Abstract

Topological solitons, such as skyrmions, arise in field theories of systems ranging from Bose-Einstein condensates to optics, particle physics, and cosmology, but they are rarely accessible experimentally. Chiral nematic liquid crystals provide a platform to study skyrmions because of their natural tendency to form twisted structures arising from the lack of mirror symmetry at the molecular level. However, large-scale dynamic control and technological utility of skyrmions remain limited. Combining experiments and numerical modeling of chiral liquid crystals with optically controlled helical pitch, we demonstrate that low-intensity, unstructured light can control stability, dimensions, interactions, spatial patterning, self-assembly, and dynamics of these topological solitons.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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  50. I. I. Smalyukh, D. S. Kaputa, A. V. Kachynski, A. N. Kuzmin, and P. N. Prasad, “Optical trapping of director structures and defects in liquid crystals using laser tweezers,” Opt. Express 15(7), 4359–4371 (2007).
    [Crossref]
  51. O. Trushkevych, P. Ackerman, W. A. Crossland, and I. I. Smalyukh, “Optically Generated Adaptive Localized Structures in Confined Chiral Liquid Crystals Doped with Fullerene,” Appl. Phys. Lett. 97(20), 201906 (2010).
    [Crossref]

2019 (4)

T. Van Mechelen and Z. Jacob, “Photonic Dirac monopoles and skyrmions: spin-1 quantization,” Opt. Mater. Express 9(1), 95–111 (2019).
[Crossref]

L. Du, A. Yang, A. V. Zayats, and X. Yuan, “Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum,” Nat. Phys. 15(7), 650–654 (2019).
[Crossref]

D. Foster, C. Kind, P. J. Ackerman, J.-S. B. Tai, M. R. Dennis, and I. I. Smalyukh, “Two-dimensional skyrmion bags in liquid crystals and ferromagnets,” Nat. Phys. 15(7), 655–659 (2019).
[Crossref]

Y. Yuan, Q. Liu, B. Senyuk, and I. I. Smalyukh, “Elastic colloidal monopoles and out of equilibrium interactions in liquid crystals,” Nature 570, 214–218 (2019).
[Crossref]

2018 (4)

H. R. O. Sohn, P. J. Ackerman, T. J. Boyle, G. H. Sheetah, B. Fornberg, and I. I. Smalyukh, “Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals,” Phys. Rev. E 97(5), 052701 (2018).
[Crossref]

W. Yang, H. Yang, Y. Cao, and P. Yan, “Photonic orbital angular momentum transfer and magnetic skyrmion rotation,” Opt. Express 26(7), 8778–8790 (2018).
[Crossref]

S. Tsesses, E. Ostrovsky, K. Cohen, B. Gjonaj, N. H. Lindner, and G. Bartal, “Optical skyrmion lattice in evanescent electromagnetic fields,” Science 361(6406), 993–996 (2018).
[Crossref]

Y. Yuan, G. N. Abuhaimed, Q. Liu, and I. I. Smalyukh, “Self-assembled nematic colloidal motors powered by light,” Nat. Commun. 9(1), 5040 (2018).
[Crossref]

2017 (4)

P. J. Ackerman, T. Boyle, and I. I. Smalyukh, “Squirming motion of baby skyrmions in nematic fluids,” Nat. Commun. 8(1), 673 (2017).
[Crossref]

Y. C. Hsiao, K. C. Huang, and W. Lee, “Photo-switchable chiral liquid crystal with optical tristability enabled by a photoresponsive azo-chiral dopant,” Opt. Express 25(3), 2687–2693 (2017).
[Crossref]

P. J. Ackerman and I. I. Smalyukh, “Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions,” Phys. Rev. X 7(1), 011006 (2017).
[Crossref]

P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16(4), 426–432 (2017).
[Crossref]

2016 (1)

H. Mundoor, B. Senyuk, and I. I. Smalyukh, “Triclinic nematic colloidal crystals from competing elastic and electrostatic interactions,” Science 352(6281), 69–73 (2016).
[Crossref]

2015 (1)

P. J. Ackerman, J. van de Lagemaat, and I. I. Smalyukh, “Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals,” Nat. Commun. 6(1), 6012 (2015).
[Crossref]

2014 (1)

P. J. Ackerman, R. P. Trivedi, B. Senyuk, J. van de Lagemaat, and I. I. Smalyukh, “Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics,” Phys. Rev. E 90(1), 012505 (2014).
[Crossref]

2013 (6)

P. Milde, D. Köhler, J. Seidel, L. M. Eng, A. Bauer, A. Chacon, J. Kindervater, S. Mühlbauer, C. Pfeiderer, S. Buhrandt, C. Schütte, and A. Rosch, “Unwinding of a skyrmion lattice by magnetic monopoles,” Science 340(6136), 1076–1080 (2013).
[Crossref]

J. S. Evans, P. J. Ackerman, D. J. Broer, J. van de Lagemaat, and I. I. Smalyukh, “Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles,” Phys. Rev. E 87(3), 032503 (2013).
[Crossref]

N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341(6146), 636–639 (2013).
[Crossref]

A. Fert, V. Cros, and J. Sampaio, “Skyrmions on the track,” Nat. Nanotechnol. 8(3), 152–156 (2013).
[Crossref]

N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions,” Nat. Nanotechnol. 8(12), 899–911 (2013).
[Crossref]

Y. V. Izdebskaya, A. S. Desyatnikov, G. Assanto, and Y. S. Kivshar, “Deflection of nematicons through interaction with dielectric particles,” J. Opt. Soc. Am. B 30(6), 1432 (2013).
[Crossref]

2012 (4)

Z. Chen, M. Segev, and D. N. Christodoulides, “Optical spatial solitons: historical overview and recent advances,” Rep. Prog. Phys. 75(8), 086401 (2012).
[Crossref]

Y. Wang and Q. Li, “Light-driven chiral molecular switches or motors in liquid crystals,” Adv. Mater. 24(15), 1926–1945 (2012).
[Crossref]

P. J. Ackerman, Z. Qi, and I. I. Smalyukh, “Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams,” Phys. Rev. E 86(2), 021703 (2012).
[Crossref]

P. J. Ackerman, Z. Qi, Y. Lin, C. W. Twombly, M. J. Laviada, Y. Lansac, and I. I. Smalyukh, “Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities,” Sci. Rep. 2(1), 414 (2012).
[Crossref]

2011 (1)

2010 (5)

A. Alberucci, A. Piccardi, U. Bortolozzo, S. Residori, and G. Assanto, “Nematicon all-optical control in liquid crystal light valves,” Opt. Lett. 35(3), 390–392 (2010).
[Crossref]

X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagosa, and Y. Tokura, “Real-space observation of a two-dimensional skyrmion crystal,” Nature 465(7300), 901–904 (2010).
[Crossref]

I. I. Smalyukh, Y. Lansac, N. A. Clark, and R. P. Trivedi, “Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids,” Nat. Mater. 9(2), 139–145 (2010).
[Crossref]

J. Ma, Y. Li, T. White, A. Urbas, and Q. Li, “Light-driven nanoscale chiral molecular switch: reversible dynamic full range color phototuning,” Chem. Commun. 46(20), 3463–3465 (2010).
[Crossref]

O. Trushkevych, P. Ackerman, W. A. Crossland, and I. I. Smalyukh, “Optically Generated Adaptive Localized Structures in Confined Chiral Liquid Crystals Doped with Fullerene,” Appl. Phys. Lett. 97(20), 201906 (2010).
[Crossref]

2009 (2)

G. Assanto and M. A. Karpierz, “Nematicons: self-localized beams in nematic liquid crystals,” Liq. Cryst. 36(10-11), 1161–1172 (2009).
[Crossref]

T. J. White, R. L. Bricker, L. V. Natarajan, N. V. Tabiryan, L. Green, Q. Li, and T. J. Bunning, “Phototunable azobenzene cholesteric liquid crystals with 2000nm range,” Adv. Funct. Mater. 19(21), 3484–3488 (2009).
[Crossref]

2007 (2)

Q. Li, L. Green, N. Venkataraman, I. Shiyanovskaya, A. Khan, A. Urbas, and J. W. Doane, “Reversible photoswitchable axially chiral dopants with high helical twisting power,” J. Am. Chem. Soc. 129(43), 12908–12909 (2007).
[Crossref]

I. I. Smalyukh, D. S. Kaputa, A. V. Kachynski, A. N. Kuzmin, and P. N. Prasad, “Optical trapping of director structures and defects in liquid crystals using laser tweezers,” Opt. Express 15(7), 4359–4371 (2007).
[Crossref]

2006 (2)

G. S. Chilaya, “Light-controlled change in the helical pitch and broadband tunable cholesteric liquid-crystal lasers,” Crystallogr. Rep. 51(S1), S108–S118 (2006).
[Crossref]

U. K. Rößler, A. N. Bogdanov, and C. Pfleiderer, “Spontaneous skyrmion ground states in magnetic metals,” Nature 442(7104), 797–801 (2006).
[Crossref]

2005 (1)

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collings, and A. G. Yodh, “Premelting at defects within bulk colloidal crystals,” Science 309(5738), 1207–1210 (2005).
[Crossref]

1994 (2)

M. J. Bowick, L. Chandar, E. A. Schiff, and A. M. Srivastava, “The cosmological Kibble mechanism in the laboratory: string formation in liquid crystals,” Science 263(5149), 943–945 (1994).
[Crossref]

A. Bogdanov and A. Hubert, “Thermodynamically stable magnetic vortex states in magnetic crystals,” J. Magn. Magn. Mater. 138(3), 255–269 (1994).
[Crossref]

1991 (1)

I. Chuang, R. Durrer, N. Turok, and B. Yurke, “Cosmology in the laboratory: Defect dynamics in liquid crystals,” Science 251(4999), 1336–1342 (1991).
[Crossref]

1961 (1)

T. H. R. Skyrme, “A Non-Linear Field Theory,” Proc. R. Soc. A 260(1300), 127–138 (1961).
[Crossref]

Ablowitz, M. J.

M. J. Ablowitz, Nonlinear dispersive waves: asymptotic analysis and solitons (Vol. 47). Cambridge University Press. (2011).

Abuhaimed, G. N.

Y. Yuan, G. N. Abuhaimed, Q. Liu, and I. I. Smalyukh, “Self-assembled nematic colloidal motors powered by light,” Nat. Commun. 9(1), 5040 (2018).
[Crossref]

Ackerman, P.

O. Trushkevych, P. Ackerman, W. A. Crossland, and I. I. Smalyukh, “Optically Generated Adaptive Localized Structures in Confined Chiral Liquid Crystals Doped with Fullerene,” Appl. Phys. Lett. 97(20), 201906 (2010).
[Crossref]

Ackerman, P. J.

D. Foster, C. Kind, P. J. Ackerman, J.-S. B. Tai, M. R. Dennis, and I. I. Smalyukh, “Two-dimensional skyrmion bags in liquid crystals and ferromagnets,” Nat. Phys. 15(7), 655–659 (2019).
[Crossref]

H. R. O. Sohn, P. J. Ackerman, T. J. Boyle, G. H. Sheetah, B. Fornberg, and I. I. Smalyukh, “Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals,” Phys. Rev. E 97(5), 052701 (2018).
[Crossref]

P. J. Ackerman, T. Boyle, and I. I. Smalyukh, “Squirming motion of baby skyrmions in nematic fluids,” Nat. Commun. 8(1), 673 (2017).
[Crossref]

P. J. Ackerman and I. I. Smalyukh, “Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions,” Phys. Rev. X 7(1), 011006 (2017).
[Crossref]

P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16(4), 426–432 (2017).
[Crossref]

P. J. Ackerman, J. van de Lagemaat, and I. I. Smalyukh, “Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals,” Nat. Commun. 6(1), 6012 (2015).
[Crossref]

P. J. Ackerman, R. P. Trivedi, B. Senyuk, J. van de Lagemaat, and I. I. Smalyukh, “Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics,” Phys. Rev. E 90(1), 012505 (2014).
[Crossref]

J. S. Evans, P. J. Ackerman, D. J. Broer, J. van de Lagemaat, and I. I. Smalyukh, “Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles,” Phys. Rev. E 87(3), 032503 (2013).
[Crossref]

P. J. Ackerman, Z. Qi, and I. I. Smalyukh, “Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams,” Phys. Rev. E 86(2), 021703 (2012).
[Crossref]

P. J. Ackerman, Z. Qi, Y. Lin, C. W. Twombly, M. J. Laviada, Y. Lansac, and I. I. Smalyukh, “Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities,” Sci. Rep. 2(1), 414 (2012).
[Crossref]

Agrawal, G.

Y. S. Kivshar and G. Agrawal, Optical solitons: from fibers to photonic crystals. Academic press. (2003).

Alberucci, A.

Alsayed, A. M.

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collings, and A. G. Yodh, “Premelting at defects within bulk colloidal crystals,” Science 309(5738), 1207–1210 (2005).
[Crossref]

Assanto, G.

Bartal, G.

S. Tsesses, E. Ostrovsky, K. Cohen, B. Gjonaj, N. H. Lindner, and G. Bartal, “Optical skyrmion lattice in evanescent electromagnetic fields,” Science 361(6406), 993–996 (2018).
[Crossref]

S. Tsesses, K. Cohen, E. Ostrovsky, B. Gjonaj, N. H. Lindner, and G. Bartal, “Optical skyrmions: a new topological state of light,” In CLEO: QELS_Fundamental Science (pp. FTu3D-5). J. Opt. Soc. Am. (2019).

Bauer, A.

P. Milde, D. Köhler, J. Seidel, L. M. Eng, A. Bauer, A. Chacon, J. Kindervater, S. Mühlbauer, C. Pfeiderer, S. Buhrandt, C. Schütte, and A. Rosch, “Unwinding of a skyrmion lattice by magnetic monopoles,” Science 340(6136), 1076–1080 (2013).
[Crossref]

Bickel, J. E.

N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341(6146), 636–639 (2013).
[Crossref]

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H. R. O. Sohn, P. J. Ackerman, T. J. Boyle, G. H. Sheetah, B. Fornberg, and I. I. Smalyukh, “Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals,” Phys. Rev. E 97(5), 052701 (2018).
[Crossref]

P. J. Ackerman, T. Boyle, and I. I. Smalyukh, “Squirming motion of baby skyrmions in nematic fluids,” Nat. Commun. 8(1), 673 (2017).
[Crossref]

P. J. Ackerman and I. I. Smalyukh, “Static three-dimensional topological solitons in fluid chiral ferromagnets and colloids,” Nat. Mater. 16(4), 426–432 (2017).
[Crossref]

P. J. Ackerman and I. I. Smalyukh, “Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions,” Phys. Rev. X 7(1), 011006 (2017).
[Crossref]

H. Mundoor, B. Senyuk, and I. I. Smalyukh, “Triclinic nematic colloidal crystals from competing elastic and electrostatic interactions,” Science 352(6281), 69–73 (2016).
[Crossref]

P. J. Ackerman, J. van de Lagemaat, and I. I. Smalyukh, “Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals,” Nat. Commun. 6(1), 6012 (2015).
[Crossref]

P. J. Ackerman, R. P. Trivedi, B. Senyuk, J. van de Lagemaat, and I. I. Smalyukh, “Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics,” Phys. Rev. E 90(1), 012505 (2014).
[Crossref]

J. S. Evans, P. J. Ackerman, D. J. Broer, J. van de Lagemaat, and I. I. Smalyukh, “Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles,” Phys. Rev. E 87(3), 032503 (2013).
[Crossref]

P. J. Ackerman, Z. Qi, Y. Lin, C. W. Twombly, M. J. Laviada, Y. Lansac, and I. I. Smalyukh, “Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities,” Sci. Rep. 2(1), 414 (2012).
[Crossref]

P. J. Ackerman, Z. Qi, and I. I. Smalyukh, “Optical generation of crystalline, quasicrystalline, and arbitrary arrays of torons in confined cholesteric liquid crystals for patterning of optical vortices in laser beams,” Phys. Rev. E 86(2), 021703 (2012).
[Crossref]

I. I. Smalyukh, Y. Lansac, N. A. Clark, and R. P. Trivedi, “Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids,” Nat. Mater. 9(2), 139–145 (2010).
[Crossref]

O. Trushkevych, P. Ackerman, W. A. Crossland, and I. I. Smalyukh, “Optically Generated Adaptive Localized Structures in Confined Chiral Liquid Crystals Doped with Fullerene,” Appl. Phys. Lett. 97(20), 201906 (2010).
[Crossref]

I. I. Smalyukh, D. S. Kaputa, A. V. Kachynski, A. N. Kuzmin, and P. N. Prasad, “Optical trapping of director structures and defects in liquid crystals using laser tweezers,” Opt. Express 15(7), 4359–4371 (2007).
[Crossref]

H. R. O. Sohn, C. D. Liu, and I. I. Smalyukh, “Schools of skyrmions with electrically tunable elastic interactions,”Nat. Commun.(2019).

Sohn, H. R. O.

H. R. O. Sohn, P. J. Ackerman, T. J. Boyle, G. H. Sheetah, B. Fornberg, and I. I. Smalyukh, “Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals,” Phys. Rev. E 97(5), 052701 (2018).
[Crossref]

H. R. O. Sohn, C. D. Liu, and I. I. Smalyukh, “Schools of skyrmions with electrically tunable elastic interactions,”Nat. Commun.(2019).

Srivastava, A. M.

M. J. Bowick, L. Chandar, E. A. Schiff, and A. M. Srivastava, “The cosmological Kibble mechanism in the laboratory: string formation in liquid crystals,” Science 263(5149), 943–945 (1994).
[Crossref]

Sutcliffe, P.

N. Manton and P. Sutcliffe, Topological solitons. Cambridge University Press. (2004).

Tabiryan, N. V.

T. J. White, R. L. Bricker, L. V. Natarajan, N. V. Tabiryan, L. Green, Q. Li, and T. J. Bunning, “Phototunable azobenzene cholesteric liquid crystals with 2000nm range,” Adv. Funct. Mater. 19(21), 3484–3488 (2009).
[Crossref]

Tai, J.-S. B.

D. Foster, C. Kind, P. J. Ackerman, J.-S. B. Tai, M. R. Dennis, and I. I. Smalyukh, “Two-dimensional skyrmion bags in liquid crystals and ferromagnets,” Nat. Phys. 15(7), 655–659 (2019).
[Crossref]

Tokura, Y.

N. Nagaosa and Y. Tokura, “Topological properties and dynamics of magnetic skyrmions,” Nat. Nanotechnol. 8(12), 899–911 (2013).
[Crossref]

X. Z. Yu, Y. Onose, N. Kanazawa, J. H. Park, J. H. Han, Y. Matsui, N. Nagosa, and Y. Tokura, “Real-space observation of a two-dimensional skyrmion crystal,” Nature 465(7300), 901–904 (2010).
[Crossref]

Trivedi, R. P.

P. J. Ackerman, R. P. Trivedi, B. Senyuk, J. van de Lagemaat, and I. I. Smalyukh, “Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics,” Phys. Rev. E 90(1), 012505 (2014).
[Crossref]

I. I. Smalyukh, Y. Lansac, N. A. Clark, and R. P. Trivedi, “Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids,” Nat. Mater. 9(2), 139–145 (2010).
[Crossref]

Trushkevych, O.

O. Trushkevych, P. Ackerman, W. A. Crossland, and I. I. Smalyukh, “Optically Generated Adaptive Localized Structures in Confined Chiral Liquid Crystals Doped with Fullerene,” Appl. Phys. Lett. 97(20), 201906 (2010).
[Crossref]

Tsesses, S.

S. Tsesses, E. Ostrovsky, K. Cohen, B. Gjonaj, N. H. Lindner, and G. Bartal, “Optical skyrmion lattice in evanescent electromagnetic fields,” Science 361(6406), 993–996 (2018).
[Crossref]

S. Tsesses, K. Cohen, E. Ostrovsky, B. Gjonaj, N. H. Lindner, and G. Bartal, “Optical skyrmions: a new topological state of light,” In CLEO: QELS_Fundamental Science (pp. FTu3D-5). J. Opt. Soc. Am. (2019).

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[Crossref]

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P. J. Ackerman, Z. Qi, Y. Lin, C. W. Twombly, M. J. Laviada, Y. Lansac, and I. I. Smalyukh, “Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities,” Sci. Rep. 2(1), 414 (2012).
[Crossref]

Urbas, A.

J. Ma, Y. Li, T. White, A. Urbas, and Q. Li, “Light-driven nanoscale chiral molecular switch: reversible dynamic full range color phototuning,” Chem. Commun. 46(20), 3463–3465 (2010).
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Q. Li, L. Green, N. Venkataraman, I. Shiyanovskaya, A. Khan, A. Urbas, and J. W. Doane, “Reversible photoswitchable axially chiral dopants with high helical twisting power,” J. Am. Chem. Soc. 129(43), 12908–12909 (2007).
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P. J. Ackerman, J. van de Lagemaat, and I. I. Smalyukh, “Self-assembly and electrostriction of arrays and chains of hopfion particles in chiral liquid crystals,” Nat. Commun. 6(1), 6012 (2015).
[Crossref]

P. J. Ackerman, R. P. Trivedi, B. Senyuk, J. van de Lagemaat, and I. I. Smalyukh, “Two-dimensional skyrmions and other solitonic structures in confinement-frustrated chiral nematics,” Phys. Rev. E 90(1), 012505 (2014).
[Crossref]

J. S. Evans, P. J. Ackerman, D. J. Broer, J. van de Lagemaat, and I. I. Smalyukh, “Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles,” Phys. Rev. E 87(3), 032503 (2013).
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Venkataraman, N.

Q. Li, L. Green, N. Venkataraman, I. Shiyanovskaya, A. Khan, A. Urbas, and J. W. Doane, “Reversible photoswitchable axially chiral dopants with high helical twisting power,” J. Am. Chem. Soc. 129(43), 12908–12909 (2007).
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von Bergmann, K.

N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341(6146), 636–639 (2013).
[Crossref]

Wang, Y.

Y. Wang and Q. Li, “Light-driven chiral molecular switches or motors in liquid crystals,” Adv. Mater. 24(15), 1926–1945 (2012).
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J. Ma, Y. Li, T. White, A. Urbas, and Q. Li, “Light-driven nanoscale chiral molecular switch: reversible dynamic full range color phototuning,” Chem. Commun. 46(20), 3463–3465 (2010).
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White, T. J.

T. J. White, R. L. Bricker, L. V. Natarajan, N. V. Tabiryan, L. Green, Q. Li, and T. J. Bunning, “Phototunable azobenzene cholesteric liquid crystals with 2000nm range,” Adv. Funct. Mater. 19(21), 3484–3488 (2009).
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N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341(6146), 636–639 (2013).
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Wolter, B.

N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341(6146), 636–639 (2013).
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Yan, P.

Yang, A.

L. Du, A. Yang, A. V. Zayats, and X. Yuan, “Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum,” Nat. Phys. 15(7), 650–654 (2019).
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Yang, W.

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P. Yeh and C. Gu, Optics of liquid crystal displays (Vol. 67). John Wiley & Sons. (2010).

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[Crossref]

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L. Du, A. Yang, A. V. Zayats, and X. Yuan, “Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum,” Nat. Phys. 15(7), 650–654 (2019).
[Crossref]

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Y. Yuan, Q. Liu, B. Senyuk, and I. I. Smalyukh, “Elastic colloidal monopoles and out of equilibrium interactions in liquid crystals,” Nature 570, 214–218 (2019).
[Crossref]

Y. Yuan, G. N. Abuhaimed, Q. Liu, and I. I. Smalyukh, “Self-assembled nematic colloidal motors powered by light,” Nat. Commun. 9(1), 5040 (2018).
[Crossref]

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I. Chuang, R. Durrer, N. Turok, and B. Yurke, “Cosmology in the laboratory: Defect dynamics in liquid crystals,” Science 251(4999), 1336–1342 (1991).
[Crossref]

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L. Du, A. Yang, A. V. Zayats, and X. Yuan, “Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum,” Nat. Phys. 15(7), 650–654 (2019).
[Crossref]

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A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collings, and A. G. Yodh, “Premelting at defects within bulk colloidal crystals,” Science 309(5738), 1207–1210 (2005).
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Adv. Mater. (1)

Y. Wang and Q. Li, “Light-driven chiral molecular switches or motors in liquid crystals,” Adv. Mater. 24(15), 1926–1945 (2012).
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Appl. Phys. Lett. (1)

O. Trushkevych, P. Ackerman, W. A. Crossland, and I. I. Smalyukh, “Optically Generated Adaptive Localized Structures in Confined Chiral Liquid Crystals Doped with Fullerene,” Appl. Phys. Lett. 97(20), 201906 (2010).
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Chem. Commun. (1)

J. Ma, Y. Li, T. White, A. Urbas, and Q. Li, “Light-driven nanoscale chiral molecular switch: reversible dynamic full range color phototuning,” Chem. Commun. 46(20), 3463–3465 (2010).
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Nat. Mater. (2)

I. I. Smalyukh, Y. Lansac, N. A. Clark, and R. P. Trivedi, “Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids,” Nat. Mater. 9(2), 139–145 (2010).
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L. Du, A. Yang, A. V. Zayats, and X. Yuan, “Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum,” Nat. Phys. 15(7), 650–654 (2019).
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Opt. Mater. Express (1)

Phys. Rev. E (4)

H. R. O. Sohn, P. J. Ackerman, T. J. Boyle, G. H. Sheetah, B. Fornberg, and I. I. Smalyukh, “Dynamics of topological solitons, knotted streamlines, and transport of cargo in liquid crystals,” Phys. Rev. E 97(5), 052701 (2018).
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P. J. Ackerman, Z. Qi, Y. Lin, C. W. Twombly, M. J. Laviada, Y. Lansac, and I. I. Smalyukh, “Laser-directed hierarchical assembly of liquid crystal defects and control of optical phase singularities,” Sci. Rep. 2(1), 414 (2012).
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P. Milde, D. Köhler, J. Seidel, L. M. Eng, A. Bauer, A. Chacon, J. Kindervater, S. Mühlbauer, C. Pfeiderer, S. Buhrandt, C. Schütte, and A. Rosch, “Unwinding of a skyrmion lattice by magnetic monopoles,” Science 340(6136), 1076–1080 (2013).
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[Crossref]

N. Romming, C. Hanneken, M. Menzel, J. E. Bickel, B. Wolter, K. von Bergmann, A. Kubetzka, and R. Wiesendanger, “Writing and deleting single magnetic skyrmions,” Science 341(6146), 636–639 (2013).
[Crossref]

H. Mundoor, B. Senyuk, and I. I. Smalyukh, “Triclinic nematic colloidal crystals from competing elastic and electrostatic interactions,” Science 352(6281), 69–73 (2016).
[Crossref]

A. M. Alsayed, M. F. Islam, J. Zhang, P. J. Collings, and A. G. Yodh, “Premelting at defects within bulk colloidal crystals,” Science 309(5738), 1207–1210 (2005).
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N. Manton and P. Sutcliffe, Topological solitons. Cambridge University Press. (2004).

S. Tsesses, K. Cohen, E. Ostrovsky, B. Gjonaj, N. H. Lindner, and G. Bartal, “Optical skyrmions: a new topological state of light,” In CLEO: QELS_Fundamental Science (pp. FTu3D-5). J. Opt. Soc. Am. (2019).

Y. M. Shnir, Magnetic monopoles. Springer Science & Business Media (2006).

T. Dauxois and M. Peyrard, Physics of solitons. Cambridge University Press. (2006).

M. J. Ablowitz, Nonlinear dispersive waves: asymptotic analysis and solitons (Vol. 47). Cambridge University Press. (2011).

Y. S. Kivshar and G. Agrawal, Optical solitons: from fibers to photonic crystals. Academic press. (2003).

H. R. O. Sohn, C. D. Liu, and I. I. Smalyukh, “Schools of skyrmions with electrically tunable elastic interactions,”Nat. Commun.(2019).

P. Yeh and C. Gu, Optics of liquid crystal displays (Vol. 67). John Wiley & Sons. (2010).

P. G. De Gennes and J. Prost, The physics of liquid crystals (Vol. 83). Oxford University Press. (1995).

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Figures (10)

Fig. 1.
Fig. 1. Vectorized director field structure of the studied topological soliton. (a,b) Vectorized director structure of a skyrmion in the cross-sectional plane (a) orthogonal to the far-field director n0 and (b) parallel to n0, where two hyperbolic point defects terminate the skyrmionic tube near the confining surfaces (black crosses), forming an elementary toron [19]. The structure was numerically modeled for a confined chiral nematic mixture (E7 – QL-76) with vertical surface boundary conditions. Arrows represent the vectorized director field, n(r), colored according to corresponding points on the ${\mathbb{S}}^2$ sphere shown in the inset of (a). (c) Schematic representation of the experimental geometry, with cell thickness, d, labeled and the thin homeotropic alignment layer (see Methods) deposited on the confining glass substrates represented in orange (inset).
Fig. 2.
Fig. 2. Helicoidal structure of a photo-sensitive chiral nematic LC. (a) Molecular structure of the QL-76 chiral additive. [34] (b) Schematics of helicoidal structures for initial twisting rate defined by p0 and maximum pe pitch value achieved upon illumination. (c) Pitch dependence on chiral additive (QL-76) concentration and photoexcitation, where the red line represents concentration-dependent p0 and the blue line represents that of the maximum excited-state pe. For the used E7 sample with QL-76, the black dashed lines mark the minimum and maximum possible pitch values that can be achieved at different light exposures.
Fig. 3.
Fig. 3. Skyrmion dimensions with changing pitch. (a, b) Computer-simulated skyrmions in a chiral nematic LC shown at (a) d/p = 0.925 and (b) d/p = 1.25, where the vectorized n(r) is colored according to orientations on the ${\mathbb{S}}^2$ sphere (inset). (c) Simulated skyrmion diameter measured within the d/p stability range, where sample thickness is fixed at 10 µm and corresponding diameters from (a) and (b) are marked in red, inset with simulated polarizing optical microscopy images corresponding to parts (a) and (b). (d, e) Experimentally measured skyrmion diameter upon 5s of blue-light exposure, with corresponding polarizing optical images (inset) shown for (d) Sample A and (e) Sample B. Crossed polarizers orientations are marked with white double arrows. Numerical simulations are based on material parameters of nematic host E7 and left-handed chiral additive QL-76 (see Methods). A similar E7 – QL-76 mixture was used in experiment, details of which are reported in Table 1.
Fig. 4.
Fig. 4. Patterned light projection for controlled skyrmion motion. (a) Elastic free energy dependence of the twisted skyrmionic state (red) and the unwound or homeotropic state (black) on d/p. Energy was computed numerically on a 100 µm x 100 µm x 32 µm computational volume. (b) Experimental setup for blue-light patterning projection with red imaging light, polarizer (P), analyzer (A), dichroic mirror (DM 505LP), and charge-coupled device camera (CCD, PointGrey, FlyCap) labeled. 4x, 10x, and 20x Olympus dry objectives were used. (c) Computer-simulated demonstration of skyrmion propagation, where the blue region represents illumination and black rods represent n(r) orientation. (d) Experimental patterned-light-induced motion of a skyrmion in a spiral path, the trajectory of which is shown overlaid on the polarizing images and colored according to elapsed time in seconds (right-side inset). Crossed polarizer and analyzer orientations are marked with white double arrows.
Fig. 5.
Fig. 5. Skyrmion-toron structure evolution with changing pitch. (a, b) Numerically simulated vertical cross-sections of torons in a chiral nematic LC shown in the cross-sectional plane containing the far-field director at (a) d/p = 0.925 and (b) d/p = 1.25, where the vectorized n(r) is colored according to orientation on the ${\mathbb{S}}^2$ sphere (inset). (c, d) Computer-simulated demonstration of photo-induced skyrmion propagation shown in the cross-sectional plane containing the far-field director, where the blue region represents the part of sample under illumination and black rods represent n(r) orientation. Numerical simulations are based on material parameters of nematic host E7 and left-handed chiral additive QL-76 (see Methods), with d = 10 µm. A similar E7 – QL-76 mixture was used in experiment, details of which are reported in Table 1.
Fig. 6.
Fig. 6. Photo-induced skyrmion lattice rearrangement. (a-e) Polarizing optical microscopy images of (a) initial hexagonal skyrmion lattice before illumination, (b) a square-patterned blue-light illumination mask and (c) resulting square lattice skyrmion arrangement. (d) A hexagonal-patterned blue-light illumination mask and (e) resulting hexagonal lattice. (f) Trajectories of skyrmion motion throughout rearrangement, colored according to elapsed time in seconds (right-side inset). The time-coded motion trajectories are consistent with the motions of the dark regions in the illumination patterns. Crossed polarizer and analyzer orientations are marked with white double arrows and elapsed time is noted in the bottom right corners of images. The material is E7 doped with QL-76.
Fig. 7.
Fig. 7. Robust control of skyrmion lattices with spatially patterned light. (a) Polarizing optical images of a grain boundary in a skyrmion lattice and subsequent lattice healing upon illumination at the boundaries of the frame. White dashed lines mark the grain boundary in the initial frame. (b) Time-coded trajectories of skyrmion motion following illumination. (c) Polarizing optical images of formation of a photo-induced crack in a close-packed hexagonal lattice of skyrmions and subsequent lattice healing with time. The blue-light illumination pattern is shown as an overlay in the first frame. (d) Time-coded trajectories of the skyrmion manipulation to create a crack in the lattice. Crossed polarizer and analyzer orientations are marked with white double arrows and elapsed time is noted in the bottom right corners of images. The material is E7 doped with QL-76.
Fig. 8.
Fig. 8. Solitonic lattice compression with patterned light. (a, b) Polarizing optical images of (a) a square-periodic lattice being compressed by illumination at the boundaries of the frame and (b) a square lattice with an edge dislocation (marked with a yellow circle) being compressed on all sides by patterned illumination through a mask. Crossed polarizer and analyzer orientations are marked with white double arrows and elapsed time is noted in the bottom right corner of images. The material is E7 doped with QL-76.
Fig. 9.
Fig. 9. Merging of skyrmion crystallites. (a) Polarizing optical microscopy images of three aligned skyrmion crystallites nucleating upon circular boundary illumination to form one large crystallite. (b) Schematics of aligned crystallites upon nucleation, with boundary skyrmions colored according to number of nearest neighbors (red = 5, black = 6). (c) Polarizing optical microscopy images of three misaligned skyrmion crystallites nucleating under similar illumination to form one large crystallite. (d) Schematics of misaligned crystallites upon nucleation, with boundary skyrmions colored according to number of nearest neighbors (blue = 4, red = 5, black = 6). Crossed polarizer orientation is marked with white double arrows and elapsed time is noted in the bottom right corner of images. The material is E7 doped with QL-76.
Fig. 10.
Fig. 10. Skyrmion bag manipulation and transformation. (a) An S(102) skyrmion bag shrinks following 5s of blue-light illumination, to the point of greatest-possible stable compression (where a single skyrmion pops through a transformation invoking singular defects), then grows back upon dark relaxation to a stable S(101) bag. (b) Upon blue light illumination on the left side of the frame, an S(98) bag starts to move slowly to the right, but the internal pressure of large-scale movement on the inner skyrmions causes soliton popping and over time the bag shrinks down to a single skyrmion. Crossed polarizer and analyzer orientations are marked with white double arrows and elapsed time is noted in the bottom right corners of images. The material is E7 doped with QL-76.

Tables (1)

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Table 1. Material parameters for E7 nematic host and QL-76 chiral additive.

Equations (1)

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W = { K 11 2 ( n ) 2 + K 22 2 [ n ( × n ) + 2 π p 0 ] 2 + K 33 2 [ n × ( × n ) ] 2 ε 0 Δ ε 2 ( E n ) 2 } d V

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