Contact Topology and the Classification of Disclination Lines in Cholesteric Liquid Crystals
arXiv:2212.01085 · doi:10.1103/PhysRevLett.130.228102
Abstract
We give a topological classification of defect lines in cholesteric liquid crystals using methods from contact topology. By focusing on the role played by the chirality of the material, we demonstrate a fundamental distinction between `tight' and `overtwisted' disclination lines not detected by standard homotopy theory arguments. The classification of overtwisted lines is the same as nematics, however, we show that tight disclinations possess a topological layer number that is conserved as long as the twist is nonvanishing. Finally, we observe that chirality frustrates the escape of removable defect lines, and explain how this frustration underlies the formation of several structures observed in experiments.
arXiv comment6 pages, 3 figures
References in corpus (19)
- On the classification of tight contact structures I
- Disclination Loops, Hedgehogs, and All That
- Three-dimensional crystals of adaptive knots
- Review: Topology of solitons and singular defects in chiral liquid crystals
- Nematic braids: topological invariants and rewiring of disclinations
- Three-Dimensional Active Defect Loops
- Topological defects in cholesteric liquid crystal shells
- Smectics: Symmetry Breaking, Singularities, and Surfaces
- Waltzing route towards double-helix formation in cholesteric shells
- Umbilic Lines in Orientational Order
- Global Defect Topology in Nematic Liquid Crystals
- Orientation-dependent handedness and chiral design
- Aspects of Defect Topology in Smectic Liquid Crystals
- Maxwell's Theory of Solid Angle and the Construction of Knotted Fields
- The Geometry of the Cholesteric Phase
- Topological and geometric decomposition of nematic textures
- Point Defects, Chirality and Singularity Theory in Cholesteric Liquid Crystal Droplets
- Intrinsic Geometry and Director Reconstruction for Three-Dimensional Liquid Crystals
- Contact Topology and the Structure and Dynamics of Cholesterics