Woven Nematic Defects, Skyrmions and the Abelian Sandpile Model
arXiv:1808.02425 · doi:10.1103/PhysRevLett.121.237801
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.
arXiv comment5 pages, 4 figures
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