Odd elasticity and topological waves in active surfaces

TL;DR

This paper explores how odd elasticity in active surfaces leads to topologically protected unidirectional waves, revealing new elastic moduli and boundary phenomena in thick plates.

Contribution

It introduces the concept of odd elasticity in active plates, linking it to topological wave phenomena and boundary chiral edge waves in continuum elastic theory.

Findings

Active plates can exhibit two odd-elastic moduli related to shear deformations.

Odd elasticity induces a nonzero topological invariant (Chern number) in vibrational modes.

Chiral edge waves are present at the boundary, enabled by the plate's finite thickness and odd elasticity.

Abstract

Odd elasticity encompasses active elastic systems whose stress-strain relationship is not compatible with a potential energy. As the requirement of energy conservation is lifted from linear elasticity, new anti-symmetric (odd) components appear in the elastic tensor. In this work, we study the odd elasticity and non-Hermitian wave dynamics of active surfaces, specifically plates of moderate thickness. We find that a free-standing moderately thick, isotropic plate can exhibit two odd-elastic moduli, both of which are related to shear deformations of the plate. These odd moduli can endow the vibrational modes of the plate with a nonzero topological invariant known as the first Chern number. Within continuum elastic theory, we show that the Chern number is related to the presence of unidirectional shearing waves that are hosted at the plate's boundary. We show that the existence of these chiral edge waves hinges on a distinctive two-step mechanism: the finite thickness of the sample gaps the shear modes and the odd elasticity endows them with chirality.