Soft topological modes protected by symmetry in rigid mechanical metamaterials

TL;DR

This paper demonstrates how symmetry can induce topologically protected soft modes in overconstrained, rigid mechanical metamaterials, enabling robust, scale-free architectures suitable for nanoscale applications.

Contribution

It introduces a novel approach using non-Hermitian topology and symmetry to generate topological soft modes in overconstrained, rigid systems.

Findings

Topological soft modes can exist in overconstrained, rigid systems.

Symmetry and non-Hermitian topology enable interface modes.

Potential for nanoscale, robust mechanical architectures.

Abstract

Topological mechanics can realize soft modes in mechanical metamaterials in which the number of degrees of freedom for particle motion is finely balanced by the constraints provided by interparticle interactions. However, solid objects are generally hyperstatic (or overconstrained). Here, we show how symmetries may be applied to generate topological soft modes even in overconstrained, rigid systems. To do so, we consider non-Hermitian topology based on non-square matrices, and design a hyperstatic material in which low-energy modes protected by topology and symmetry appear at interfaces. Our approach presents a novel way of generating softness in robust scale-free architectures suitable for miniaturization to the nanoscale.