Classification of topological phonons in linear mechanical metamaterials

TL;DR

This paper introduces a classification scheme for topological phonons in mechanical metamaterials based on local symmetries, unifying recent research and enabling new model development.

Contribution

It adapts the electronic topological classification to mechanical systems and provides extensive examples for generating models in various symmetry classes.

Findings

Unified classification scheme for topological phonons

Examples illustrating the classification and model generation

Framework for future applications in mechanical metamaterials

Abstract

Topological phononic crystals, alike their electronic counterparts, are characterized by a bulk-edge correspondence where the interior of a material dictates the existence of stable surface or boundary modes. In the mechanical setup, such surface modes can be used for various applications such as wave-guiding, vibration isolation, or the design of static properties such as stable floppy modes where parts of a system move freely. Here, we provide a classification scheme of topological phonons based on local symmetries. We import and adapt the classification of non-interacting electron systems and embed it into the mechanical setup. Moreover, we provide an extensive set of examples that illustrate our scheme and can be used to generate new models in unexplored symmetry classes. Our works unifies the vast recent literature on topological phonons and paves the way to future applications of topological surface modes in mechanical metamaterials.