Topologically Protected Twist Edge States for a Resonant Mechanical Laser-Beam Scanner

Köpfler, Julian; Frenzel, Tobias; Kadic, Muamer; Schmalian, Jörg; Wegener, Martin

doi:10.1103/physrevapplied.11.034059

Cited by 25 publications

(17 citation statements)

References 41 publications

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“…1(k)]. The chain consists of N 1 unit cells with the rotors as well as the fixed pivots labeled A n 1 and B n 1 (1 n 1 N 1 ) and is subjected to fixed boundary conditions [111,112] at rotors B 0 and A N 1 +1 . The equilibrium configuration is that the A rotors (B rotors) make an (1,15) with ω ext = 1.13 and F = 10 −10 .…”

Section: A Non-hermitian Topological Mechanics In the 1d Rotor Chainmentioning

confidence: 99%

“…In general, the generalized Berry phase is not quantized. However, it can be quantized by imposing the condition h z = 0, which is practically achieved [111] It is notable that all eigenvalues are real in the branch bb > 0 and c 1 c 1 > 0, while they are complex in the branch bb < 0 and c 1 c 1 < 0. Although the study of topological phases apply for both branches, the mechanical responses are quite different.…”

Section: A Non-hermitian Topological Mechanics In the 1d Rotor Chainmentioning

confidence: 99%

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Non-Hermitian topological metamaterials with odd elasticity

Zhou

Zhang

2020

Phys. Rev. Research

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We establish non-Hermitian topological mechanics in one-dimensional (1D) and 2D lattices consisting of mass points connected by metabeams that lead to odd elasticity. Extended from the "non-Hermitian skin effect" in 1D systems, we demonstrate this effect in 2D lattices in which bulk elastic waves exponentially localize in both lattice directions. We clarify a proper definition of Berry phase in non-Hermitian systems, with which we characterize the lattice topology and show the emergence of topological modes on lattice boundaries. The eigenfrequencies of topological modes are complex due to the breaking of PT symmetry and the excitations could exponentially grow in time in the damped regime. Besides the bulk modes, additional localized modes arise in the bulk band and they are easily affected by perturbations. These distinguishing features may manifest themselves in various active materials and biological systems.

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Section: A Non-hermitian Topological Mechanics In the 1d Rotor Chainmentioning

confidence: 99%

Section: A Non-hermitian Topological Mechanics In the 1d Rotor Chainmentioning

confidence: 99%

Non-Hermitian topological metamaterials with odd elasticity

Zhou

Zhang

2020

Phys. Rev. Research

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“…Models of one-dimensional (1D) lattices that include additional degrees of freedom have also gained significant recent attention [37][38][39][40][41][42][43][44]. For example, the standard model of the granular crystal accounts for axial (translational) motion of the particles but ignores any rotation.…”

Section: Introductionmentioning

confidence: 99%

“…Models that account for the additional degree of freedom in the form of rotation have the obvious benefit of being more realistic representations of the physical system, but such models can also lead to other novel dynamics such as rotational-translational modes [37]. Further studies have demonstrated the localized translational-rotational modes in the coupled linear systems [38], which can offer mechanisms for energy transfer from one degree-of-freedom to another by utilizing topologically protected modes [39]. The wave propagation in the linear, multi degree-of-freedom 1D lattice has also been shown to facilitate the energy spreading [40], or be easily manipulated by tuning the lattice configura-tion by using one of the degrees of freedom as a control knob in the magneto-granular crystal [41].…”

Section: Introductionmentioning

confidence: 99%

Rogue and solitary waves in coupled phononic crystals

Miyazawa,

Chong,

Kevrekidis

et al. 2021

Preprint

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In this work we present an analytical and numerical study of rogue and solitary waves in a coupled one-dimensional nonlinear lattice that involves both axial and rotational degrees of freedom. Using a multiple-scale analysis we derive a system of coupled nonlinear Schrödinger type equations in order to approximate solitary waves and rogue waves of the coupled lattice model. Numerical simulations are found to agree with the analytical approximations. We also consider generic initialization data in the form of a Gaussian profile and observe that they can result in the spontaneous formation of rogue wave-like patterns in the lattice. The solitary and rogue waves in the lattice demonstrate both energy isolation and exchange between the axial and rotational degrees of freedom of the system. This suggests that the studied coupled lattice has the potential to be an efficient energy isolation, transfer, and focusing medium.

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“…One possible application is to combine such chiral metamaterials with a linear piezoelectric actuator, enabling to convert the actuator motion into a rotation (also cf. 15 ). There, overall millimeter-sized metamaterial crystals exhibiting large twist effects are desirable.…”

mentioning

confidence: 99%

Large characteristic lengths in 3D chiral elastic metamaterials

et al. 2021

Self Cite

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Three-dimensional (3D) chiral mechanical metamaterials enable behaviors not accessible in ordinary materials. In particular, a coupling between displacements and rotations can occur, which is symmetry-forbidden without chirality. In this work, we solve three open challenges of chiral metamaterials. First, we provide a simple analytical model, which we use to rationalize the design of the chiral characteristic length. Second, using rapid multi-photon multi-focus 3D laser microprinting, we manufacture samples with more than 105 micrometer-sized 3D chiral unit cells. This number surpasses previous work by more than two orders of magnitude. Third, using analytical and numerical modeling, we realize chiral characteristic lengths of the order of ten unit cells, changing the sample-size dependence qualitatively and quantitatively. In the small-sample limit, the twist per axial strain is initially proportional to the sample side length, reaching a maximum at the characteristic length. In the thermodynamic limit, the twist per axial strain is proportional to the square of the characteristic length. We show that chiral micropolar continuum elasticity can reproduce this behavior.

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Topologically Protected Twist Edge States for a Resonant Mechanical Laser-Beam Scanner

Cited by 25 publications

References 41 publications

Non-Hermitian topological metamaterials with odd elasticity

Non-Hermitian topological metamaterials with odd elasticity

Rogue and solitary waves in coupled phononic crystals

Large characteristic lengths in 3D chiral elastic metamaterials

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