Aspects of Defect Topology in Smectic Liquid Crystals

Abstract

We study the topology of smectic defects in two and three dimensions. We give a topological classification of smectic point defects and disclination lines in three dimensions. In addition we describe the combination rules for smectic point defects in two and three dimensions, showing how the broken translational symmetry of the smectic confers a path dependence on the result of defect addition.

arXiv comment19 pages, 13 figures

References in corpus (7)

• Disclination Loops, Hedgehogs, and All That
• Smectics: Symmetry Breaking, Singularities, and Surfaces
• Helical Ribbons as Isometric Textures
• Modeling Smectic Layers in Confined Geometries: Order Parameter and Defects
• Composite Dislocations in Smectic Liquid Crystals
• The Topology of Dislocations in Smectic Liquid Crystals
• Constructing a polynomial whose nodal set is the three-twist knot $5_2$

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• The Topological Origin of the Peierls-Nabarro Barrier
• Contact Topology and the Classification of Disclination Lines in Cholesteric Liquid Crystals
• Colloidal smectics in button-like confinements: experiment and theory
• Network topology of interlocked chiral particles
• Magnetic properties of the spiral spin liquid and surrounding phases in the square lattice XY model
• Singular Contact Geometry and Beltrami Fields in Cholesteric Liquid Crystals
• Layer topology of smectic grain boundaries
• Dislocations and Fibrations: The Topological Structure of Knotted Smectic Defects
• Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals
• Topology of orientational defects in confined smectic liquid crystals