Signatures of Topological Phonons in Superisostatic Lattices

Abstract

Soft topological surface phonons in idealized ball-and-spring lattices with coordination number $z=2d$ in $d$ dimensions become finite-frequency surface phonons in physically realizable superisostatic lattices with $z>2d$. We study these finite-frequency modes in model lattices with added next-nearest-neighbor springs or bending forces at nodes with an eye to signatures of the topological surface modes that are retained in the physical lattices. Our results apply to metamaterial lattices, prepared with modern printing techniques, that closely approach isostaticity.

arXiv comment14 pages, 7 figures

References in corpus (21)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Topological invariants of time-reversal-invariant band structures
• Topological Boundary Modes in Isostatic Lattices
• Topological modes bound to dislocations in mechanical metamaterials
• Selective buckling via states of self-stress in topological metamaterials
• Topological mechanics of origami and kirigami
• Mechanical Weyl Modes in Topological Maxwell Lattices
• Topological phonons and Weyl lines in 3 dimensions
• Intrinsically polar elastic metamaterials
• Geared topological metamaterials with tunable mechanical stability
• Edge Modes and Asymmetric Wave Transport in Topological Lattices: Experimental Characterization at Finite Frequencies
• Topological edge floppy modes in disordered fiber networks
• Coherent potential approximation of random nearly isostatic kagome lattice
• Localizing softness and stress along loops in three-dimensional topological metamaterials
• Topological boundary modes in jammed matter
• Penrose Tilings as Jammed Solids

Cited by in corpus (12)

• Universal Continuum Theory for Topological Edge Soft Modes
• Soft mechanical metamaterials with transformable topology protected by stress caching
• Symmetry of the phonon landscape across the duality boundary of twisted kagomes lattices
• Multi-functional Twisted-Kagome lattices: Tuning by Pruning Mechanical Metamaterials
• Topological Flexural Modes in Polarized Bilayer Lattices
• Omnimodal topological polarization of bilayer networks: analysis in the Maxwell limit and experiments on a 3D-printed prototype
• Fully-Polarized Topological Isostatic Metamaterials in Three Dimensions
• Robustness of stress focusing in soft lattices under topology-switching deformation
• Topological switching in bilayer magnons via electrical control
• Cell augmentation framework for topological lattices
• 3D Topologically Polarized Elastic Metamaterials Enable Asymmetric Energy Isolation at Low Frequencies
• Topological Floppy Modes in Epithelial Tissues