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.

14 pages, 7 figures

References in corpus (3)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological modes bound to dislocations in mechanical metamaterials
• Intrinsically polar elastic metamaterials

Cited by in corpus (10)

• Soft mechanical metamaterials with transformable topology protected by stress caching
• Symmetry of the phonon landscape across the duality boundary of twisted kagomes lattices
• 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