Self-Assembly and Electrostriction of Arrays and Chains of Hopfion Particles in Chiral Liquid Crystals
Abstract
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.
- Authors:
-
- Univ. of Colorado, Boulder, CO (United States)
- National Renewable Energy Lab. (NREL), Golden, CO (United States); Univ. of Colorado, Boulder, CO (United States)
- Publication Date:
- Research Org.:
- National Renewable Energy Laboratory (NREL), Golden, CO (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1169777
- Report Number(s):
- NREL/JA-5900-62667
Journal ID: ISSN 2041-1723; MainId:14291;UUID:354b1404-b229-e411-b769-d89d67132a6d;MainAdminID:2771
- Grant/Contract Number:
- AC36-08GO28308
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Nature Communications
- Additional Journal Information:
- Journal Volume: 6; Journal ID: ISSN 2041-1723
- Publisher:
- Nature Publishing Group
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 77 NANOSCIENCE AND NANOTECHNOLOGY; liquid crystals; self assembly
Citation Formats
Ackerman, P. J., van de Lagemaat, J., and Smalyukh, I. I. Self-Assembly and Electrostriction of Arrays and Chains of Hopfion Particles in Chiral Liquid Crystals. United States: N. p., 2015.
Web. doi:10.1038/ncomms7012.
Ackerman, P. J., van de Lagemaat, J., & Smalyukh, I. I. Self-Assembly and Electrostriction of Arrays and Chains of Hopfion Particles in Chiral Liquid Crystals. United States. https://doi.org/10.1038/ncomms7012
Ackerman, P. J., van de Lagemaat, J., and Smalyukh, I. I. Wed .
"Self-Assembly and Electrostriction of Arrays and Chains of Hopfion Particles in Chiral Liquid Crystals". United States. https://doi.org/10.1038/ncomms7012. https://www.osti.gov/servlets/purl/1169777.
@article{osti_1169777,
title = {Self-Assembly and Electrostriction of Arrays and Chains of Hopfion Particles in Chiral Liquid Crystals},
author = {Ackerman, P. J. and van de Lagemaat, J. and Smalyukh, I. I.},
abstractNote = {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.},
doi = {10.1038/ncomms7012},
journal = {Nature Communications},
number = ,
volume = 6,
place = {United States},
year = {Wed Jan 21 00:00:00 EST 2015},
month = {Wed Jan 21 00:00:00 EST 2015}
}
Web of Science
Works referenced in this record:
Colloquium : Disclination loops, point defects, and all that in nematic liquid crystals
journal, April 2012
- Alexander, Gareth P.; Chen, Bryan Gin-ge; Matsumoto, Elisabetta A.
- Reviews of Modern Physics, Vol. 84, Issue 2
Geometrical frustration and defects in condensed matter systems
journal, March 2008
- Mosseri, Rémy
- Comptes Rendus Chimie, Vol. 11, Issue 3
Skyrmion Lattice in a Chiral Magnet
journal, February 2009
- Muhlbauer, S.; Binz, B.; Jonietz, F.
- Science, Vol. 323, Issue 5916
Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids
journal, December 2009
- Smalyukh, Ivan I.; Lansac, Yves; Clark, Noel A.
- Nature Materials, Vol. 9, Issue 2
Generating the Hopf Fibration Experimentally in Nematic Liquid Crystals
journal, June 2013
- Chen, Bryan Gin-ge; Ackerman, Paul J.; Alexander, Gareth P.
- Physical Review Letters, Vol. 110, Issue 23
Self-assembly of skyrmion-dressed chiral nematic colloids with tangential anchoring
journal, June 2014
- Pandey, M. B.; Porenta, T.; Brewer, J.
- Physical Review E, Vol. 89, Issue 6
Novel Colloidal Interactions in Anisotropic Fluids
journal, March 1997
- Poulin, P.
- Science, Vol. 275, Issue 5307
Creation and dynamics of knotted vortices
journal, March 2013
- Kleckner, Dustin; Irvine, William T. M.
- Nature Physics, Vol. 9, Issue 4
Isolated optical vortex knots
journal, January 2010
- Dennis, Mark R.; King, Robert P.; Jack, Barry
- Nature Physics, Vol. 6, Issue 2
Spontaneous motion in hierarchically assembled active matter
journal, November 2012
- Sanchez, Tim; Chen, Daniel T. N.; DeCamp, Stephen J.
- Nature, Vol. 491, Issue 7424
Defect Annihilation and Proliferation in Active Nematics
journal, May 2013
- Giomi, Luca; Bowick, Mark J.; Ma, Xu
- Physical Review Letters, Vol. 110, Issue 22
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
- Ackerman, Paul J.; Qi, Zhiyuan; Smalyukh, Ivan I.
- Physical Review E, Vol. 86, Issue 2
Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities
journal, June 2012
- Ackerman, Paul J.; Qi, Zhiyuan; Lin, Yiheng
- Scientific Reports, Vol. 2, Issue 1
Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles
journal, March 2013
- Evans, Julian S.; Ackerman, Paul J.; Broer, Dirk J.
- Physical Review E, Vol. 87, Issue 3
A Self-Quenched Defect Glass in a Colloid-Nematic Liquid Crystal Composite
journal, October 2011
- Wood, T. A.; Lintuvuori, J. S.; Schofield, A. B.
- Science, Vol. 334, Issue 6052
Reconfigurable Knots and Links in Chiral Nematic Colloids
journal, June 2011
- Tkalec, U.; Ravnik, M.; Copar, S.
- Science, Vol. 333, Issue 6038
Topological colloids
journal, December 2012
- Senyuk, Bohdan; Liu, Qingkun; He, Sailing
- Nature, Vol. 493, Issue 7431
Toward a Tetravalent Chemistry of Colloids
journal, October 2002
- Nelson, David R.
- Nano Letters, Vol. 2, Issue 10
Static and dynamic properties of cholesteric fingers in electric field
journal, October 2000
- Oswald, P.; Baudry, J.; Pirkl, S.
- Physics Reports, Vol. 337, Issue 1-2
Pattern formation outside of equilibrium
journal, July 1993
- Cross, M. C.; Hohenberg, P. C.
- Reviews of Modern Physics, Vol. 65, Issue 3
Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies
journal, June 1993
- Sondhi, S. L.; Karlhede, A.; Kivelson, S. A.
- Physical Review B, Vol. 47, Issue 24
Crystalline liquids: the blue phases
journal, April 1989
- Wright, David C.; Mermin, N. David
- Reviews of Modern Physics, Vol. 61, Issue 2
Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal
journal, March 2011
- Fukuda, Jun-ichi; Žumer, Slobodan
- Nature Communications, Vol. 2, Issue 1
Spontaneous skyrmion ground states in magnetic metals
journal, August 2006
- Rößler, U. K.; Bogdanov, A. N.; Pfleiderer, C.
- Nature, Vol. 442, Issue 7104, p. 797-801
Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics
journal, July 2014
- Ackerman, Paul J.; Trivedi, Rahul P.; Senyuk, Bohdan
- Physical Review E, Vol. 90, Issue 1
Theory of skyrmion states in liquid crystals
journal, October 2014
- Leonov, A. O.; Dragunov, I. E.; Rößler, U. K.
- Physical Review E, Vol. 90, Issue 4
Electromagnetic knots
journal, July 1995
- Rañada, Antonio F.; Trueba, JoséL.
- Physics Letters A, Vol. 202, Issue 5-6
Torus knots as Hopfions
journal, January 2014
- Kobayashi, Michikazu; Nitta, Muneto
- Physics Letters B, Vol. 728
3-sphere fibrations: a tool for analyzing twisted materials in condensed matter
journal, October 2009
- Sadoc, J. F.; Charvolin, J.
- Journal of Physics A: Mathematical and Theoretical, Vol. 42, Issue 46
A geometrical template for toroidal aggregates of chiral macromolecules
journal, March 2008
- Charvolin, J.; Sadoc, J. -F.
- The European Physical Journal E, Vol. 25, Issue 3
Ball lightning an electromagnetic knot?
journal, September 1996
- Rañada, Antonio F.; Trueba, José L.
- Nature, Vol. 383, Issue 6595
Knots in a Spinor Bose-Einstein Condensate
journal, May 2008
- Kawaguchi, Yuki; Nitta, Muneto; Ueda, Masahito
- Physical Review Letters, Vol. 100, Issue 18
3D skyrmion and knot in two-component Bose–Einstein condensates
journal, December 2013
- Liu, Yong-Kai; Zhang, Cong; Yang, Shi-Jie
- Physics Letters A, Vol. 377, Issue 45-48
Propagating Magnetic Vortex Rings in Ferromagnets
journal, February 1999
- Cooper, N. R.
- Physical Review Letters, Vol. 82, Issue 7
Vortex rings in ferromagnets: Numerical simulations of the time-dependent three-dimensional Landau-Lifshitz equation
journal, November 2007
- Sutcliffe, Paul
- Physical Review B, Vol. 76, Issue 18
Dynamical toroidal Hopfions in a ferromagnet with easy-axis anisotropy
journal, December 2009
- Borisov, A. B.; Rybakov, F. N.
- JETP Letters, Vol. 90, Issue 7
Multimodal nonlinear optical polarizing microscopy of long-range molecular order in liquid crystals
journal, January 2010
- Lee, Taewoo; Trivedi, Rahul P.; Smalyukh, Ivan I.
- Optics Letters, Vol. 35, Issue 20
Three dimensional optical manipulation and structural imaging of soft materials by use of laser tweezers and multimodal nonlinear microscopy
journal, January 2010
- Trivedi, Rahul P.; Lee, Taewoo; Bertness, Kris A.
- Optics Express, Vol. 18, Issue 26
Electrically variable diffraction in spherulitic liquid crystals
journal, September 1974
- Haas, Werner E. L.; Adams, James E.
- Applied Physics Letters, Vol. 25, Issue 5
Self-assembly of colloid-cholesteric composites provides a possible route to switchable optical materials
journal, June 2014
- Stratford, K.; Henrich, O.; Lintuvuori, J. S.
- Nature Communications, Vol. 5, Issue 1
Persistent tangled vortex rings in generic excitable media
journal, September 1994
- Winfree, A. T.
- Nature, Vol. 371, Issue 6494
Knots as Stable Soliton Solutions in a Three-Dimensional Classical Field Theory
journal, November 1998
- Battye, Richard A.; Sutcliffe, P. M.
- Physical Review Letters, Vol. 81, Issue 22
Winding Hopfions on
journal, November 2013
- Kobayashi, Michikazu; Nitta, Muneto
- Nuclear Physics B, Vol. 876, Issue 2
Electrically tunable diffraction of light from 2D nematic colloidal crystals
journal, July 2008
- Humar, M.; Škarabot, M.; Ravnik, M.
- The European Physical Journal E, Vol. 27, Issue 1
Assembly and control of 3D nematic dipolar colloidal crystals
journal, February 2013
- Nych, A.; Ognysta, U.; Škarabot, M.
- Nature Communications, Vol. 4, Issue 1
Multiple chiral topological states in liquid crystals from unstructured light beams
journal, February 2014
- Loussert, Charles; Brasselet, Etienne
- Applied Physics Letters, Vol. 104, Issue 5
Electromagnetic knots
journal, July 1995
- Rañada, Antonio F.; Trueba, JoséL.
- Physics Letters A, Vol. 202, Issue 5-6
Geometrical frustration and defects in condensed matter systems
journal, March 2008
- Mosseri, Rémy
- Comptes Rendus Chimie, Vol. 11, Issue 3
Torus knots as Hopfions
journal, January 2014
- Kobayashi, Michikazu; Nitta, Muneto
- Physics Letters B, Vol. 728
Persistent tangled vortex rings in generic excitable media
journal, September 1994
- Winfree, A. T.
- Nature, Vol. 371, Issue 6494
Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal
journal, March 2011
- Fukuda, Jun-ichi; Žumer, Slobodan
- Nature Communications, Vol. 2, Issue 1
Assembly and control of 3D nematic dipolar colloidal crystals
journal, February 2013
- Nych, A.; Ognysta, U.; Škarabot, M.
- Nature Communications, Vol. 4, Issue 1
Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities
journal, June 2012
- Ackerman, Paul J.; Qi, Zhiyuan; Lin, Yiheng
- Scientific Reports, Vol. 2, Issue 1
Multiple chiral topological states in liquid crystals from unstructured light beams
journal, February 2014
- Loussert, Charles; Brasselet, Etienne
- Applied Physics Letters, Vol. 104, Issue 5
Novel Colloidal Interactions in Anisotropic Fluids
journal, March 1997
- Poulin, P.
- Science, Vol. 275, Issue 5307
Electrically tunable diffraction of light from 2D nematic colloidal crystals
journal, July 2008
- Humar, M.; Škarabot, M.; Ravnik, M.
- The European Physical Journal E, Vol. 27, Issue 1
Dynamical Toroidal Hopfions in a Ferromagnet with Easy-Axis Anisotropy
text, January 2009
- Borisov, A. B.; Rybakov, F. N.
- arXiv
Three dimensional optical manipulation and structural imaging of soft materials by use of laser tweezers and multimodal nonlinear microscopy
text, January 2010
- Trivedi, Rahul P.; Lee, Taewoo; Bertness, Kris A.
- arXiv
Self-assembly of colloid-cholesteric composites provides a possible route to switchable optical materials
text, January 2014
- Stratford, K.; Henrich, O.; Lintuvuori, J. S.
- arXiv
Theory of skyrmion states in liquid crystals: axisymmetric cholesteric bubbles (spherulites)
text, January 2014
- Leonov, A. O.; Dragunov, I. E.; Rößler, U. K.
- arXiv
Spontaneous Skyrmion Ground States in Magnetic Metals
text, January 2006
- Roessler, U. K.; Bogdanov, A. N.; Pfleiderer, C.
- arXiv
Works referencing / citing this record:
Light-Driven Electrohydrodynamic Instabilities in Liquid Crystals
journal, April 2018
- Zhan, Yuanyuan; Schenning, Albertus P. H. J.; Broer, Dirk J.
- Advanced Functional Materials, Vol. 28, Issue 21
Periodic Planar-Homeotropic Anchoring Realized by Photoalignment for Stabilization of Chiral Superstructures
journal, January 2018
- Nys, Inge; Chen, Ke; Beeckman, Jeroen
- Advanced Optical Materials, Vol. 6, Issue 6
Cholesteric Liquid Crystal Materials for Tunable Diffractive Optics
journal, June 2018
- Ryabchun, Alexander; Bobrovsky, Alexey
- Advanced Optical Materials, Vol. 6, Issue 15
Dynamic Spirals of Nanoparticles in Light‐Responsive Polygonal Fields
journal, August 2019
- Orlova, Tetiana; Plamont, Rémi; Depauw, Alexis
- Small, Vol. 15, Issue 39
Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids
journal, December 2016
- Ackerman, Paul J.; Smalyukh, Ivan I.
- Nature Materials, Vol. 16, Issue 4
Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film
journal, August 2017
- Nych, Andriy; Fukuda, Jun-ichi; Ognysta, Uliana
- Nature Physics, Vol. 13, Issue 12
Schools of skyrmions with electrically tunable elastic interactions
journal, October 2019
- Sohn, Hayley R. O.; Liu, Changda D.; Smalyukh, Ivan I.
- Nature Communications, Vol. 10, Issue 1
Two-dimensional skyrmion bags in liquid crystals and ferromagnets
journal, April 2019
- Foster, David; Kind, Charles; Ackerman, Paul J.
- Nature Physics, Vol. 15, Issue 7
Liquid-crystalline half-Skyrmion lattice spotted by Kossel diagrams
journal, November 2018
- Fukuda, Jun-ichi; Nych, Andriy; Ognysta, Uliana
- Scientific Reports, Vol. 8, Issue 1
Current-induced shuttlecock-like movement of non-axisymmetric chiral skyrmions
journal, January 2020
- Murooka, Remi; Leonov, Andrey O.; Inoue, Katsuya
- Scientific Reports, Vol. 10, Issue 1
Dynamics of electrically driven solitons in nematic and cholesteric liquid crystals
journal, January 2020
- Shen, Yuan; Dierking, Ingo
- Communications Physics, Vol. 3, Issue 1
Topological states in chiral active matter: Dynamic blue phases and active half-skyrmions
journal, February 2019
- Metselaar, Luuk; Doostmohammadi, Amin; Yeomans, Julia M.
- The Journal of Chemical Physics, Vol. 150, Issue 6
Two-dimensional, blue phase tactoids
journal, July 2018
- Metselaar, Luuk; Doostmohammadi, Amin; Yeomans, Julia M.
- Molecular Physics, Vol. 116, Issue 21-22
Helicoids in chiral liquid crystals under external fields
journal, November 2019
- De Matteis, G.; Martina, L.; Naya, C.
- Physical Review E, Vol. 100, Issue 5
Optically enriched and guided dynamics of active skyrmions
journal, January 2020
- Sohn, Hayley R. O.; Liu, Changda D.; Voinescu, Robert
- Optics Express, Vol. 28, Issue 5
Thermo-Optical Generation of Particle-Like Structures in Frustrated Chiral Nematic Film
journal, October 2019
- Shvetsov, Sergey; Orlova, Tetiana; Emelyanenko, Alexander V.
- Crystals, Vol. 9, Issue 11
Skyrmion and bimeron excitations in bilayer quantum Hall systems
journal, February 2010
- Ezawa, Z. F.; Tsitsishvili, G.
- Physica E: Low-dimensional Systems and Nanostructures, Vol. 42, Issue 4
Dynamic Spirals of Nanoparticles in Light-Responsive Polygonal Fields
preprint, April 2019
- Orlova, Tetiana; Plamont, Rémi; Depauw, Alexis
Dynamic Spirals of Nanoparticles in Light-Responsive Polygonal Fields
preprint, April 2019
- Orlova, Tetiana; Plamont, Rémi; Depauw, Alexis
Current-induced shuttlecock-like movement of non-axisymmetric chiral skyrmions
null, January 2020
- Murooka, Remi; Leonov, Andrey O.; Inoue, Katsuya
- Washington, D.C. : American Association for the Advancement of Science
Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions
text, January 2017
- Ackerman, P. J.; Smalyukh, I. I.
- arXiv
Topological states in chiral active matter: dynamic blue phases and active half-skyrmions
text, January 2018
- Metselaar, Luuk; Doostmohammadi, Amin; Yeomans, Julia M.
- arXiv
Helicoids in chiral liquid crystals under external fields
text, January 2019
- De Matteis, G.; Martina, L.; Naya, C.
- arXiv
Light-controlled skyrmions and torons as reconfigurable particles
text, January 2019
- Sohn, Hayley R. O.; Liu, Changda D.; Smalyukh, Ivan I.
- arXiv
Optically enriched and guided dynamics of active skyrmions
text, January 2019
- Sohn, Hayley R. O.; Liu, Changda D.; Voinescu, Robert
- arXiv
Squirming motion of baby skyrmions in nematic fluids
journal, September 2017
- Ackerman, Paul J.; Boyle, Timothy; Smalyukh, Ivan I.
- Nature Communications, Vol. 8, Issue 1
Schools of skyrmions with electrically tunable elastic interactions
journal, October 2019
- Sohn, Hayley R. O.; Liu, Changda D.; Smalyukh, Ivan I.
- Nature Communications, Vol. 10, Issue 1
Topology-commanded optical properties of bistable electric-field-induced torons in cholesteric bubble domains
journal, November 2017
- Varanytsia, Andrii; Posnjak, Gregor; Mur, Urban
- Scientific Reports, Vol. 7, Issue 1
Current-induced shuttlecock-like movement of non-axisymmetric chiral skyrmions
journal, January 2020
- Murooka, Remi; Leonov, Andrey O.; Inoue, Katsuya
- Scientific Reports, Vol. 10, Issue 1
Superior electro-optic response in multiferroic bismuth ferrite nanoparticle doped nematic liquid crystal device
journal, June 2015
- Nayek, Prasenjit; Li, Guoqiang
- Scientific Reports, Vol. 5, Issue 1