Topological elasticity of non-orientable ribbons

TL;DR

This paper explores the unique elastic properties of non-orientable surfaces like Moebius strips, revealing their complex stress responses and topological excitations, with implications across various physical systems.

Contribution

It establishes a novel link between elasticity and topology in non-orientable surfaces, challenging existing concepts like bulk-boundary correspondence and demonstrating new elastic behaviors.

Findings

Elastic response of non-orientable surfaces is non-additive and non-reciprocal.

Identifies solitonic excitations propagating through non-orientable ribbons.

Connects interface modes with topological phases in elastic systems.

Abstract

In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology that classifies their global shape. Focusing on Moebius strips, we establish that the elastic response of surfaces with non-orientable topology is: non-additive, non-reciprocal and contingent on stress-history. Investigating the elastic instabilities of non-orientable ribbons, we then challenge the very concept of bulk-boundary-correspondence of topological phases. We establish a quantitative connection between the modes found at the interface between inequivalent topological insulators and solitonic bending excitations that freely propagate through the bulk non-orientable ribbons. Beyond the specifics of mechanics, we argue that non-orientability offers a versatile platform to tailor the response of systems as diverse as liquid crystals, photonic and electronic matter.