Topological mechanics of gyroscopic metamaterials

Abstract

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial -- comprised of coupled gyroscopes on a lattice -- that breaks time-reversal symmetry. The vibrational spectrum of these novel structures displays a sonic gap populated by topologically protected edge modes which propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We envision applications of these edges modes to the design of loss-free, one-way, acoustic waveguides and demonstrate this functionality in experiment.

References in corpus (10)

• Reflection-Free One-Way Edge Modes in a Gyromagnetic Photonic Crystal
• Topological Acoustics
• Analogs of quantum Hall effect edge states in photonic crystals
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Topological modes bound to dislocations in mechanical metamaterials
• Nonlinear conduction via solitons in a topological mechanical insulator
• Selective buckling via states of self-stress in topological metamaterials
• Topological phonon modes in filamentous structures
• Phonons and elasticity in critically coordinated lattices

Cited by in corpus (353)

• Exceptional Topology of Non-Hermitian Systems
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• Observation of a phononic quadrupole topological insulator
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Anatomy of skin modes and topology in non-Hermitian systems
• Topologically protected elastic waves in phononic metamaterials
• Floquet Topological Insulators for Sound
• Observation of non-Hermitian topology and its bulk-edge correspondence in an active mechanical metamaterial
• Exciton-polariton topological insulator
• Experimental realization of a symmetry protected topological phase of interacting bosons with Rydberg atoms
• Non-reciprocal robotic metamaterials
• Topologically protected acoustic helical edge states and interface states in strongly coupled metamaterial ring lattices
• Static non-reciprocity in mechanical metamaterials
• Elastic higher-order topological insulator with topologically protected corner states
• Topological active matter
• Photonic Topological Anderson Insulators
• Topological Sound
• Experimental Realization of Acoustic Chern Insulator
• Double-Weyl phonons in transition-metal monosilicides
• Observation of Topological Band Gap Solitons
• Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect
• Odd elasticity
• Three-Dimensional All-Dielectric Photonic Topological Insulator
• Chiral voltage propagation in a self-calibrated topolectrical Chern circuit
• Amorphous topological insulators constructed from random point sets
• Classification of topological phonons in linear mechanical metamaterials
• Depinning and nonequilibrium dynamic phases of particle assemblies driven over random and ordered substrates: a review
• Observation of topological valley modes in an elastic hexagonal lattice
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Valley Topological Phases in Bilayer Sonic Crystals
• Fracton hydrodynamics
• Experimental realization of on-chip topological nanoelectromechanical metamaterials
• Artificial gauge fields in materials and engineered systems
• Tunable Acoustic Valley-Hall Edge States in Reconfigurable Phononic Elastic Waveguides
• Odd Viscosity and Odd Elasticity
• Observation of Double Weyl Phonons in Parity-Breaking FeSi
• Topological mechanics of origami and kirigami
• Topological waves in fluids with odd viscosity
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Designing Perturbative Metamaterials from Discrete Models: From Veselago lenses to topological insulators
• Transformable topological mechanical metamaterials
• Tailoring Structure-borne Sound Through Bandgap Engineering in Phononic Crystals and Metamaterials: A Comprehensive Review
• Infrared Topological Plasmons in Graphene
• Topological defect engineering and PT-symmetry in non-Hermitian electrical circuits
• Topological Phase Transition in Mechanical Honeycomb Lattice
• Demonstration of a 3rd order hierarchy of higher order topological states in a three-dimensional acoustic metamaterial
• Non-Hermitian band topology and skin modes in active elastic media
• Topological phononic insulator with robustly pseudospin-dependent transport
• Topological framework for directional amplification in driven-dissipative cavity arrays
• Demonstration of a quantized acoustic octupole topological insulator
• Observation of topologically protected helical edge modes in Kagome elastic plates
• Subwavelength and directional control of flexural waves in zone-folding induced topological plates
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Actively controllable topological phase transition in phononic beam systems
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• Manipulation of Dirac Cones in Mechanical Graphene
• Probing the Berry Curvature and Fermi Arcs of a Weyl Circuit
• Topological rainbow trapping for elastic energy harvesting in graded SSH systems
• Pseudospins and topological effects of phonons in a Kekule lattice
• Topological phases without crystalline counterparts
• Pseudomagnetic fields for sound at the nanoscale
• Snowflake Topological Insulator for Sound Waves
• Design and Experimental Observation of Valley-Hall Edge States in Diatomic-Graphene-like Elastic Waveguides
• Experimental observation of temporal pumping in electro-mechanical waveguides
• Experimental observation of non-reciprocal band-gaps in a space-time modulated beam using a shunted piezoelectric array
• Topological quantum fluctuations and travelling wave amplifiers
• Measuring the knot of non-Hermitian degeneracies and non-commuting braids
• Topological phase transitions and chiral inelastic transport induced by the squeezing of light
• Topological Sound and Flocking on Curved Surfaces
• Observation of unidirectional soliton-like edge states in nonlinear Floquet topological insulators
• Valley based splitting of topologically protected helical waves in elastic plates
• Quantized Fractional Thouless Pumping of Solitons
• Observation of Light Guiding by Artificial Gauge Fields
• Coexisted Three-component Bosons and Two-component Weyl Bosons in TiS, ZrSe and HfTe
• Three-component bosons in TiS, ZrSe and HfTe
• Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions
• Observation of topological edge modes in a quasi-periodic acoustic waveguide
• Active topolectrical circuits
• Sonic Landau-level lasing and synthetic gauge fields in mechanical metamaterials
• Topological insulators and semimetals in classical magnetic systems
• Direct demonstration of topological stability of magnetic skyrmions via topology manipulation
• Demonstrating an in-situ topological band transition in cylindrical granular chains
• Experimental Demonstration of Dynamic Topological Pumping Across Incommensurate Bilayered Acoustic Metamaterials
• Elastic quantum spin-Hall effect in Kagome lattices
• Programming nonreciprocity and reversibility in multistable mechanical metamaterials
• Observation of Gigahertz Topological Valley Hall Effect in Nanoelectromechanical Phononic Crystals
• Experimental demonstration of topological waveguiding in elastic plates with local resonators
• Acoustic spin-Chern insulator induced by synthetic spin-orbit coupling with spin conservation breaking
• Edge States and Topological Pumping in Stiffness Modulated Elastic Plates
• Topological nodal states in circuit lattice
• Amplitude-dependent topological edge states in nonlinear phononic lattices
• Many-Body Topological and Skin States without Open Boundaries
• Phononic Weyl Nodal Straight Lines in High-Temperature Superconductor MgB${}_2$
• Topological circuits of inductors and capacitors
• Theory and Experimental Investigation of the Quantum Valley Hall Effect
• Coupling between Exciton-Polariton Corner Modes through Edge States
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• Ice Rule and Emergent Frustration in Particle Ice and Beyond
• Topological quantum optics using atom-like emitter arrays coupled to photonic crystals
• Experimental evidence of robust acoustic valley Hall edge states in a non-resonant topological elastic waveguide
• Learning hydrodynamic equations for active matter from particle simulations and experiments
• Topological Phononic Logic
• Topological networks for quantum communication between distant qubits
• Robust Edge States in Amorphous Gyromagnetic Photonic Lattices
• Observation of edge waves in a two-dimensional Su-Schrieffer-Heeger acoustic network
• Self-ordering induces multiple topological transitions for elastic waves in phononic crystals
• Bulk-boundary correspondence in non-Hermitian systems: stability analysis for generalized boundary conditions
• Geared topological metamaterials with tunable mechanical stability
• Topological localization in out-of-equilibrium dissipative systems
• Quantized classical response from spectral winding topology
• Tunable magneto-granular phononic crystals
• Observation of topological edge states of sound at a momentum away from the high-symmetry point
• Soft self-assembly of Weyl materials for light and sound
• Supervised learning in a mechanical system
• Topological Gaseous Plasmon Polariton in Realistic Plasma
• Dynamical Majorana Edge Modes in a Broad Class of Topological Mechanical Systems
• Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies
• The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps
• Weyl Josephson Circuits
• Exceptional non-Hermitian topological edge mode and its application to active matter
• Mechanical analogue of a Majorana bound state
• Topological defects in solids with odd elasticity
• Fracturing of topological Maxwell lattices
• Anomalous Topological Active Matter
• Dial-in Topological Metamaterials Based on Bistable Stewart Platform
• Nonlinear non-Hermitian higher-order topological laser
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• Non-Hermitian Topological Metamaterials with Odd Elasticity
• van der Waals metamaterials
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• Non-Newtonian Topological Mechanical Metamaterials Using Feedback Control
• Simulation of interaction-induced chiral topological dynamics on a digital quantum computer
• Optically-Controlled Orbitronics on a Triangular Lattice
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• Inverse Design of Discrete Mechanical Metamaterials
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• Topological Edge Modes by Smart Patterning
• Non-Commutative Chern Numbers for Generic Aperiodic Discrete Systems
• Valley-projected edge modes observed in underwater sonic crystals
• Topological Invariant and Anomalous Edge Modes of Strongly Nonlinear Systems
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• L lines, C points and Chern numbers: understanding band structure topology using polarization fields
• Disorder-induced topological phase transition in a 1D mechanical system
• Line nodes, Dirac points and Lifshitz transition in 2D nonsymmorphic photonic crystals
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• Elastic Valley Spin Controlled Chiral Coupling in Topological Valley Phononic Crystals
• Adiabatic pumping via avoided crossings in stiffness modulated quasiperiodic beams
• Stabilizing multiple topological fermions on a quantum computer
• Real-Time Steering of Curved Sound Beams in a Feedback-based Topological Acoustic Metamaterial
• Valley-Hall In-Plane Edge States as Building Blocks for Elastodynamic Logic Circuits
• Smart patterning for topological pumping of elastic surface waves
• Topological phase transition in coupled rock-paper-scissor cycles
• Artificial non-Abelian lattice gauge fields for photons in the synthetic frequency dimension
• Interfacial waveforms in chiral lattices with gyroscopic spinners
• Topological spin-Hall edge states of flexural wave in perforated metamaterial plates
• Switchable phonon diodes using nonlinear topological Maxwell lattices
• Chiral edge mode in the coupled dynamics of magnetic solitons in a honeycomb lattice
• Edge states in a two-dimensional honeycomb lattice of massive magnetic skyrmions
• Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
• Anharmonic interatomic force constants and thermal conductivity from Grüneisen parameters: an application to graphene
• Nanomechanical resonators with ultra-high-$Q$ perimeter modes
• Topology in non-linear mechanical systems
• Tunable Band Topology in Gyroscopic Lattices
• Anomalous Quadrupole Topological Insulators in 2D Nonsymmorphic Sonic Crystals
• Variational control forces for enhanced sampling of nonequilibrium molecular dynamics simulations
• Nonreciprocal Elasticity
• Topological valley transport under long-range deformations
• Non-Abelian braiding of Majorana-like edge states and topological quantum computations in electric circuits
• Valley Anisotropy in Elastic Metamaterials
• Klein-Gordon representation of acoustic waves and topological origin of surface acoustic modes
• Directional mechanical response in the bulk of topological metamaterials
• Magic-Angle Semimetals with Chiral Symmetry
• Localizing softness and stress along loops in three-dimensional topological metamaterials
• Topological mechanics in quasicrystals
• Autonomous actuation of zero modes in mechanical networks far from equilibrium
• Buckling of thermalized elastic sheets
• Ice Rule Fragility via Topological Charge Transfer in Artificial Colloidal Ice
• Topologically protected elastic waves in one-dimensional phononic crystals of continuous media
• Topological Classification Table Implemented with Classical Passive Meta-Materials
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• Amorphous topological phases protected by continuous rotation symmetry
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• Mechanical Graphene
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• Topological dynamics of gyroscopic and Floquet lattices from Newton's laws
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• Realization of a Topological Phase Transition in a Gyroscopic Lattice
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• Lattice symmetries and the topological protected transport of colloidal particles
• Synthetic Kramers pair in phononic elastic plates and helical edge states on a dislocation interface
• One-dimensional topological metal
• Existence of Corner Modes in Elastic Twisted Kagome Lattices
• Uncovering and experimental realization of multimodal 3D topological metamaterials for low-frequency and multiband elastic wave control
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• Hamiltonian Tomography of Photonic Lattices
• Topological phase in plasma physics
• Topological elasticity of non-orientable ribbons
• Acoustic metamaterials with spinning components
• Switchable topological phonon channels
• Time-dependent high-contrast subwavelength resonators
• Breakdown of Conventional Winding Number Calculation in One-Dimensional Lattices with Interactions Beyond Nearest Neighbors
• Double Dirac Cones and Topologically Non-Trivial Phonons for Continuous, Square Symmetric (C${}_{4v}$ and C${}_{2v}$) Unit Cells
• Chiral Maxwell waves in continuous media from Berry monopoles
• Material vs. structure: Topological origins of band-gap truncation resonances in periodic structures
• A diagnosis scheme for topological degeneracies at high-symmetry momenta
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• Origin and localization of topological band gaps in gyroscopic metamaterials
• Topological braiding of non-Abelian mid-gap defects in classical meta-materials
• Broadband Frequency and Spatial On-Demand Tailoring of Topological Wave Propagation Harnessing Piezoelectric Metamaterials
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• Polarization-dependent and Valley-protected Lamb Waves in Asymmetric Pillared Phononic Crystals
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• Characterization of edge states in perturbed honeycomb structures
• Programming tunable active dynamics in a self-propelled robot
• The dispersion and propagation of topological Langmuir-cyclotron waves in cold magnetized plasmas
• Edge states of mechanical diamond and its topological origin
• Odd elasticity and topological waves in active surfaces
• Non-Hermitian spectral flows and Berry-Chern monopoles
• Weyl points of mechanical diamond
• Origami Lattices and Folding-induced Lattice Transformations
• Edge-following topological states
• Quasicrystalline Weyl points and dense Fermi-Bragg arcs
• Generating Synthetic Magnetism via Floquet Engineering Auxiliary Qubits in Phonon-Cavity-Based Lattice
• Entangled multi-component 4D quantum Hall states from photonic crystal defects
• Dissipative nonequilibrium synchronization of topological edge states via self-oscillation
• Second-order topological modes in two-dimensional continuous media
• Unidirectional modes induced by nontraditional Coriolis force in stratified fluids
• Wave polarisation and dynamic degeneracy in a chiral elastic lattice
• Omnimodal topological polarization of bilayer networks: analysis in the Maxwell limit and experiments on a 3D-printed prototype
• Topological waveguide based on metamaterials of magnetic solitons
• Edge states at the boundary between topologically equivalent lattices
• Bulk-boundary correspondance for Sturmian Kohmoto like models
• Topological defects in Floquet systems: Anomalous chiral modes and topological invariant
• Experimental demonstration of position-controllable topological interface states in high-frequency topological integrated circuits
• Topological sound in active-liquid metamaterials
• Triple nodal points characterized by their nodal-line structure in all magnetic space groups
• Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems
• Fractional solitons in non-Euclidian elastic plates
• Revealing the boundary Weyl physics of the four-dimensional Hall effect via phason engineering in metamaterials
• Edge modes in 2D electromagnetic slab waveguides: analogues of acoustic plasmons
• High-order topological pumping on a superconducting quantum processor
• Synthetic Mechanical Lattices with Synthetic Interactions
• Topology of rotating stratified fluids with and without background shear flow
• Wavefront dislocations reveal the topology of quasi-1D photonic insulators
• A simple approach to characterizing band topology in bosonic pairing Hamiltonians
• Topological protection can arise from thermal fluctuations and interactions
• Manifestation of Berry curvature in geophysical ray tracing
• Tunneling in the Brillouin Zone: Theory of Backscattering in Valley Hall Edge Channels
• Bulk soliton dynamics in bosonic topological insulators
• Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
• Controlling the Deformation of Metamaterials: Corner Modes via Topology
• Su-Schrieffer-Heeger quasicrystal: Topology, localization, and mobility edge
• Simultaneous and independent topological control of identical microparticles in non-periodic energy landscapes
• Electric Circuit Realizations of Fracton Physics
• Subradiant edge states in an atom chain with waveguide-mediated hopping
• Rayleigh Edge Waves in Two-Dimensional Crystals with Lorentz Forces -- from Skyrmion Crystals to Gyroscopic Media
• Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics
• Rectification of energy and motion in non-equilibrium parity violating metamaterials
• Topological band structure of surface acoustic waves on a periodically corrugated surface
• Hard topological versus soft geometrical magnetic particle transport
• Supersymmetry on the lattice: Geometry, Topology, and Flat Bands
• Strain Tunable Phononic Topological Bandgaps in Two-Dimensional Hexagonal Boron Nitride
• From the geometry of Foucault pendulum to the topology of planetary waves
• Macroscopic Floquet topological crystalline steel pump
• Soft topological modes protected by symmetry in rigid mechanical metamaterials
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Chiral Edge Currents for ac Driven Skyrmions in Confined Pinning Geometries
• Rayleigh waves and cyclotron surface modes of gyroscopic metamaterials
• Dynamics in non-Hermitian systems with nonreciprocal coupling
• Nonlinearity and Topology
• Topologically protected dynamics in three-dimensional nonlinear antisymmetric Lotka-Volterra systems
• Complete absorption of topologically protected waves
• Dynamically Generated Synthetic Electric Fields for Photons
• Topological mechanical metamaterial with nonrectilinear constraints
• Predicting topological materials: symmetry-based indicator theories and beyond
• Valley and Valley-like Split-ring Topological Photonic Crystal
• Scalable 3D printing for topological mechanical metamaterials
• Scattering theory from artificial piezoelectric-like meta-atoms and molecules
• A Monolithic Topologically Protected Phononic Circuit
• Bloch Oscillations, Landau-Zener Transition, and Topological Phase Evolution in a Pendula Array
• Optimal design of fast topological pumping
• Confining and channeling sound through coupled resonators
• Brillouin-zone definition in non-reciprocal Willis monatomic lattices
• Topological pump of $SU(Q)$ quantum chain and Diophantine equation
• Corner states in second-order mechanical topological insulator
• Visualized Wave Mechanics by Coupled Macroscopic Pendula: Classical Analogue to Driven Quantum Bits
• Topology in a one-dimensional plasmonic crystal
• The effects of dissipation on topological mechanical systems
• Vortical waves in a quantum fluid with vector, axial, and helical charges. I. Non-dissipative transport
• Hermitian and non-Hermitian topology in active matter
• Classifying topological floppy modes in the continuum
• Topological Micro-Electro-Mechanical Systems
• Energy rectification in active gyroscopic networks under time-periodic modulations
• Topological invariants and topological charges in photonic systems
• Resonant laser excitation and time-domain imaging of chiral topological polariton edge states
• Dynamical Generation of Synthetic Electric Fields for Photons in the Quantum Regime
• Topological Mechanics of Micromorphic Metamaterials
• Physical rendering of synthetic spaces for topological sound transport
• Chiral topological phases in designed mechanical networks
• Topological phase transition in anti-symmetric Lotka-Volterra doublet chain
• Chiral motion in colloidal electrophoresis
• Symmetry breaking, strain solitons and mechanical edge modes in monolayer antimony
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• Edge Solitons in a Nonlinear Mechanical Topological Insulator
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• Helical boundary modes from synthetic spin in a plasmonic lattice
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• Odd elasticity in Hamiltonian formalism
• Classical periodic trajectories and quantum scars in many-spin systems
• Steerable sound transport in a 3D acoustic network
• Robust wall states in rapidly rotating Rayleigh-Bénard convection
• Nonlinearity-induced transition in heat conduction through a topological metamaterial of rotors
• Mechanical activity and odd elasticity of passive, 2D chiral metamaterials
• Topological defect states in elastic phononic plates
• Rotating effects on the Hall conductivity in a quantum dot
• Adiabatic and irreversible classical discrete time crystals
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• Observation of the topological edge state in X-ray band
• SAW interdigitated transducers as topological mechanical metamaterial
• Nonlinear edge modes from topological 1D lattices
• Topological optical and phononic interface mode by simultaneous band inversion
• Dynamics of entanglement asymmetry for space-inversion symmetry of free fermions on honeycomb lattices
• Hierarchical Topological States without Dimension Reduction