Rayleigh Edge Waves in Two-Dimensional Crystals with Lorentz Forces -- from Skyrmion Crystals to Gyroscopic Media
arXiv:2004.09517 · doi:10.1103/PhysRevB.104.024435
Abstract
We investigate, within the framework of linear elasticity theory, edge Rayleigh waves of a two-dimensional elastic solid with broken time-reversal and parity symmetries due to a Berry term. As our prime example, we study the elastic edge wave traveling along the boundary of a two-dimensional skyrmion lattice hosted inside a thin-film chiral magnet. We find that the direction of propagation of the Rayleigh modes is determined not only by the chirality of the thin-film, but also by the Poisson ratio of the crystal. We discover three qualitatively different regions distinguished by the chirality of the low-frequency edge waves, and study their properties. To illustrate the Rayleigh edge waves in real time, we have carried out finite-difference simulations of the model. Apart from skyrmion crystals, our results are also applicable to edge waves of gyroelastic media and screened Wigner crystals in magnetic fields. Our work opens a pathway towards controlled manipulation of elastic signals along boundaries of crystals with broken time-reversal symmetry.
arXiv commentPublished version: 10 pages, 5 figures. See https://youtu.be/yf7MzCQC5y4 for supplementary video
References in corpus (24)
- Skyrmion Lattice in a Chiral Magnet
- Topological Phononic Crystals with One-Way Elastic Edge Waves
- Topological Boundary Modes in Isostatic Lattices
- Topological mechanics of gyroscopic metamaterials
- Dynamics of Skyrmion Crystals in Metallic Thin Films
- Odd elasticity
- Topological Origin of Equatorial Waves
- Isostaticity, auxetic response, surface modes, and conformal invariance in twisted kagome lattices
- Topological waves in fluids with odd viscosity
- Inertia and chiral edge modes of a skyrmion magnetic bubble
- Spin waves in a skyrmion crystal
- The Magnus Force on Skyrmions in Ferromagnets and the Quantum Hall Effect
- Tkachenko modes of vortex lattices in rapidly rotating Bose-Einstein condensates
- Topological Sound and Flocking on Curved Surfaces
- Anomalous bulk-edge correspondence in continuous media
- Active viscoelasticity of odd materials
- Dissipationless Phonon Hall Viscosity
- Odd surface waves in two-dimensional incompressible fluids
- Vortex-type elastic structured media and dynamic shielding
- Topology in shallow-water waves: a violation of bulk-edge correspondence
- Edge wave and boundary layer of vortex matter
- Hydrodynamics of two-dimensional compressible fluid with broken parity: variational principle and free surface dynamics in the absence of dissipation
- Continuum elasticity theory of edge excitations in a two-dimensional electron liquid with finite range interactions
- Chiral topological phases in designed mechanical networks
Cited by in corpus (8)
- Odd Viscosity and Odd Elasticity
- Topological defects in solids with odd elasticity
- Odd Cosserat elasticity in active materials
- Equatorial Waves in Rotating Bubble-Trapped Superfluids
- Odd elasticity and topological waves in active surfaces
- Surface waves and bulk Ruderman mode of a bosonic superfluid vortex crystal in the lowest Landau level
- Rayleigh waves and cyclotron surface modes of gyroscopic metamaterials
- Odd elasticity in Hamiltonian formalism