Woven Nematic Defects, Skyrmions and the Abelian Sandpile Model

TL;DR

This paper explores the connection between woven defect lines in nematic liquid crystals and stable configurations in the Abelian sandpile model, revealing a physical correspondence and novel topological states.

Contribution

It introduces a mapping between nematic defect states and sandpile configurations, and analyzes energy minima and domain wall Skyrmion solitons in this context.

Findings

Mapping between nematic defects and sandpile configurations

Identification of energy minima related to topological classes

Existence of domain wall Skyrmion solitons

Abstract

We show that a fixed set of woven defect lines in a nematic liquid crystal supports a set of non-singular topological states which can be mapped on to recurrent stable configurations in the Abelian sandpile model or chip-firing game. The physical correspondence between local Skyrmion flux and sandpile height is made between the two models. Using a toy model of the elastic energy, we examine the structure of energy minima as a function of topological class and show that the system admits domain wall Skyrmion solitons.