Theory of helicoids and skyrmions in confined cholesteric liquid crystals

Afghah, Sajedeh; Selinger, Jonathan V.

doi:10.1103/physreve.96.012708

Cited by 39 publications

(27 citation statements)

References 36 publications

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“…To be sure, variations on this liquid-crystal model (perhaps with anisotropy arising from surface anchoring) might have skyrmions as a ground state, as in Ref. [10]. Even so, they are stabi-lized by a fairly delicate balance of free energies, not by the simple field as in the magnetic case.…”

Section: Discussionmentioning

confidence: 95%

“…This analysis can be compared with a recent paper from our group [10], which modeled skyrmions using a very different theoretical formalism based on a director field (with constant order parameter S) in a 3D cell with strong homeotropic anchoring. That paper found a phase diagram with three structures: vertical nematic, cholesteric, and skyrmion lattice.…”

Section: Phase Diagrammentioning

confidence: 99%

“…(18) for the same L and ∆ E 2 is shown by the solid line in the same figure. These results are consistent up to a factor of 2, which is reasonable for such an approximate model. As noted in the Introduction, many experiments have studied skyrmions in confined cholesteric liquid crystals [4][5][6][7][8][9][10][11]. These experiments generally cannot determine whether skyrmions are metastable, as predicted by the calculations in this section, or whether they are actually stable structures.…”

Section: B Metastable Skyrmionsmentioning

confidence: 99%

“…In some cases, these defects are walls with a one-dimensional (1D) twist of the director field n(x) [3]. In other cases the defects are skyrmions, which have a 2D variation of the director field n(x, y) with double twist going outward from the center, covering all possible orientations on the unit sphere [4][5][6][7][8][9][10][11]. In even more complex cases, the defects are hopfions, with a 3D variation of the director field n(x, y, z) in a knotted texture [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Comparing skyrmions and merons in chiral liquid crystals and magnets

2018

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When chiral liquid crystals or magnets are subjected to applied fields or other anisotropic environments, the competition between favored twist and anisotropy leads to the formation of complex defect structures. In some cases, the defects are skyrmions, which have 180^{∘} double twist going outward from the center, and hence can pack together without singularities in the orientational order. In other cases, the defects are merons, which have 90^{∘} double twist going outward from the center; packing such merons requires singularities in the orientational order. In the liquid crystal context, a lattice of merons is equivalent to a blue phase. Here we perform theoretical and computational studies of skyrmions and merons in chiral liquid crystals and magnets. Through these studies, we calculate the phase diagrams for liquid crystals and magnets in terms of dimensionless ratios of energetic parameters. We also predict the range of metastability for liquid crystal skyrmions and show that these skyrmions can move and interact as effective particles. The results show how the properties of skyrmions and merons depend on the vector or tensor nature of the order parameter.

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Section: Discussionmentioning

confidence: 95%

Section: Phase Diagrammentioning

confidence: 99%

Section: B Metastable Skyrmionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Comparing skyrmions and merons in chiral liquid crystals and magnets

2018

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“…This idea was already applied several times [35][36][37][38] and it can be implemented by the assumption θ = 4 arctan [X (x) Z (z)]. Boundary conditions (2.7) give rise to line disclinations on the confining planes, as analysed in [11] in the absence of external fields. Thus, one should look for functions X(x) and Z(z) such that the former is monotonic and unbounded (with possible singularities at finite points) and the latter assume the value Z ± L 2 = const on the boundaries.…”

Section: Discussionmentioning

confidence: 99%

Skyrmion States in Chiral Liquid Crystals

2018

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Within the framework of Oseen-Frank theory, we analyse the static configurations for chiral liquid crystals. In particular, we find numerical solutions for localised axisymmetric states in confined chiral liquid crystals with weak homeotropic anchoring at the boundaries. These solutions describe the distortions of two-dimensional skyrmions, known as either spherulites or cholesteric bubbles, which have been observed experimentally in these systems. Relations with nonlinear integrable equations have been outlined and are used to study asymptotic behaviors of the solutions. By using analytical methods, we build approximated solutions of the equilibrium equations and we analyse the generation and stabilization of these states in relation to the material parameters, the external fields and the anchoring boundary conditions.

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Liquid Crystalline Half‐Skyrmions and Their Optical Properties

et al. 2022

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Liquid crystals have intrigued physicists as a platform that facilitates direct visualization of topological concepts. Here, the theoretical and experimental studies demonstrating that a thin film of a chiral liquid crystal forms topological entities known as half-Skyrmions, swirl-like orientational order that spans the hemisphere of the order parameter space S 2 ∕Z 2 , are reviewed. They appear in the form of a hexagonal lattice or in an isolated manner, accompanied by topological line defects to satisfy topological constraints. Under an optical microscope, half-Skyrmions appear as dark spots, and their hexagonal lattice yields a Kossel diagram comprising a hexagonal arrangement of circular arcs. These experimental observations are corroborated by numerical calculations of the orientational order based on the Landau-de Gennes theory with an orientational order parameter of a second-rank tensor, and construction of its optical images and Kossel diagrams by directly solving Maxwell equations for light wave. A thin film of a chiral liquid crystal thus provides an interesting system for the investigation of topological concepts, and spontaneous formation of a half-Skyrmion lattice whose periodicity is of the order of the wavelength of visible light has a potential for photonics applications as well as poses a challenging problem on optics.

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Theory of helicoids and skyrmions in confined cholesteric liquid crystals

Cited by 39 publications

References 36 publications

Comparing skyrmions and merons in chiral liquid crystals and magnets

Comparing skyrmions and merons in chiral liquid crystals and magnets

Skyrmion States in Chiral Liquid Crystals

Liquid Crystalline Half‐Skyrmions and Their Optical Properties

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