Edge States and Topological Pumping in Stiffness Modulated Elastic Plates

Abstract

We demonstrate that modulations of the stiffness properties of an elastic plate along a spatial dimension induce edge states spanning non-trivial gaps characterized by integer valued Chern numbers. We also show that topological pumping is induced by smooth variations of the phase of the modulation profile along one spatial dimension, which results in adiabatic edge-to-edge transitions of the edge states. The concept is first illustrated numerically for sinusoidal stiffness modulations, and then experimentally demonstrated in a plate with square-wave thickness profile. The presented numerical and experimental results show how continuous modulations of properties may be exploited in the quest for topological phases of matter. This opens new possibilities for topology-based waveguiding through slow modulations along a second dimension, spatial or temporal.

References in corpus (36)

• Topological Insulators
• Topological Photonics
• Topological Field Theory of Time-Reversal Invariant Insulators
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Topological Acoustics
• Topological States and Adiabatic Pumping in Quasicrystals
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Observation of topological valley transport of sound in sonic crystals
• Topological Phononic Crystals with One-Way Elastic Edge Waves
• Topological mechanics of gyroscopic metamaterials
• Topologically protected elastic waves in phononic metamaterials
• A Thouless Quantum Pump with Ultracold Bosonic Atoms in an Optical Superlattice
• Topological Thouless Pumping of Ultracold Fermions
• Floquet Topological Insulators for Sound
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Synthetic dimensions in integrated photonics: From optical isolation to 4D quantum Hall physics
• Topological phonon modes and their role in dynamic instability of microtubules
• Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect
• Amorphous topological insulators constructed from random point sets
• Observation of topological valley modes in an elastic hexagonal lattice
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Tunable Acoustic Valley-Hall Edge States in Reconfigurable Phononic Elastic Waveguides
• Observation of topologically protected helical edge modes in Kagome elastic plates
• Subwavelength and directional control of flexural waves in zone-folding induced topological plates
• Edge states and topological pumping in elastic lattices with periodically modulated coupling
• Edge states in trimer lattices
• Helical edge states and topological phase transitions in phononic systems using bi-layered lattices
• Observation of topological edge modes in a quasi-periodic acoustic waveguide
• Topological pumping of edge states via adiabatic passage
• Elastic quantum spin-Hall effect in Kagome lattices
• The 6D quantum Hall effect and 3D topological pumps
• Experimental evidence of robust acoustic valley Hall edge states in a non-resonant topological elastic waveguide
• Electromagnetic response of quantum Hall systems in dimensions five and six and beyond
• Topological Edge Modes by Smart Patterning

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• Bidirectional elastic diode with frequency-preserved nonreciprocity
• Adiabatic edge-to-edge transformations in time-modulated elastic lattices and non-Hermitian shortcuts
• Elastic Temporal Waveguiding
• Existence of Corner Modes in Elastic Twisted Kagome Lattices
• Optimised graded metamaterials for mechanical energy confinement and amplification via reinforcement learning
• Material vs. structure: Topological origins of band-gap truncation resonances in periodic structures
• Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
• Mechanics and dynamics of two-dimensional quasiperiodic composites
• Harnessing $\mathcal{P}\mathcal{T}$-symmetry in non-Hermitian stiffness-modulated waveguides
• Quantum transport in a one-dimensional quasicrystal with mobility edges
• Optimal design of fast topological pumping
• Non-Local Elastic Lattices with $\mathcal{P}\mathcal{T}$-Symmetry and Time Modulation: From Perfect Trapping to the Wave Boomerang Effect
• Capillary control of collapse in soft composite columns
• Physical rendering of synthetic spaces for topological sound transport
• Mapping Chern numbers in quasi-periodic interacting spin chains
• Topological power pumping in quantum circuits
• Elastic Lattices Inspired by Ulam-Warburton Cellular Automaton