained through the smooth variation of the parameters defining the projection. This study contributes to the recent investigations of the dynamic response of QP continuous elastic media [27][28][29]. For example, the self-similar and invariant nature of stop and pass bands in beams and rods embedd...

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Edge States and Topological Pumping in Spatially Modulated Elastic Lattices

Cited by 134 publications

References 34 publications

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

Topological Sound Pumping of Zero‐Dimensional Bound States

Topological bands and localized vibration modes in quasiperiodic beams

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