Abstract
We describe the geometry of bend distortions in liquid crystals and their fundamental degeneracies, which we call β lines; these represent a new class of linelike topological defect in twist-bend nematics. We present constructions for smecticlike textures containing screw and edge dislocations and also for vortexlike structures of double twist and Skyrmions. We analyze 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 geometric perspective on the fractionalization of Skyrmions.
Highlights
We describe the geometry of bend distortions in liquid crystals and their fundamental degeneracies, which we call β lines; these represent a new class of linelike topological defect in twist-bend nematics
Fresh perspectives invariably accompany the discovery of a new phase: The experimental discovery of the twistbend nematic phase [1,2,3] invites fresh consideration of nematic geometry and topology
In this Letter, we introduce a linelike geometric degeneracy associated to zeros of the bend in a unit vector field, that we call β lines
Summary
Fresh perspectives invariably accompany the discovery of a new phase: The experimental discovery of the twistbend nematic phase [1,2,3] invites fresh consideration of nematic geometry and topology. The geometrical and topological features of bend are a natural vehicle for describing the degeneracies and defects of the twist-bend phase, they arise more generally and apply to any material described by a unit vector, or line, field.
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