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Senyuk B, Meng C, Smalyukh II. Design and Preparation of Nematic Colloidal Particles. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2022; 38:9099-9118. [PMID: 35866261 DOI: 10.1021/acs.langmuir.2c00611] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Colloidal systems are abundant in technology, in biomedical settings, and in our daily life. The so-called "colloidal atoms" paradigm exploits interparticle interactions to self-assemble colloidal analogs of atomic and molecular crystals, liquid crystal glasses, and other types of condensed matter from nanometer- or micrometer-sized colloidal building blocks. Nematic colloids, which comprise colloidal particles dispersed within an anisotropic nematic fluid host medium, provide a particularly rich variety of physical behaviors at the mesoscale, not only matching but even exceeding the diversity of structural and phase behavior in conventional atomic and molecular systems. This feature article, using primarily examples of works from our own group, highlights recent developments in the design, fabrication, and self-assembly of nematic colloidal particles, including the capabilities of preprogramming their behavior by controlling the particle's surface boundary conditions for liquid crystal molecules at the colloidal surfaces as well as by defining the shape and topology of the colloidal particles. Recent progress in defining particle-induced defects, elastic multipoles, self-assembly, and dynamics is discussed along with open issues and challenges within this research field.
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Affiliation(s)
- Bohdan Senyuk
- Department of Physics, University of Colorado, Boulder, Colorado 80309, United States
| | - Cuiling Meng
- Department of Physics, University of Colorado, Boulder, Colorado 80309, United States
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, United States
- Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, United States
- Soft Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, United States
- Chemical Physics Program, Departments of Chemistry and Physics, University of Colorado, Boulder, Colorado 80309, United States
- Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, United States
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2
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Recent Progresses on Experimental Investigations of Topological and Dissipative Solitons in Liquid Crystals. CRYSTALS 2022. [DOI: 10.3390/cryst12010094] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Solitons in liquid crystals have received increasing attention due to their importance in fundamental physical science and potential applications in various fields. The study of solitons in liquid crystals has been carried out for over five decades with various kinds of solitons being reported. Recently, a number of new types of solitons have been observed, among which, many of them exhibit intriguing dynamic behaviors. In this paper, we briefly review the recent progresses on experimental investigations of solitons in liquid crystals.
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Leonov AO. Surface anchoring as a control parameter for shaping skyrmion or toron properties in thin layers of chiral nematic liquid crystals and noncentrosymmetric magnets. Phys Rev E 2021; 104:044701. [PMID: 34781482 DOI: 10.1103/physreve.104.044701] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Accepted: 10/01/2021] [Indexed: 11/07/2022]
Abstract
Existence of topological localized states (skyrmions and torons) and the mechanism of their condensation into modulated states are the ruling principles of condensed matter systems, such as chiral nematic liquid crystals (CLCs) and chiral magnets (ChM). In bulk helimagnets, skyrmions are rendered into thermodynamically stable hexagonal skyrmion lattice due to the combined effect of a magnetic field and, e.g., small anisotropic contributions. In thin glass cells of CLCs, skyrmions are formed in response to the geometrical frustration and field coupling effects. By numerical modeling, I undertake a systematic study of skyrmion or toron properties in thin layers of CLCs and ChMs with competing surface-induced and bulk anisotropies. The conical phase with a variable polar angle serves as a suitable background, which shapes skyrmion internal structure, guides the nucleation processes, and substantializes the skyrmion-skyrmion interaction. I show that the hexagonal lattice of torons can be stabilized in a vast region of the constructed phase diagram for both easy-axis bulk and surface anisotropies. A topologically trivial droplet is shown to form as a domain boundary between two cone states with different rotational fashion, which underpins its stability. The findings provide a recipe for controllably creating skyrmions and torons, possessing the features on demand for potential applications.
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Affiliation(s)
- Andrey O Leonov
- Chirality Research Center, Hiroshima University, Higashi-Hiroshima, Hiroshima 739-8526, Japan; Department of Chemistry, Faculty of Science, Hiroshima University Kagamiyama, Higashi Hiroshima, Hiroshima 739-8526, Japan; and IFW Dresden, Postfach 270016, D-01171 Dresden, Germany
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Smalyukh II. Review: knots and other new topological effects in liquid crystals and colloids. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 83:106601. [PMID: 32721944 DOI: 10.1088/1361-6633/abaa39] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Humankind has been obsessed with knots in religion, culture and daily life for millennia, while physicists like Gauss, Kelvin and Maxwell already involved them in models centuries ago. Nowadays, colloidal particles can be fabricated to have shapes of knots and links with arbitrary complexity. In liquid crystals, closed loops of singular vortex lines can be knotted by using colloidal particles and laser tweezers, as well as by confining nematic fluids into micrometer-sized droplets with complex topology. Knotted and linked colloidal particles induce knots and links of singular defects, which can be interlinked (or not) with colloidal particle knots, revealing the diversity of interactions between topologies of knotted fields and topologically nontrivial surfaces of colloidal objects. Even more diverse knotted structures emerge in nonsingular molecular alignment and magnetization fields in liquid crystals and colloidal ferromagnets. The topological solitons include hopfions, skyrmions, heliknotons, torons and other spatially localized continuous structures, which are classified based on homotopy theory, characterized by integer-valued topological invariants and often contain knotted or linked preimages, nonsingular regions of space corresponding to single points of the order parameter space. A zoo of topological solitons in liquid crystals, colloids and ferromagnets promises new breeds of information displays and a plethora of data storage, electro-optic and photonic applications. Their particle-like collective dynamics echoes coherent motions in active matter, ranging from crowds of people to schools of fish. This review discusses the state of the art in the field, as well as highlights recent developments and open questions in physics of knotted soft matter. We systematically overview knotted field configurations, the allowed transformations between them, their physical stability and how one can use one form of knotted fields to model, create and imprint other forms. The large variety of symmetries accessible to liquid crystals and colloids offer insights into stability, transformation and emergent dynamics of fully nonsingular and singular knotted fields of fundamental and applied importance. The common thread of this review is the ability to experimentally visualize these knots in real space. The review concludes with a discussion of how the studies of knots in liquid crystals and colloids can offer insights into topologically related structures in other branches of physics, with answers to many open questions, as well as how these experimentally observable knots hold a strong potential for providing new inspirations to the mathematical knot theory.
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Affiliation(s)
- Ivan I Smalyukh
- Department of Physics, Department of Electrical, Computer and Energy Engineering, Materials Science and Engineering Program and Soft Materials Research Center, University of Colorado, Boulder, CO 80309, United States of America
- Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, CO 80309, United States of America
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De Matteis G, Martina L, Naya C, Turco V. Helicoids in chiral liquid crystals under external fields. Phys Rev E 2019; 100:052703. [PMID: 31869894 DOI: 10.1103/physreve.100.052703] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/11/2019] [Indexed: 11/07/2022]
Abstract
Cholesteric liquid crystals, subject to externally applied magnetic fields and confined between two parallel planar surfaces with strong homeotropic anchoring conditions, are found to undergo transitions to different types of helicoidal configurations with disclinations. Analytical and numerical studies are performed in order to characterize their properties. In particular, we produce a phase diagram for the transitions from the nematic state to the helicoidal phases in terms of the molecular chirality and the strength of the applied magnetic field.
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Affiliation(s)
- G De Matteis
- Dipartimento di Matematica e Fisica, Università del Salento, Via Arnesano, 73100 Lecce, Italy.,GNFM-INDAM, Città Universitaria, Piazzale Aldo Moro 5, Casella Postale 00185 Roma, Italy
| | - L Martina
- Dipartimento di Matematica e Fisica, Università del Salento, Via Arnesano, 73100 Lecce, Italy.,INFN, Sezione di Lecce, Via Arnesano, Casella Postale 193I-73100 Lecce, Italy
| | - C Naya
- INFN, Sezione di Lecce, Via Arnesano, Casella Postale 193I-73100 Lecce, Italy
| | - V Turco
- Dipartimento di Matematica e Fisica, Università del Salento, Via Arnesano, 73100 Lecce, Italy.,INFN, Sezione di Lecce, Via Arnesano, Casella Postale 193I-73100 Lecce, Italy
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Affiliation(s)
- Thomas Machon
- H.H. Wills Physics Laboratory, Tyndall Avenue, United Kingdom
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Hashemi SM, Ravnik M. Nematic colloidal knots in topological environments. SOFT MATTER 2018; 14:4935-4945. [PMID: 29740657 DOI: 10.1039/c8sm00539g] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
The role of environment in shaping material properties is of great significance, but less is known about how non-trivial topology of the environment couples to material states, which can be of non-trivial topology themselves. In this paper, we demonstrate the role of the topology of the environment on the formation of complex nematic fields and defect structures, specifically in the system of nematic colloidal knots. The topological environments around knotted colloidal particles are suggested to exist as spherical surface-patterned nematic cavities imposing radial, uniform or hyperbolic nematic profiles. We show that topologically different nematic environments significantly affect and create differences in the colloidal field structure created within the environment, such as the location, profile and number of topological defects. Specifically, we demonstrate that topological environments in combination with knotted colloidal particles of non-trivial topology lead to the formation of diverse nematic knotted and linked fields. These fields are different adaptations of the knotted shape of the colloidal particles, creating knots and links of topological defects as well as escaped-core defect-like solitonic structures. These are observed in chiral nematic media but here are stabilised in achiral nematic media as a result of the distinct shape of the knotted colloidal particle, with a double helix segment and nematic environmental patterns. More generally, this paper is a contribution towards understanding the role of environment, especially its topology, on the response and defect formation in elastic fields, such as in nematic liquid crystal colloids.
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Affiliation(s)
- S Masoomeh Hashemi
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, Ljubljana, 1000, Slovenia.
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Topology-commanded optical properties of bistable electric-field-induced torons in cholesteric bubble domains. Sci Rep 2017; 7:16149. [PMID: 29170409 PMCID: PMC5701030 DOI: 10.1038/s41598-017-16241-4] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/06/2017] [Accepted: 10/20/2017] [Indexed: 11/24/2022] Open
Abstract
Nowadays, complicated topological defects enable many experimental manipulations and configurational simulations of active soft matter for optical and photonic applications. Investigation of topological defects in soft anisotropic materials enables one to better understand three-dimensional orientation fields in cholesteric liquid crystals. Here, we describe optical properties of bistable bubble domain (BD) texture torons in a thin layer of cholesteric liquid crystal (CLC), frustrated by homeotropic anchoring conditions, and reliably switchable by a random process. The control of macroscopic optical density and diffraction efficiency of the BD texture is demonstrated by a selection of a confinement ratio of the CLC. Experimentally reconstructed CLC director profile reveals the topology of BD torons allowing consideration of naturally occurring BD texture for applications in optical and photonic devices, which are bistably switchable between active and transparent optical states.
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Abstract
We give the global homotopy classification of nematic textures for a general domain with weak anchoring boundary conditions and arbitrary defect set in terms of twisted cohomology, and give an explicit computation for the case of knotted and linked defects in R3, showing that the distinct homotopy classes have a 1–1 correspondence with the first homology group of the branched double cover, branched over the disclination loops. We show further that the subset of those classes corresponding to elements of order 2 in this group has representatives that are planar and characterize the obstruction for other classes in terms of merons. The planar textures are a feature of the global defect topology that is not reflected in any local characterization. Finally, we describe how the global classification relates to recent experiments on nematic droplets and how elements of order 4 relate to the presence of τ lines in cholesterics.
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Affiliation(s)
- Thomas Machon
- Department of Physics and Centre for Complexity Science , University of Warwick , Coventry CV4 7AL, UK
| | - Gareth P Alexander
- Department of Physics and Centre for Complexity Science , University of Warwick , Coventry CV4 7AL, UK
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11
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Schlotthauer S, Skutnik RA, Stieger T, Schoen M. Defect topologies in chiral liquid crystals confined to mesoscopic channels. J Chem Phys 2015; 142:194704. [DOI: 10.1063/1.4920979] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sergej Schlotthauer
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, Berlin 10623, Germany
| | - Robert A. Skutnik
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, Berlin 10623, Germany
| | - Tillmann Stieger
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, Berlin 10623, Germany
| | - Martin Schoen
- Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Sekr. C7, Straße des 17. Juni 135, Berlin 10623, Germany
- Department of Chemical and Biomolecular Engineering, North Carolina State University, 911 Partners Way, Raleigh, North Carolina 27695, USA
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Ackerman PJ, van de Lagemaat J, Smalyukh II. Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals. Nat Commun 2015; 6:6012. [PMID: 25607778 PMCID: PMC4354077 DOI: 10.1038/ncomms7012] [Citation(s) in RCA: 44] [Impact Index Per Article: 4.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2014] [Accepted: 12/01/2014] [Indexed: 12/22/2022] Open
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. Topological defects can be spontaneously generated to thermodynamically stabilize a variety of peculiar condensed matter phases for technological applications. Here, Ackerman et al. show electrically controllable self-assembly of knotted defects into periodic arrays in chiral liquid crystals.
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Affiliation(s)
- Paul J Ackerman
- 1] Department of Physics, University of Colorado, Boulder, Colorado 80309, USA [2] Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - Jao van de Lagemaat
- 1] Department of Physics, University of Colorado, Boulder, Colorado 80309, USA [2] National Renewable Energy Laboratory, Golden, Colorado 80401, USA [3] Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
| | - Ivan I Smalyukh
- 1] Department of Physics, University of Colorado, Boulder, Colorado 80309, USA [2] Department of Electrical, Computer and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA [3] Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA [4] Liquid Crystal Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA
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13
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Pandey MB, Ackerman PJ, Burkart A, Porenta T, Žumer S, Smalyukh II. Topology and self-assembly of defect-colloidal superstructure in confined chiral nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012501. [PMID: 25679632 DOI: 10.1103/physreve.91.012501] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2014] [Indexed: 06/04/2023]
Abstract
We describe formation of defect-colloidal superstructures induced by microspheres with normal surface anchoring dispersed in chiral nematic liquid crystals in confinement-unwound homeotropic cells. Using three-dimensional nonlinear optical imaging of the director field, we demonstrate that some of the induced defects have nonsingular solitonic nature while others are singular point and line topological defects. The common director structures induced by individual microspheres have dipolar symmetry. These topological dipoles are formed by the particle and a hyperbolic point defect (or small disclination loop) of elementary hedgehog charge opposite to that of a sphere with perpendicular boundary conditions, which in cells with thickness over equilibrium cholesteric pitch ratio approaching unity are additionally interspaced by a looped double-twist cylinder of continuous director deformations. The long-range elastic interactions are probed by holographic optical tweezers and videomicroscopy, providing insights to the physical underpinnings behind self-assembled colloidal structures entangled by twisted solitons. Computer-simulated field and defect configurations induced by the colloidal particles and their assemblies, which are obtained by numerically minimizing the Landau-de Gennes free energy, are in agreement with the experimental findings.
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Affiliation(s)
- M B Pandey
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - P J Ackerman
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA
| | - A Burkart
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA
| | - T Porenta
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - S Žumer
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia and J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
| | - Ivan I Smalyukh
- Department of Physics, University of Colorado, Boulder, Colorado 80309, USA and Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, Colorado 80309, USA and Liquid Crystal Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, Colorado 80309, USA and Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, Colorado 80309, USA
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Porenta T, Copar S, Ackerman PJ, Pandey MB, Varney MCM, Smalyukh II, Žumer S. Topological switching and orbiting dynamics of colloidal spheres dressed with chiral nematic solitons. Sci Rep 2014; 4:7337. [PMID: 25477195 PMCID: PMC4256655 DOI: 10.1038/srep07337] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/16/2014] [Accepted: 11/13/2014] [Indexed: 12/29/2022] Open
Abstract
Metastable configurations formed by defects, inclusions, elastic deformations and topological solitons in liquid crystals are a promising choice for building photonic crystals and metamaterials with a potential for new optical applications. Local optical modification of the director or introduction of colloidal inclusions into a moderately chiral nematic liquid crystal confined to a homeotropic cell creates localized multistable chiral solitons. Here we induce solitons that “dress” the dispersed spherical particles treated for tangential degenerate boundary conditions, and perform controlled switching of their state using focused optical beams. Two optically switchable distinct metastable states, toron and hopfion, bound to colloidal spheres into structures with different topological charges are investigated. Their structures are examined using Q-tensor based numerical simulations and compared to the profiles reconstructed from the experiments. A topological explanation of observed multistability is constructed.
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Affiliation(s)
- T Porenta
- Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
| | - S Copar
- 1] Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia [2] J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia [3] Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd Street, Philadelphia, Pennsylvania 19104, USA
| | - P J Ackerman
- 1] Department of Physics, University of Colorado, Boulder, CO 80309, USA [2] Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 80309, USA
| | - M B Pandey
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - M C M Varney
- Department of Physics, University of Colorado, Boulder, CO 80309, USA
| | - I I Smalyukh
- 1] Department of Physics, University of Colorado, Boulder, CO 80309, USA [2] Department of Electrical, Computer, and Energy Engineering, University of Colorado, Boulder, CO 80309, USA [3] Liquid Crystal Materials Research Center and Materials Science and Engineering Program, University of Colorado, Boulder, CO 80309, USA [4] Renewable and Sustainable Energy Institute, National Renewable Energy Laboratory and University of Colorado, Boulder, CO 80309, USA
| | - S Žumer
- 1] Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia [2] J. Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia
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15
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Leonov AO, Dragunov IE, Rößler UK, Bogdanov AN. Theory of skyrmion states in liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:042502. [PMID: 25375510 DOI: 10.1103/physreve.90.042502] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2014] [Indexed: 06/04/2023]
Abstract
Within the Oseen-Frank theory we derive numerically exact solutions for axisymmetric localized states in chiral liquid crystal layers with homeotropic anchoring. These solutions describe recently observed two-dimensional skyrmions in confinement-frustrated chiral nematics [P. J. Ackerman et al., Phys. Rev. E 90, 012505 (2014)]. We stress that these solitonic states arise due to a fundamental stabilization mechanism responsible for the formation of skyrmions in cubic helimagnets and other noncentrosymmetric condensed-matter systems.
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Affiliation(s)
- A O Leonov
- IFW Dresden, Postfach 270016, D-01171 Dresden, Germany and Zernike Institute for Advanced Materials, University of Groningen, Groningen, 9700AB, The Netherlands
| | - I E Dragunov
- Donetsk Institute for Physics and Technology, 340114 Donetsk, Ukraine
| | - U K Rößler
- IFW Dresden, Postfach 270016, D-01171 Dresden, Germany
| | - A N Bogdanov
- IFW Dresden, Postfach 270016, D-01171 Dresden, Germany
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