Defect Dynamics in Cholesterics: Beyond the Peach-Koehler Force

TL;DR

This paper reveals that in cholesteric liquid crystals, defect interactions involve complex topological solitons called merons, requiring a new framework beyond traditional Peach-Koehler forces, especially at high chirality levels.

Contribution

It introduces a novel approach using contact topology to analyze defect dynamics in cholesterics, highlighting the role of merons in defect interactions beyond classical theories.

Findings

Merons dominate defect interactions at high chirality.

Defects can change winding by emitting merons.

Traditional Peach-Koehler forces are insufficient for these systems.

Abstract

The Peach-Koehler force between disclination lines was originally formulated in the study of crystalline solids, and has since been adopted to provide a notion of interactions between disclination lines in nematic liquid crystals. Here, we argue that the standard formulation of this interaction force seemingly fails for materials where there is a symmetry-broken ground state, and suggest that this is due to the interaction between disclination lines and merons: non-singular yet non-trivial topological solitons. We examine this in the context of chiral nematic (cholesteric) liquid crystals, which provide a natural setting for studying these interactions due to their energetic preference for meron tubes in the form of double-twist cylinders. Through a combination of theory and simulation we demonstrate that, for sufficiently strong chirality, defects of $+1/2$ winding will change their winding through the emission of a meron line, and that interactions between the merons and defects dominate over defect-defect interactions. Instead of Peach-Koehler framework, we employ a method based on contact topology - the Gray stability theorem - to directly calculate the velocity field of the material. We apply our framework to point defects as well as disclination lines. Our results have implications not just for chiral materials, but also for other phases with modulated ground states, such as the twist-bend and splay-bend nematics.