Topological modes bound to dislocations in mechanical metamaterials

Abstract

Mechanical metamaterials are artificial structures with unusual properties, such as negative Poisson ratio, bistability or tunable vibrational properties, that originate in the geometry of their unit cell. At the heart of such unusual behaviour is often a soft mode: a motion that does not significantly stretch or compress the links between constituent elements. When activated by motors or external fields, soft modes become the building blocks of robots and smart materials. Here, we demonstrate the existence of topological soft modes that can be positioned at desired locations in a metamaterial while being robust against a wide range of structural deformations or changes in material parameters. These protected modes, localized at dislocations, are the mechanical analogue of topological states bound to defects in electronic systems. We create physical realizations of the topological modes in prototypes of kagome lattices built out of rigid triangular plates. We show mathematically that they originate from the interplay between two Berry phases: the Burgers vector of the dislocation and the topological polarization of the lattice. Our work paves the way towards engineering topologically protected nano-mechanical structures for molecular robotics or information storage and read-out.

13 pages, 6 figures; changes to text and figures and added analysis on mode localization; see http://www.lorentz.leidenuniv.nl/~paulose/dislocation-modes/ for accompanying videos

References in corpus (4)

• Topological Defects and Gapless Modes in Insulators and Superconductors
• Helical Metal Inside a Topological Band Insulator
• Anyons and the quantum Hall effect - a pedagogical review
• Nonlinear conduction via solitons in a topological mechanical insulator

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• Mechanical Graphene
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• Liquid Structures: a novel Computational Fluid Dynamics (CFD) inspired metamaterial