Edge waves in plates with resonators: An elastic analogue of the quantum valley Hall effect
arXiv:1611.08919 · doi:10.1088/1367-2630/aa56a2
Abstract
We investigate elastic periodic structures characterized by topologically nontrivial bandgaps supporting backscattering suppressed edge waves. These edge waves are topologically protected and are obtained by breaking inversion symmetry within the unit cell. Examples for discrete one and two-dimensional lattices elucidate the concept and illustrate parallels with the quantum valley Hall effect. The concept is implemented on an elastic plate featuring an array of resonators arranged according to a hexagonal topology. The resulting continuous structures have non-trivial bandgaps supporting edge waves at the interface between two media having different topological invariants. The topological properties of the considered configurations are predicted by unit cell and finite strip dispersion analyses. Numerical simulations on finite structures demonstrate edge wave propagation for excitation at frequencies belonging to the bulk bandgaps. The considered plate configurations define a framework for the implementation of topological concepts on continuous elastic structures of potential engineering relevance.
arXiv comment28 pages, 13 figures
References in corpus (24)
- Topological Insulators
- Quantum Spin Hall Effect in Graphene
- Topological Photonics
- Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
- Valley contrasting physics in graphene: magnetic moment and topological transport
- Valley filter and valley valve in graphene
- Topological Acoustics
- Observation of phononic helical edge states in a mechanical 'topological insulator'
- Topological Phononic Crystals with One-Way Elastic Edge Waves
- Topological mechanics of gyroscopic metamaterials
- Topologically protected elastic waves in phononic metamaterials
- Surface Impedance and Bulk Band Geometric Phases in One-Dimensional Systems
- Spontaneous Quantum Hall States in Chirally-stacked Few-Layer Graphene Systems
- Valley Vortex States in Sonic Crystals
- Valley Chern Numbers and Boundary Modes in Gapped Bilayer Graphene
- Time Reversal Invariant Topologically Insulating Circuits
- Topological phonon modes and their role in dynamic instability of microtubules
- Classification of topological phonons in linear mechanical metamaterials
- Topological Phases of Sound and Light
- Topological mechanics of origami and kirigami
- Mechanical Weyl Modes in Topological Maxwell Lattices
- Manipulation of Dirac Cones in Mechanical Graphene
- Helical edge states and topological phase transitions in phononic systems using bi-layered lattices
- Topological phase transitions and chiral inelastic transport induced by the squeezing of light
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