Review: Topology of solitons and singular defects in chiral liquid crystals
arXiv:2112.14325 · doi:10.1080/21680396.2022.2040058
Abstract
Widely known for their uses in displays and electro-optics, liquid crystals are more than just technological marvels. They vividly reveal the topology and structure of various solitonic and singular field configurations, often markedly resembling the ones arising in many field theories and in the areas ranging from particle physics to optics, hard condensed matter and cosmology. In this review, we focus on chiral nematic liquid crystals to show how these experimentally highly accessible systems provide valuable insights into the structure and behavior of fractional, full, and multi-integer two-dimensional skyrmions, dislocations and both abelian and non-abelian defect lines, as well as various three-dimensionally localized, often knotted structures that include hopfions, heliknotons, torons and twistions. We provide comparisons of some of these field configurations with their topological counterparts in chiral magnets, discussing close analogies between these two condensed matter systems.
96 pages including 22 figures. Submitted to Liquid Crystals Reviews
References in corpus (28)
- Novel type of phase transition in a system of self-driven particles
- Magnetic skyrmion logic gates: conversion, duplication and merging of skyrmions
- Topological colloids
- Disclinations, dislocations and continuous defects: a reappraisal
- Ferroelectric-ferroelastic phase transition in a nematic liquid crystal
- Command of active matter by topological defects and patterns
- Physical foundations and basic properties of magnetic skyrmions
- Particle-like topologies in light
- Compact Skyrmions, Merons and Bimerons in Thin Chiral Magnetic Films
- Modeling planar degenerate wetting and anchoring in nematic liquid crystals
- Liquid Crystal Colloids
- Giant Skyrmions Stabilized by Dipole-Dipole Interactions in Thin Ferromagnetic Films
- Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics
- Three-dimensional crystals of adaptive knots
- Observation of Spontaneous Helielectric Nematic Fluids: Electric Analogy to Helimagnets
- Interpretation of saddle-splay and the Oseen-Frank free energy in liquid crystals
- Elastic and viscous properties of nematic dimer CB7CB
- Nematic liquid crystal boojums with handles on colloidal handlebodies
- Hopf solitons in helical and conical backgrounds of chiral magnetic solids
- Reconfigurable interactions and three-dimensional patterning of colloidal particles and defects in lamellar soft media
- Nematic braids: topological invariants and rewiring of disclinations
- Schools of skyrmions with electrically tunable elastic interactions
- Field-driven metamorphoses of isolated skyrmions within the conical state of cubic helimagnets
- Light-controlled skyrmions and torons as reconfigurable particles
- Topological carnival: electrically-powered motions of toron crystallites in chiral liquid crystals
- Geometric transformation and three-dimensional hopping of Hopf solitons
- Edge pinning and transformation of defect lines induced by faceted colloidal rings in nematic liquid crystals
- Colloidal Surfaces with Boundaries, Apex Boojums and Nested Elastic Self-Assembly of Nematic Colloids
Cited by in corpus (20)
- Geometric transformation and three-dimensional hopping of Hopf solitons
- Photonic torons, topological phase transition and tunable spin monopoles
- Topological solitonic macromolecules
- Sculpting liquid crystal skyrmions with external flows
- Splay-bend elastic inequalities shape tactoids, toroids, umbilics, and conic section walls in paraelectric, twist-bend, and ferroelectric nematics
- Topological invariants of vortices, merons, skyrmions, and their combinations in continuous and discrete systems
- Contact Topology and the Classification of Disclination Lines in Cholesteric Liquid Crystals
- Nanofluidic logic based on chiral skyrmion flows
- Photonic Shankar skyrmion
- Domain Wall Networks as Skyrmion Crystals in Chiral Magnets
- Unavoidable emergent biaxiality in chiral molecular-colloidal hybrid liquid crystals
- Spontaneous Chiral Symmetry Breaking in Polydisperse Achiral Near-Rigid Nematogens
- Electrically controlled propulsion of skyrmions in chiral nematic
- Topological Rigidity and Non-Abelian defect junctions in chiral nematic systems with effective biaxial symmetry
- Deformed states in paraelectric and ferroelectric nematic liquid crystals
- Construction of Hopfion Crystals
- Multiscale geometrical and topological learning in the analysis of soft matter collective dynamics
- Screw Symmetry, Chiral Hydrodynamics and Odd Instability in Active Cholesterics
- Quantum Skyrmions in Mixed States of Light and Their Nested Topology
- Helix alignment, chevrons, and edge dislocations in twist-bend ferroelectric nematics