Embedding 1D BDI topological dynamics into continuous elastic plates

Abstract

This study presents an approach that leverages the existing knowledge acquired in one-dimensional BDI class discrete metamaterials, such as mass-spring systems or acoustic resonators, and exploits it to realize fully continuous elastic two-dimensional topological waveguides. The design relies on the concept of evanescently coupled waveguides and defect resonances in order to reproduce the equivalent dynamics of prototypical BDI discrete systems, such as the Su-Schrieffer-Heeger (SSH) model. Starting with a continuous plate waveguide based on a periodic distribution of pillars, local resonators and waveguides are created by eliminating selected pillars and by exploiting the concept of point and line defects. The height of selected pillars is adjusted to tune the coupling strength between different resonators. The approach is validated by designing fully continuous elastic analogs of both the SSH chain and ladder systems. Numerical simulations and experimental results confirm the validity of the design by showing the emergence of topological edge modes at the interface of topologically distinct systems. In addition, the edge modes obtained in the elastic analog of the SSH ladder are shown to be Majorana-like modes.

References in corpus (29)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• Fault-tolerant quantum computation by anyons
• Classification of topological quantum matter with symmetries
• Majorana Zero Modes and Topological Quantum Computation
• Classification of topological phonons in linear mechanical metamaterials
• Topological Fano Resonances
• Interplay between long range hopping and disorder in topological systems
• Acoustic type-II Weyl nodes from stacking dimerized chains
• Topological rainbow trapping for elastic energy harvesting in graded SSH systems
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Zero modes of two-dimensional chiral p-wave superconductors
• Demonstrating an in-situ topological band transition in cylindrical granular chains
• Su-Schrieffer-Heeger Model Inspired Acoustic Interface States and Edge States
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Acoustic Su-Schrieffer-Heeger lattice: Direct mapping of acoustic waveguides to Su-Schrieffer-Heeger model
• Topological phases, edge modes, and the Hofstadter butterfly in coupled Su-Schrieffer-Heeger systems
• Dynamical Majorana Edge Modes in a Broad Class of Topological Mechanical Systems
• Non-Local Phononic Crystals for Dispersion Customization and Undulation-point Dynamics
• Disorder-induced topological phase transition in a 1D mechanical system
• Designing topological interface states in phononic crystals based on the full phase diagrams
• Topological Classification Table Implemented with Classical Passive Meta-Materials
• Topologically protected elastic waves in one-dimensional phononic crystals of continuous media
• Creating p-wave superfluids and topological excitations in optical lattices
• Topological braiding of non-Abelian mid-gap defects in classical meta-materials
• Strain topological metamaterials
• Duality of Topological Edge States in a Mechanical Kitaev Chain
• Elementary models of 3D topological insulators with chiral symmetry
• Topological Computation by non-Abelian Braiding in Classical Metamaterials