Contact Topology and the Structure and Dynamics of Cholesterics

Abstract

Using tools and concepts from contact topology we show that non-vanishing twist implies conservation of the layer structure in cholesteric liquid crystals. This leads to a number of additional topological invariants for cholesteric textures, such as layer numbers, that are not captured by traditional descriptions, characterises the nature and size of the chiral energy barriers between metastable configurations, and gives a geometric characterisation of cholesteric dynamics in any context, including active systems, those in confined geometries or under the influence of an external field.

8 pages, 4 figures

References in corpus (6)

• Reconfigurable knots and links in chiral nematic colloids
• Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics
• Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions
• A change in stripes for cholesteric shells via anchoring in moderation
• Hydrodynamic instabilities in active cholesteric liquid crystals
• Reversal of Helicoidal Twist Handedness Near Point Defects of Confined Chiral Liquid Crystals

Cited by in corpus (8)

• Review: Topology of solitons and singular defects in chiral liquid crystals
• Surface anchoring as a control parameter for stabilizing torons, skyrmions, twisted walls, fingers and their hybrids in chiral nematics
• Helfrich-Hurault elastic instabilities driven by geometrical frustration
• 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 Classification of Disclination Lines in Cholesteric Liquid Crystals
• On toral posets and contact Lie algebras
• Screw Symmetry, Chiral Hydrodynamics and Odd Instability in Active Cholesterics