Geometry of Bend: Singular Lines and Defects in Twist-Bend Nematics

Abstract

We describe the geometry of bend distortions in twist-bend nematic liquid crystals in terms of their fundamental degeneracies, which we call $\beta$ lines. These represent a new class of line-like topological defect. We use them to construct and characterise novel structures, including grain boundary and focal conic smectic-like defects, Skyrmions, and knotted merons. We analyse their local geometry and global structure, showing that their intersection with any surface is twice the Skyrmion number. Finally, we demonstrate how arbitrary knots and links can be created and describe them in terms of merons, giving a new geometric perspective on the fractionalisation of Skyrmions.

arXiv comment27 pages, 18 figures

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Cited by in corpus (4)

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• Intrinsic Geometry and Director Reconstruction for Three-Dimensional Liquid Crystals
• Helical microstructures in molluscan biomineralization are a biological example of close packed helices that may form from a colloidal liquid crystal precursor in a twist-bend nematic phase
• Helix alignment, chevrons, and edge dislocations in twist-bend ferroelectric nematics