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arXiv · 1808.02425

Woven Nematic Defects, Skyrmions and the Abelian Sandpile Model

Thomas Machon·Gareth P. Alexander
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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.

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Thomas Machon, Gareth P. Alexander. 2018-08-07. Woven Nematic Defects, Skyrmions and the Abelian Sandpile Model. https://doi.org/10.1103/physrevlett.121.237801

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