skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Self-Assembly and Electrostriction of Arrays and Chains of Hopfion Particles in Chiral Liquid Crystals

Journal Article · · Nature Communications
DOI:https://doi.org/10.1038/ncomms7012· OSTI ID:1169777
 [1];  [2];  [2]
  1. Univ. of Colorado, Boulder, CO (United States)
  2. National Renewable Energy Lab. (NREL), Golden, CO (United States); Univ. of Colorado, Boulder, CO (United States)

Some of the most exotic condensed matter phases, such as twist grain boundary and blue phases in liquid crystals and Abrikosov phases in superconductors, contain arrays of topological defects in their ground state. Comprised of a triangular lattice of double-twist tubes of magnetization, the so-called ‘A-phase’ in chiral magnets is an example of a thermodynamically stable phase with topologically nontrivial solitonic field configurations referred to as two-dimensional skyrmions, or baby-skyrmions. Here we report that three-dimensional skyrmions in the form of double-twist tori called ‘hopfions’, or ‘torons’ when accompanied by additional self-compensating defects, self-assemble into periodic arrays and linear chains that exhibit electrostriction. In confined chiral nematic liquid crystals, this self-assembly is similar to that of liquid crystal colloids and originates from long-range elastic interactions between particle-like skyrmionic torus knots of molecular alignment field, which can be tuned from isotropic repulsive to weakly or highly anisotropic attractive by low-voltage electric fields.

Research Organization:
National Renewable Energy Laboratory (NREL), Golden, CO (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC36-08GO28308
OSTI ID:
1169777
Report Number(s):
NREL/JA-5900-62667; MainId:14291; UUID:354b1404-b229-e411-b769-d89d67132a6d; MainAdminID:2771
Journal Information:
Nature Communications, Vol. 6; ISSN 2041-1723
Publisher:
Nature Publishing GroupCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 81 works
Citation information provided by
Web of Science

References (51)

Colloquium : Disclination loops, point defects, and all that in nematic liquid crystals journal April 2012
Geometrical frustration and defects in condensed matter systems journal March 2008
Skyrmion Lattice in a Chiral Magnet journal February 2009
Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids journal December 2009
Generating the Hopf Fibration Experimentally in Nematic Liquid Crystals journal June 2013
Self-assembly of skyrmion-dressed chiral nematic colloids with tangential anchoring journal June 2014
Novel Colloidal Interactions in Anisotropic Fluids journal March 1997
Creation and dynamics of knotted vortices journal March 2013
Isolated optical vortex knots journal January 2010
Spontaneous motion in hierarchically assembled active matter journal November 2012
Defect Annihilation and Proliferation in Active Nematics journal May 2013
Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams journal August 2012
Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities journal June 2012
Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles journal March 2013
A Self-Quenched Defect Glass in a Colloid-Nematic Liquid Crystal Composite journal October 2011
Reconfigurable Knots and Links in Chiral Nematic Colloids journal June 2011
Topological colloids journal December 2012
Toward a Tetravalent Chemistry of Colloids journal October 2002
Static and dynamic properties of cholesteric fingers in electric field journal October 2000
Pattern formation outside of equilibrium journal July 1993
Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies journal June 1993
Crystalline liquids: the blue phases journal April 1989
Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal journal March 2011
Spontaneous skyrmion ground states in magnetic metals journal August 2006
Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics journal July 2014
Theory of skyrmion states in liquid crystals journal October 2014
Electromagnetic knots journal July 1995
Torus knots as Hopfions journal January 2014
3-sphere fibrations: a tool for analyzing twisted materials in condensed matter journal October 2009
A geometrical template for toroidal aggregates of chiral macromolecules journal March 2008
Ball lightning an electromagnetic knot? journal September 1996
Knots in a Spinor Bose-Einstein Condensate journal May 2008
3D skyrmion and knot in two-component Bose–Einstein condensates journal December 2013
Propagating Magnetic Vortex Rings in Ferromagnets journal February 1999
Vortex rings in ferromagnets: Numerical simulations of the time-dependent three-dimensional Landau-Lifshitz equation journal November 2007
Dynamical toroidal Hopfions in a ferromagnet with easy-axis anisotropy journal December 2009
Multimodal nonlinear optical polarizing microscopy of long-range molecular order in liquid crystals journal January 2010
Three dimensional optical manipulation and structural imaging of soft materials by use of laser tweezers and multimodal nonlinear microscopy journal January 2010
Electrically variable diffraction in spherulitic liquid crystals journal September 1974
Self-assembly of colloid-cholesteric composites provides a possible route to switchable optical materials journal June 2014
Persistent tangled vortex rings in generic excitable media journal September 1994
Knots as Stable Soliton Solutions in a Three-Dimensional Classical Field Theory journal November 1998
Winding Hopfions on journal November 2013
Electrically tunable diffraction of light from 2D nematic colloidal crystals journal July 2008
Assembly and control of 3D nematic dipolar colloidal crystals journal February 2013
Multiple chiral topological states in liquid crystals from unstructured light beams journal February 2014
Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy text January 2009
Three dimensional optical manipulation and structural imaging of soft materials by use of laser tweezers and multimodal nonlinear microscopy text January 2010
Self-assembly of colloid-cholesteric composites provides a possible route to switchable optical materials text January 2014
Theory of skyrmion states in liquid crystals: axisymmetric cholesteric bubbles (spherulites) text January 2014
Spontaneous Skyrmion Ground States in Magnetic Metals text January 2006

Cited By (28)

Light-Driven Electrohydrodynamic Instabilities in Liquid Crystals journal April 2018
Periodic Planar-Homeotropic Anchoring Realized by Photoalignment for Stabilization of Chiral Superstructures journal January 2018
Cholesteric Liquid Crystal Materials for Tunable Diffractive Optics journal June 2018
Dynamic Spirals of Nanoparticles in Light‐Responsive Polygonal Fields journal August 2019
Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids journal December 2016
Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film journal August 2017
Schools of skyrmions with electrically tunable elastic interactions journal October 2019
Two-dimensional skyrmion bags in liquid crystals and ferromagnets journal April 2019
Liquid-crystalline half-Skyrmion lattice spotted by Kossel diagrams journal November 2018
Current-induced shuttlecock-like movement of non-axisymmetric chiral skyrmions journal January 2020
Dynamics of electrically driven solitons in nematic and cholesteric liquid crystals journal January 2020
Topological states in chiral active matter: Dynamic blue phases and active half-skyrmions journal February 2019
Two-dimensional, blue phase tactoids journal July 2018
Helicoids in chiral liquid crystals under external fields journal November 2019
Optically enriched and guided dynamics of active skyrmions journal January 2020
Thermo-Optical Generation of Particle-Like Structures in Frustrated Chiral Nematic Film journal October 2019
Skyrmion and bimeron excitations in bilayer quantum Hall systems journal February 2010
Dynamic Spirals of Nanoparticles in Light-Responsive Polygonal Fields preprint April 2019
Dynamic Spirals of Nanoparticles in Light-Responsive Polygonal Fields preprint April 2019
Current-induced shuttlecock-like movement of non-axisymmetric chiral skyrmions
  • Murooka, Remi; Leonov, Andrey O.; Inoue, Katsuya
  • Washington, D.C. : American Association for the Advancement of Science https://doi.org/10.34657/4191
null January 2020
Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions text January 2017
Topological states in chiral active matter: dynamic blue phases and active half-skyrmions text January 2018
Helicoids in chiral liquid crystals under external fields text January 2019
Light-controlled skyrmions and torons as reconfigurable particles text January 2019
Optically enriched and guided dynamics of active skyrmions text January 2019
Squirming motion of baby skyrmions in nematic fluids journal September 2017
Topology-commanded optical properties of bistable electric-field-induced torons in cholesteric bubble domains journal November 2017
Superior electro-optic response in multiferroic bismuth ferrite nanoparticle doped nematic liquid crystal device journal June 2015

Similar Records

Two-Dimensional Skyrmions and Other Solitonic Structures in Confinement-Frustrated Chiral Nematics
Journal Article · Thu Jul 10 00:00:00 EDT 2014 · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics · OSTI ID:1169777

Review: knots and other new topological effects in liquid crystals and colloids
Journal Article · Tue Sep 08 00:00:00 EDT 2020 · Reports on Progress in Physics · OSTI ID:1169777

Field-Driven Dynamics of Magnetic Hopfions
Journal Article · Fri Dec 17 00:00:00 EST 2021 · Physical Review Letters · OSTI ID:1169777