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Cited by 469Orbital Angular Momentum in OpticsTopological Materials and PhenomenaQuantum Mechanics and Non-Hermitian Physics

The DOI matches its Crossref record; 102 of the 103 references it cites were found in a registry or an index, and 1 are not checked yet; 24 of the 129 sources its claims cite were checked for support.

Optical skyrmions and other topological quasiparticles of light

Open access
Shen, Yijie, Zhang, Qiang, Shi, Peng, Du, Luping, Yuan, Xiaocong, Zayats, Anatoly V.·2024·Nature Photonics
DOI 10.1038/s41566-023-01325-7
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Verified 2026-11-10 · 1 reference not checked yet

Overview

AI snapshot

Written from the paper’s full text.

TL;DR

This review presents a unified topological framework for optical skyrmions and related quasiparticles, covering their classification, generation, control, and applications. It surveys realizations in evanescent, structured, free-space, space-time, and momentum-space optical fields and outlines open challenges.

Key findings

  • Optical skyrmions are topologically protected vector textures in electromagnetic fields, classified by skyrmion number \(s\), polarity \(p\), vorticity \(m\), and helicity \(\gamma\); types include Néel, Bloch, anti-skyrmion, higher-order skyrmions, skyrmionium, bimeron, bimeronium, and 3D hopfions.
  • They have been realized or proposed in evanescent SPP fields (field-skyrmion lattices and spin skyrmions), structured media (chiral liquid crystals, nonlinear photonic crystals), free-space beams (Stokes skyrmions, tightly focused beams), space-time pulses (toroidal/supertoroidal pulses), and momentum space (meron textures in photonic crystal bands).
  • Reported application-relevant features include deep-subwavelength spin features down to \(\lambda/60\) or \(\sim 10\) nm, frequency sensing with sensitivity \(>4.82\%\) and accuracy \(\approx 99.99\%\) in an area \(26\times10^{-5}\lambda^2\), and displacement sensing with pico-metric resolution and angstrom/picometer sensitivity over a linear range exceeding hundreds of nanometers.
  • Topological protection is described for free-space skyrmionic beams and vectorial structured light, which can be resilient to perturbations in complex media except for catastrophic events such as strong scattering.

Methods

  • This is a review article, not a primary experimental or theoretical study; it synthesizes existing literature within a unified topological framework based on the Skyrme model and mappings from parameter space to real space.
  • The framework defines skyrmion number and additional topological numbers (polarity, vorticity, helicity) and applies them across optical field types: electric field, spin angular momentum, polarization Stokes vector, pseudospin, and space-time or momentum-space representations.
  • The review surveys generation, topological control, and potential applications across evanescent, structured, free-space, space-time, and momentum-space optical systems.

Limitations

  • Stated: the field is still in its infancy, with many fundamental theoretical questions unresolved and applications still to be explored; the exact Hamiltonian for photonic skyrmionic interactions is yet to be fully formulated; higher-order skyrmions in ultrashort pulses remain to be explored; and the \(k\pi\)-bimeron is yet to be found experimentally.
  • Stated: care should be taken to distinguish vector textures exhibiting true topological quasiparticle properties from lookalikes without topological protection.
  • Evident: as a review, it reports and interprets results and proposals from other works rather than presenting new primary data; several cited realizations are theoretical or proposed rather than experimentally demonstrated.

Model-written summary. Check it against the paper before relying on it.

Integrity signals

Registry

Crossref · 10.1038/s41566-023-01325-7

Cites

102 of 103 references verified0 citation errors · 0 not checkable

Statistics

Nothing to recompute.

Verification

Claims the paper makes

24 of 129 cited sources checked · 0 supported · 1 flagged · accuracy not yet measured

  • Premisecitation

    Meron textures of the polarization Stokes field were experimentally generated by confining light into a liquid-crystal-filled microcavity.

    “The meron textures of the polarization Stokes field was experimentally generated by confining light into a liquid-crystal-filled microcavity (Fig. 4e) [57].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [57] Lin, W., Ota, Y., Arakawa, Y. & Iwamoto, S. Microcavity-based generation of full Poincaré beams with arbitrary skyrmion numbers. Phys. Rev. Res. 3, 023055 (2021). source

      The main text (page unavailable) says the authors numerically modeled full Poincaré beams from a silicon microring cavity, rather than experimentally generating meron textures in a liquid-crystal-filled cavity. The cited paper’s Stokes-vector discussion concerns those modeled beams; it does not change the contrary device and method descriptions. (LLM, conf=0.90)

      Checked by a reasoning model — may be wrong.

      Experimental — accuracy not yet measured
  • Premisecitation

    Tight focusing was shown to enable optical spin skyrmions where Néel- and Bloch-type textures can be controlled by slightly tuning the input light.

    “Tight focusing was shown to enable optical spin skyrmions where Néel-and Bloch-type textures can be controlled by slightly tuning the input light (Fig. 4g) [63].”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [63] Zdagkas, A. et al. Observation of toroidal pulses of light. Nat. Photon. 16, 523–528 (2022). source

      The Abstract reports generating toroidal light pulses and mentions skyrmions only as a possible subject of future light–matter interaction studies. Searches for optical spin skyrmions and for skyrmions found no passage about tight focusing or controlling Néel- and Bloch-type textures by tuning the input light. The indexed passages provide no page numbers. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
  • Premisecitation

    This results in an effective magnetization of an especially designed nonlinear medium.

    “This results in an effective”
    Quote in the paperSubstantial claim2 of 2 sources checked
    • cites [59] Nape, I. et al. Revealing the invariance of vectorial structured light in complex media. Nat. Photon. 16, 538–546 (2022). source

      The Experimental demonstration and Discussion and conclusion sections address distortion and invariance of vectorial structured light, not effective magnetization. A search for magnetization and nonlinear media found no passage in our copy supporting the attributed claim. Page numbers were not available. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [60] Zdagkas, A., Papasimakis, N., Savinov, V. & Zheludev, N. I. Space-time nonseparable pulses: constructing isodiffracting donut pulses from plane waves and single cycle pulses. Phys. Rev. A 102, 063512 (2020). source

      The Introduction (page unavailable) discusses flying-donut pulses engaging toroidal and anapole excitations in dielectric particles, but does not describe effective magnetization in a specially designed nonlinear medium. Searches for the quoted phrase and for nonlinear-medium magnetization found no passage addressing that claim. (LLM, conf=0.74)

      Experimental — accuracy not yet measured
  • Premisecitation

    Optical field-skyrmion lattice was first observed in the evanescent electric field of surface-plasmon polariton waves interfering in a six-fold symmetry resonator.

    “Optical field-skyrmion lattice was first observed in the evanescent electric field of the SPP waves interfering in a resonator of a six-fold symmetry [18].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [18] Ward, R. S. Hopf solitons on $${{\mathscr{S}}}^{3}$$ and $${{\mathscr{S}}}^{3}$$. Nonlinearity 12, 241–246 (1999). source

      The Introduction and Concluding Remarks discuss theoretical Hopf solitons in the Skyrme-Faddeev model, not an optical observation. Searches for optical skyrmion lattices, surface-plasmon polaritons, evanescent electric fields, and six-fold resonators found no passage addressing the claimed first observation. (LLM, conf=0.78)

      Experimental — accuracy not yet measured
  • Premisecitation

    Bloch-type spin-skyrmions were theoretically proposed in a designer multilayer chiral liquid crystal structure, in which chirality-dependent twisted features occur in the spin vector field.

    “Bloch-type spin-skyrmions were theoretically proposed in a designer multilayer chiral liquid crystal structure [56], in which chirality-dependent twisted features occur in the spin vector field.”
    Quote in the paperSubstantial claim1 of 1 sources checked
    • cites [56] Shen, Y., Mart´ınez, E. C. & Rosales-Guzm´an, C. Generation of optical skyrmions with tunable topological textures. ACS Photon. 9, 296–303 (2022). source

      The Introduction reports Bloch-type optical skyrmions in optical chiral multilayers, so it supports that part of the claim. It does not describe a designer multilayer chiral liquid-crystal structure or chirality-dependent twisting of a spin vector field; its mention of spin-field skyrmions concerns a separate, tightly focused vortex beam. Page numbers are unavailable in our copy. (LLM, conf=0.86)

      Experimental — accuracy not yet measured
  • Probably not a substantial claim. 37
  • It may state two separate claims as one. 34

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Stokes bimerons were recently generalized into multiskyrmion structures with increasingly complex topologies.

    “The Stokes bimerons were recently generalized into multiskyrmion structures with increasingly complex topologies [89,90].”
    Quote in the paperNot a substantial claim2 of 2 sources checked
    • cites [89] Jiang, Y. et al. Twisted magnon as a magnetic tweezer. Phys. Rev. Lett. 124, 217204 (2020). source

      The paper’s discussion and conclusion describe twisted magnons driving the motion of a magnetic skyrmion (section “Twisted magnon as a magnetic tweezer”; page unavailable). Searches for “Stokes bimerons” and “multiskyrmion” found no passage about generalizing bimerons into more complex structures. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
    • cites [90] Wang, X.-G. et al. The optical tweezer of skyrmions. npj Comput. Mater. 6, 140 (2020). source

      The Abstract (page unavailable) describes magnetic skyrmions and a laser-based method for trapping them, but does not address Stokes bimerons or their generalization. Searches for “Stokes bimerons,” “multiskyrmion,” and related terms found no passage in our copy supporting the attributed claim. (LLM, conf=0.72)

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Premisecitation

    Skyrmions can be driven by the skyrmion Hall effect, spin-orbit torque, and light.

    “and can be driven by the skyrmion Hall effect [61,62], spin-orbit torque [99,100], and even the light [101][102][103][104][105].”
    Quote in the paperNot a substantial claim4 of 9 sources checked
    • cites [61] Hellwarth, R. & Nouchi, P. Focused one-cycle electromagnetic pulses. Phys. Rev. E 54, 889 (1996). source
    • cites [62] Shen, Y., Hou, Y., Papasimakis, N. & Zheludev, N. I. Supertoroidal light pulses as electromagnetic skyrmions propagating in free space. Nat. Commun. 12, 5891 (2021).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [99] Ornelas, P., Nape, I., Koch, R. D. M. & Forbes, A. Nonlocal skyrmions as topologically resilient quantum entangled states of light. Preprint at https://arxiv.org/abs/2210.04690 (2022).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [100] Galiffi, E. et al. Photonics of time-varying media. Adv. Photon. 4, 014002 (2022). source

      Section 5.2.2 (page unavailable) describes optical switching of magnetization and optical excitation of spin currents, but does not address driving skyrmions with light. Searches for skyrmion driving, the skyrmion Hall effect, and spin-orbit torque found no passage establishing the claim about skyrmions. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
    • cites [101] Ge, H. et al. Observation of acoustic skyrmions. Phys. Rev. Lett. 127, 144502 (2021). source
    • cites [102] Muelas-Hurtado, R. D. et al. Observation of polarization singularities and topological textures in sound waves. Phys. Rev. Lett. 129, 204301 (2022). source

      The citation is attached to the claim that skyrmions can be driven by light. The main-text passage on three-wave interference reports a skyrmion lattice in propagating sound waves, while the References list mentions optical skyrmions; neither says that light drives skyrmions. Searches for light-driven skyrmions and the cited sentence found no supporting passage in our copy. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [103] Hu, P. et al. Observation of localized acoustic skyrmions. Appl. Phys. Lett. 122, 022201 (2023). source
    • cites [104] Cao, L., Wan, S., Zeng, Y., Zhu, Y. & Assouar, B. Observation of phononic skyrmions based on hybrid spin of elastic waves. Sci. Adv. 9, eadf3652 (2023). source

      For this source, the relevant part of the citing sentence is the claim that skyrmions can be driven by light. The Discussion mentions optomechanical coupling with light as a possible route to future skyrmion systems, but the Results describe moving the observed phononic skyrmion lattice by changing excitation-source phases, not by light. The source therefore supports a possible connection to light, not the stated light-driven motion. (LLM, conf=0.82)

      Experimental — accuracy not yet measured
    • cites [105] Parmee, C. D., Dennis, M. R. & Ruostekoski, J. Optical excitations of skyrmions, knotted solitons, and defects in atoms. Commun. Phys. 5, 54 (2022). source

      The Introduction and Section II (page unavailable) describe using structured light to create skyrmionic optical excitations in atomic ensembles. This supports the light-related part for skyrmion formation, but the passages do not show light driving the motion of an existing skyrmion. The Hall effect and spin-orbit torque have separate citations in the citing sentence and are not attributed to this source. (LLM, conf=0.82)

      Experimental — accuracy not yet measured

  • It may state two separate claims as one.

    Premisecitation

    Optical skyrmions can interact with magnetic skyrmions, allowing a route to manipulate these magnetic particles.

    “Optical skyrmions can interact with magnetic skyrmions allowing for a route to manipulate these magnetic particles [103][104][105].”
    Quote in the paperNot a substantial claim2 of 3 sources checked
    • cites [103] Hu, P. et al. Observation of localized acoustic skyrmions. Appl. Phys. Lett. 122, 022201 (2023). source
    • cites [104] Cao, L., Wan, S., Zeng, Y., Zhu, Y. & Assouar, B. Observation of phononic skyrmions based on hybrid spin of elastic waves. Sci. Adv. 9, eadf3652 (2023). source

      The Introduction mentions magnetic skyrmions and the extension of skyrmions to photonics, but does not describe an interaction between them. The Discussion addresses coupling between elastic and electromagnetic waves, not using optical skyrmions to manipulate magnetic skyrmions. Searches for optical–magnetic interaction and manipulation found no supporting passage in our copy. (LLM, conf=0.76)

      Experimental — accuracy not yet measured
    • cites [105] Parmee, C. D., Dennis, M. R. & Ruostekoski, J. Optical excitations of skyrmions, knotted solitons, and defects in atoms. Commun. Phys. 5, 54 (2022). source

      The Baby-Skyrmions section describes optical fields used to prepare skyrmionic textures in an atomic ensemble, and the 3D Skyrmions section discusses light–matter coupling. Neither the supplied passages nor searches for magnetic-skyrmion interaction and manipulation address optical skyrmions interacting with magnetic skyrmions to manipulate them. No page numbers were provided in our copy. (LLM, conf=0.76)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Bimeronium is a quasiparticle obtained by adding radial kπ twist structure to a fundamental bimeron, akin to skyrmionium.

    “Similarly, bimeronium is a quasiparticle which can be obtained by adding radial kπ twist structure to a fundamental bimeron (akin to the concept of skyrmionium) [38].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [38] Xiong, L. et al. Polaritonic vortices with a half-integer charge. Nano Lett. 21, 9256–9261 (2021). source

      The discussion on p. 4 describes merons and their half-integer topological charge, but does not address bimeronium or its proposed construction. Searches for “bimeronium,” “radial kπ twist,” “bimeron,” and “skyrmionium” found no passage in our copy supporting the attributed claim. (LLM, conf=0.76)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Optical bimerons were first proposed in paraxial vector beams.

    “While the optical bimerons were only recently first proposed in paraxial vector beams [69].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [69] Loder, F., Kampf, A. P., Kopp, T. & Braak, D. Momentum-space spin texture in a topological superconductor. Phys. Rev. B 96, 024508 (2017). source

      The paper’s skyrmion and meron passages discuss momentum-space spin textures in superconductors, not optical bimerons. Searches for optical bimerons and paraxial vector beams found no passage addressing where optical bimerons were first proposed. (LLM, conf=0.76)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    The most important applications of magnetic skyrmions are high-density information storage in modern spintronics.

    “The most important applications of magnetic skyrmions are the high-density information storage in modern spintronics [98].”
    Quote in the paperNot a substantial claim1 of 1 sources checked
    • cites [98] Wan, Z., Wang, H., Liu, Q., Fu, X. & Shen, Y. Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photon. 10, 2149–2164 (2023). source

      The Ray-Wave Structured Light section discusses optical skyrmions, and the cited passages on information capacity concern structured light and optical communication. Searches for magnetic skyrmions, spintronics, and high-density information storage found no passage addressing the claimed application. (LLM, conf=0.75)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Momentum-space magnetic skyrmions were previously studied to demonstrate the anomalous Hall effect in magnets.

    “The momentum-space magnetic skyrmions were previously studied to demonstrate anomalous Hall effect in magnets [86,87].”
    Quote in the paperNot a substantial claim2 of 2 sources checked
    • cites [86] Shi, P., Du, L., Li, M. & Yuan, X. Symmetry-protected photonic chiral spin textures by spin–orbit coupling. Laser Photon. Rev. 15, 2000554 (2021). source

      The Introduction discusses momentum-space chiral textures in photonic structures and separately describes magnetic skyrmions, but it does not connect momentum-space magnetic skyrmions to the anomalous Hall effect. Searches for “anomalous Hall effect in magnets” and “momentum-space magnetic skyrmions” found no passage addressing that claim. (LLM, conf=0.72)

      Experimental — accuracy not yet measured
    • cites [87] Wu, H.-J. et al. Conformal frequency conversion for arbitrary vectorial structured light. Optica 9, 187–196 (2022). source

      The “Optical Skyrmions” passage in section C says skyrmions have previously been studied in magnetic materials. It does not say those studies concerned momentum-space magnetic skyrmions or demonstrated the anomalous Hall effect. (LLM, conf=0.78)

      Experimental — accuracy not yet measured

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Interpretationcitation

    Skyrmionium has zero total skyrmion number and a radial 2π-twist structure.

    “The skyrmionium has zero total skyrmion number and a radial 2π-twist structure (”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [31] Bai, C., Chen, J., Zhang, Y., Zhang, D. & Zhan, Q. Dynamic tailoring of an optical skyrmion lattice in surface plasmon polaritons. Opt. Express 28, 10320–10328 (2020). source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    A skyrmion with opposite vorticity m = -1, termed an anti-skyrmion, has a saddle texture different from a conventional skyrmion.

    “A skyrmion with opposite vorticity m = -1, termed anti-skyrmion, has a very different to conventional skyrmion saddle texture (Fig. ??c).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    For large values of vorticity associated with a larger skyrmion number, skyrmions are designated as higher-order skyrmions.

    “In the case of large values of vorticity associated with larger value of a skyrmion number, the skyrmions are designated as higher-order skyrmions [29] (Fig. 2).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [29] Deng, Z.-L., Shi, T., Krasnok, A., Li, X. & Alù, A. Observation of localized magnetic plasmon skyrmions. Nat. Commun. 13, 8 (2022). source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Interpretationcitation

    The radial kπ-twist structures of the spin-skyrmion possess deep-subwavelength features, opening a new pathway for super-resolution imaging and microscopy.

    “The radial kπ-twist structures of the spin-skyrmion possess deep-subwavelength features, opening a new pathway for super-resolution imaging and microscopy [19].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [19] Rybakov, F. N. et al. Magnetic hopfions in solids. APL Mater. 10, 111113 (2022). source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    A skyrmion can be divided into two merons with half skyrmion number.

    “A skyrmion can be divided into two merons with a half skyrmion number, each corresponding to a half unwrapping from the parameter sphere.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds. It may state two separate claims as one.

    Premisenone given

    In paraxial beams, the electromagnetic field is purely transverse in non-absorbing media, so field vectors lie in a plane normal to the propagation direction.

    “In paraxial beams, the electromagnetic field is a purely transverse in non-absorbing media, therefore, the field vectors always lie in a plane normal to the propagation direction.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    A bimeron has a texture composed of two merons with opposite polarities.

    “Based on the generalized topological transformation, the bimeron has the texture composed by two merons with opposite polarities [34].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [34] Shi, P., Du, L. & Yuan, X. Strong spin–orbit interaction of photonic skyrmions at the general optical interface. Nanophotonics 9, 4619–4628 (2020). source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationnone given

    A bimeron quasiparticle is obtained if the parameter sphere is unwrapped from a point on the equator rather than from the pole.

    “If the sphere is unwrapped not from the pole but from a point on the equator, a bimeron quasiparticle is obtained (Fig. ??d).”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisereasoning

    The spin vectors in a tightly focused vortex beam may look like a Néel-type skyrmion-like texture in the focal plane near the beam axis, but it is not a rigorous analogue of a skyrmion and a skyrmion number cannot be assigned.

    “The spin vectors in a tightly focused vortex beam may look like a Néel-type skyrmion-like texture in the focal plane near the beam axis, however, it is not a rigorous analogue of a skyrmion and a skyrmion number can not be assigned [19].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [19] Rybakov, F. N. et al. Magnetic hopfions in solids. APL Mater. 10, 111113 (2022). source

  • It may state two separate claims as one.

    Interpretationreasoning

    A diffraction-free propagating beam is boundary-free and therefore unable to form a well-defined topological structure, in contrast to evanescent optical vortices.

    “The reason is that a diffraction-free propagating beam is boundary-free and, therefore, is unable to form a well-defined topological structure, in contrast to an evanescent optical vortexes.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationcitation

    Optical spin-skyrmions exist in evanescent fields carrying orbital angular momentum and can be realised by exciting a waveguided mode with light having orbital angular momentum.

    “They exist in the evanescent fields carry-ing orbital angular momentum (OAM), and can be realised by exciting a waveguided mode with a light having OAM.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationnone given

    The propagation direction of a guided mode and the direction of its transverse spin are intimately locked, and one cannot be changed without the other.

    “The propagation direction of a guided mode and the direction of its transverse spin (due to the longitudinal field component) are intimately locked, and one cannot be changed without the other.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    Such optical skyrmions can exist as individual isolated quasiparticles as well as form hexagonal lattices.

    “Such optical skyrmions are most closely related to their magnetic counterparts and can exist as individual isolated quasiparticles [19] as well as form hexagonal lattices [46].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [19] Rybakov, F. N. et al. Magnetic hopfions in solids. APL Mater. 10, 111113 (2022). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [46] Karnieli, A. & Arie, A. All-optical stern-gerlach effect. Phys. Rev. Lett. 120, 053901 (2018). source

  • It may state two separate claims as one.

    Interpretationnone given

    Each pair of gratings on opposite sides of the hexagon supports a standing wave, and skyrmion textures are formed by superposition of the electric fields of the standing waves along variant spatial directions.

    “Each pair of gratings on opposite sides of the hexagon supports a standing wave and the skyrmion textures are formed by superposition of the electric fields of the standing waves along variant spatial directions (Fig. 4a).”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    Optical field-skyrmions switchable between Néel- and Bloch-types were reported, but the existence of Bloch-type skyrmions was promptly disproved.

    “While optical field-skyrmions which can be switched between Néel-and Bloch-types were reported [43], the existence of Bloch-type skyrmions was promptly disproved [44,45].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [43] Król, M. et al. Observation of second-order meron polarization textures in optical microcavities. Optica 8, 255–261 (2021). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [44] Karnieli, A., Tsesses, S., Bartal, G. & Arie, A. Emulating spin transport with nonlinear optics, from high-order skyrmions to the topological hall effect. Nat. Commun. 12, 1092 (2021). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [45] Karnieli, A., Li, Y. & Arie, A. The geometric phase in nonlinear frequency conversion. Front. Phys. 17, 12301 (2022). source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Premisecitation

    Plasmonic spin fields have been used to tailor merons with fractional topological charges, and a triplet-meron structure was designed and generated with nanometric and femtosecond space-time resolution.

    “Plasmonic spin field has recently been also used to tailor more complex skyrmionic structures, such as the merons with fractional topological charges [51,52], whereby a novel quasiparticle triplet-meron structure were designed and generated (Fig. 4c), with nanometric and femtosecond space-time resolution [51].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [51] Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [52] Beckley, A. M., Brown, T. G. & Alonso, M. A. Full Poincaré beams. Opt. Express 18, 10777–10785 (2010). source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Premisecitation

    Skyrmionium is a coupled state connecting two skyrmions with opposite polarities and has skyrmion number s = 1 - 1 = 0.

    “Skyrmions have many generalized forms in the quasiparticle family, a typical example of which is skyrmionium, a coupled state connecting two skyrmions with opposite polarities and resulting into skyrmion number of s = 1 -1 = 0 [30].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [30] Yang, J. et al. Symmetry-protected spoof localized surface plasmonic skyrmion. Laser Photon. Rev. 16, 2200007 (2022). source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    Physical realisation of different unwrapping styles is related to particular system properties.

    “Physical realisation of different unwrapping styles is related to a particular system properties.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationnone given

    A bimeron can be obtained by switching the coordinates of longitude and latitude or tilting the sphere.

    “In contrast to the skyrmion representation with a fixed spiny sphere, a bimeron can be obtained by switching the coordinates of longitude and latitude or tilting the sphere.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationnone given

    For optical skyrmions, symmetry breaking is one of the factors that defines an unwrapping style.

    “For optical skyrmions, symmetry breaking is one of the factors that defines an unwrapping style.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    A bimeron can be described by a unit sphere mapping with a more general wrapping style.

    “A bimeron can similarly be described by a unit sphere mapping but with a more general wrapping style (Box 1).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Interpretationnone given

    The vectors of an anti-skyrmion wrap around the center clockwise (-2π), while the vectors of a skyrmion wrap around the center counter-clockwise (2π).

    “Geometrically, the distinction of an anti-skyrmion is a counter-clockwise vector distribution along the perimeter encircling a skyrmion center; the vectors of an anti-skyrmion wrap around the center clockwise (-2π), while the vectors of a skyrmion wrap around the centre counter-clockwise (2π) (Fig. 2).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    The described topological classifications can be extended to any quasiparticle.

    “The described above topological classifications can be extended to considerations of any quasiparticle, for example, the kπ-bimeron with additional radial multi-twist structure in bimeronium (fourth plot in the fourth row of Fig. 2), which yet to be found experimentally.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Premisecitation

    Spoof surface-plasmon polaritons were reported to generate skyrmion-like structures for fields in a resonator, but their topological protection needs further investigation.

    “Spoof SPP, the surface electromagnetic waves that propagate along planar interfaces with sign-changing permittivities were also reported to generate skyrmion-like structures for the fields in a resonator [41,42], but their topological protection needs to be further investigated.”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [41] Ghosh, A., Yang, S., Dai, Y. & Petek, H. The spin texture topology of polygonal plasmon fields. ACS Photon. 10, 13–23 (2023). source
    • cites [42] Zhang, Q., Xie, Z., Du, L., Shi, P. & Yuan, X. Bloch-type photonic skyrmions in optical chiral multilayers. Phys. Rev. Res. 3, 023109 (2021). source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Interpretationnone given

    A skyrmion with s = 1 and vector structure arranged along the tangent direction represents a Bloch-type vortex texture with γ = π/2, different from a Néel-type hedgehog texture with γ = 0.

    “A skyrmion with s = 1 but with the vector structure arranged along tangent direction (Fig. ??b) represents a vortex (Bloch-type) texture with γ = π/2, which is different from a hedgehog (Néel-type) texture with γ = 0 (Fig. ??a).”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    Optical skyrmions in evanescent fields are limited to Néel-type topological textures, and generating optical Bloch-type skyrmions at the interface of homogeneous media is a challenge.

    “As discussed above, the optical skyrmions in evanescent fields are limited to Néel-type topological textures, and it is a challenge to generate optical Bloch-type skyrmions at the interface of homogeneous media.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. It may state two separate claims as one.

    Premisecitation

    A kπ-skyrmion is a natural generalization of skyrmionium with radial multi-(kπ-)twist structure and controls the skyrmion number between 0 and 1 (or -1).

    “A natural generalization of skyrionium is a kπ-skyrmion with the raidal multi-(kπ-)twist structure [32], also known as a target skyrmion [33], which replaces the radial 2π-twist structure with kπ-twist structure and controls the skyrmion number between 0 and 1 (or -1).”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [32] Meiler, T., Frank, B. & Giessen, H. Dynamic tailoring of an optical skyrmion lattice in surface plasmon polaritons: comment. Opt. Express 28, 33614–33615 (2020). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [33] Lei, X. et al. Photonic spin lattices: symmetry constraints for skyrmion and meron topologies. Phys. Rev. Lett. 127, 237403 (2021). source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    For m = -1, the topology is defined as an anti-skyrmion with a saddle (anti-vortex) texture.

    “In the case of m = -1, the topology is defined as anti-skyrmion with a saddle (anti-vortex) texture [28].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [28] Davis, T. J. et al. Ultrafast vector imaging of plasmonic skyrmion dynamics with deep subwavelength resolution. Science 368, eaba6415 (2020). source

  • It may state two separate claims as one.

    Premisecitation

    Spin-skyrmion and spin-meron lattices are formed due to a broken rotational symmetry of the field with orbital angular momentum, with 6-fold symmetry responsible for a skyrmion lattice and 4-fold symmetry for a meron lattice.

    “Spin-skyrmion and spinmeron lattices are formed due to a broken rotational symmetry of the field with orbital angular momentum, with 6-fold symmetry being responsible for a skyrmion lattice and 4-fold symmetry for a meron lattice in the appropriately shaped resonator (Fig. 4d) [46,[53][54][55].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [46,[53][54][55]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim.

    Interpretationnone given

    Optical skyrmions and other quasiparticles can be constructed with various 3D vector fields, such as electric field, spin angular momentum, polarization Stokes vector, and pseudospin.

    “Optical skyrmions and other quasiparticles can be constructed with various 3D vector fields, which in optics can be, for example, the electric field (E x , E y , E z ), spin angular momentum (s x , s y , s z ), polarization Stokes vec-tor (S x , S y , S z ), pseudospin (k x , k y , k z ), etc.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim.

    Premisecitation

    A Stokes skyrmion corresponds to a spatial variation of a polarization pattern in a vector beam.

    “A Stokes skyrmion was introduced corresponding to a spatial variation of a polarization pattern in a vector beam [65,66].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [65] Wan, C., Shen, Y., Chong, A. & Zhan, Q. Scalar optical hopfons. eLight 2, 22 (2022). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [66] Shen, Y., Papasimakis, N. & Zheludev, N. I. Non diffracting supertoroidal pulses: optical "Kármán vortex streets". Preprint at https://arxiv.org/abs/2204.05676 (2022). source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Bimeronium was proposed as an extension of bimeron, similar to skyrmionium evolved from skyrmion, with similar topological classification.

    “Recently, a new concept of bimeronium was proposed as an extension of bimeron [38], similar to skyrmionium evolved from skyrmion, with similar topological classification.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [38] Xiong, L. et al. Polaritonic vortices with a half-integer charge. Nano Lett. 21, 9256–9261 (2021). source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Interpretationnone given

    Spin-skyrmion and spin-meron textures correspond to the lowest energy of the electromagnetic field configuration and are therefore energetically stable.

    “The spin-skyrmion and spin-meron textures correspond to the lowest energy of the electromagnetic field configuration, therefore, energetically stable.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationnone given

    The related skyrmions in the pulse always exhibit a constant vorticity of 1, while the polarity alternates between +1 and -1 due to optical cycle evolution.

    “The related skyrmions in the pulse always exhibit a constant vorticity of 1, while the polarity alternates between +1 and -1 due to the optical cycle evolution.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationnone given

    More complex cases of topological quasiparticles are possible, such as skyrmionium, bimeron obtained with a tilted parameter sphere and unwrapping from the equator, and 3D quasiparticles.

    “More complex cases of topological quasiparticles are also possible, such as a skyrmionium, which requires a radial twisting number, a bimeron obtained with a tilted parameter sphere and unwrapping from the equator, as well as 3D quasiparticles (Box 1).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Premisenone given

    An optical bimeronium can be realized by replacing the scalar mode bases of a bimeronic beam with higher-order vortex modes or Bessel beams.

    “An optical bimeronium can be realized by replacing the scalar mode bases of a bimeronic beam with higher-order vortex modes or Bessel beams.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it.

    Interpretationreasoning

    Similar topology-based protocols of information encoding, processing and transport can be envisaged in optics.

    “Similar topology-based protocols of information encoding, processing and transport can be envisaged in optics.”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Interpretationcitation

    The topological approaches developed for optical skyrmions can also be transferred to other wave fields such as acoustic, elastic, and atomic waves.

    “The topological approaches developed for optical skyrmions can also be transferred to other wave fields such as acoustic (sound) waves [122][123][124], elastic waves [125], and atomic waves [126].”
    Quote in the paperNot a substantial claim0 of 5 sources checked
    • cites [122]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [123]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [124]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [125]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [126]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim. It may be too vague to check against evidence.

    Interpretationreasoning

    The diversity and stability of particlelike topologies allows consideration of particle physics and condensed matter physics effects in optics to study and tailor light-matter interactions for quantum and topological technologies.

    “The diversity and stability of particlelike topologies allows consideration of the particle physics and condensed matter physics effects in optics in order to study and tailor light-matter interactions for quantum and topological technologies.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    Optical hopfions were recently extended to higher-order quasiparticles and their topologically protected transport in free space was demonstrated.

    “The optical hopfions were recently extended to higher-order quasiparticles and their topologically protected transport in free space was demonstrated [92].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [92] Tengdin, P. et al. Imaging the ultrafast coherent control of a skyrmion crystal. Phys. Rev. 12, 041030 (2022). source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Premisecitation

    The skyrmion texture can be resolved on femtosecond scales and at optical single-cycle field level.

    “(ii) ultrafast-the skyrmion texture can be resolved on femtosecond scales and at optical single-cycle field level [51,75]”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [51] Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [75] Shen, Y. et al. Topological transformation and freespace transport of photonic hopfons. Adv. Photon. 5, 015001 (2023).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim. It may be too vague to check against evidence.

    Interpretationreasoning

    Optical skyrmions may lead to new protocols in optical communications and informatics by transferring methods from spintronics to structured light and utilising various degrees of freedom provided by topologically protected vectorial field textures.

    “Optical skyrmions stand at the crossroads of spintronics and structured light and may lead to new protocols in optical communications and informatics, by transferring methods from spintronics to structured light and utilising various degrees of freedom provided by topologically protected vectorial field textures.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Interpretationcitation

    Once an optical skyrmionic pattern is designed in free space by mode nonseparability and Gouy-phase locking, the topology and skyrmion number are invariant upon light propagation and resilient to perturbations, except for catastrophic events such as strong scattering.

    “Similarly, once a optical skyrmionic pattern is designed in a free-space by the mode nonseparability and Gouy-phase locking discussed above, the topology and skyrmion number is invariant upon light propagation and resilient to perturbations, except for catastrophic events, such as strong scattering.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim.

    Interpretationreasoning

    Since skyrmions are characterised by multiple topological charges, e.g. polarity and vorticity, exotic biparticle entangled states can be considered with more degrees of freedom.

    “For quantum technologies, since skyrmions are characterised by multiple topological charges, e.g.polarity and vorticity, exotic biparticle entangled states can be considered with more degrees of freedom.”
    Quote in the paperSubstantial claim

  • Probably not a substantial claim. The paper may give no reason why it holds.

    Interpretationnone given

    The realisation of optical counterparts of skyrmion quasiparticles has enabled a novel topological approach for controlling electromagnetic fields.

    “The realisation of optical counterparts of skyrmion quasiparticles has enabled the novel topological approach for controlling electromagnetic fields.”
    Quote in the paperNot a substantial claim

  • It may state two separate claims as one.

    Premisecitation

    Few-cycle ultrafast pulses represent space-time nonseparable solutions of Maxwell's equations, and propagating skyrmions can be achieved with toroidal light pulses.

    “The situation is different in the case of the few-cycle ultrafast pulses, which represent space-time nonseparable solutions of the Maxwell's equations [79].In the latter case, propagating skyrmions can be achieved with the toroidal light pulses [80].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [79] Ackerman, P. J. & Smalyukh, I. I. Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfons. Phys. Rev. 7, 011006 (2017). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [80] Yang, H., Liang, J. & Cui, Q. First-principles calculations for Dzyaloshinskii–Moriya interaction. Nat. Rev. Phys. 5, 43–61 (2023). source

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    In condensed matter physics, skyrmions can be formed due to the Dzyaloshinskii-Moriya interaction and dipole-dipole interaction.

    “In condensed matter physics, skyrmions can be formed due to the Dzyaloshinskii-Moriya interaction (DMI) [97], dipole-dipole interaction [98]”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [97] Shen, Y. et al. Optical vortices 30 years on: OAM manipulation from topological charge to multiple singularities. Light Sci. Appl. 8, 90 (2019). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [98] Wan, Z., Wang, H., Liu, Q., Fu, X. & Shen, Y. Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photon. 10, 2149–2164 (2023). source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Interpretationcitation

    Such pulses induce multiple singularities in their electromagnetic field, forming vortex-ring-like configurations, and skyrmionic topology can be observed in their transverse cross-section.

    “Such pulses induce multiple singularities in their electromagnetic field, which form vortex-ring-like configurations, and skyrmionic topology can be observed in their transverse cross-section.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisecitation

    Spin textures in momentum space provide a direct approach to visualizing local Berry curvature, enabling robust and direct manipulation of polarization of light and space-time coupling of light wave packets.

    “Spin textures in a momentum space provide a direct approach to visualizing the local Berry curvature, enabling robust and direct manipulation of polarization of light [76] and space-time coupling of light wave packets [85].”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [76] Ehrmanntraut, D. et al. Optical second-order skyrmionic hopfion. Optica 10, 725–731 (2023). source

      Checked before — its earlier verdict is held back until a new check runs.

    • cites [85] Zhao, H. J., Chen, P., Prosandeev, S., Artyukhin, S. & Bellaiche, L. Dzyaloshinskii–Moriya-like interaction in ferroelectrics and antiferroelectrics. Nat. Mater. 20, 341–345 (2021). source

  • Probably not a substantial claim.

    Interpretationnone given

    To be classified as a skyrmion, the vector texture described by a topological number must be protected upon propagation.

    “To be classified as a skyrmion, the vector texture described by a topological number must be protected upon propagation.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Interpretationreasoning

    If the modes have misaligned Gouy phases, the beam will not be topologically protected and will show variant topological charge upon propagation.

    “If the modes have misaligned Gouy phases, the beam will not be topologically protected and show variant topological charge upon propagation.”
    Quote in the paperSubstantial claim

  • It may state two separate claims as one.

    Premisenone given

    A bimeronic beam can be obtained by modifying a skyrmionic beam, requiring superposition of two specially designed spatial modes with two different non-orthogonal polarizations, whereas a skyrmionic beam requires them to be orthogonal.

    “The bimeronic beam can be obtained by modifying a skyrmionic beam, which requires a superposition with two specially designed spatial modes with two different non-orthogonal polarizations (a skyrmionic beam requires them to be orthogonal).”
    Quote in the paperNot a substantial claim

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    Magnetic skyrmions have been used as magnetic tweezers with a mechanism similar to optical tweezers with twisted light.

    “In turn, applying optical concepts to magnetism, magnetic skyrmions have been used as a magnetic tweezers with a similar mechanism to optical tweezers with twisted light [111][112][113].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [111]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [112]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

    • cites [113]

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • It may state two separate claims as one.

    Premisecitation

    Momentum-space spin textures in photonic systems promise insights related to Dirac monopoles and photon spin quantization, whereby magnetic monopole charge quantization in momentum space can arise from spin-1 skyrmion properties of polaritons.

    “Momentum-space spin textures in photonic systems promise intriguing physical insights related to Dirac monopoles and photon spin quantization, whereby the magnetic monopole charge quantization in momentum space can arise from spin-1 skyrmion properties of polaritons.[88].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [88] Wätzel, J. & Berakdar, J. Topological light fields for highly non-linear charge quantum dynamics and high harmonic generation. Opt. Express 28, 19469–19481 (2020). source

      Checked before — its earlier verdict is held back until a new check runs.

  • It may state two separate claims as one.

    Premisecitation

    The vector textures of skyrmions can be characterized by multiple topological numbers and extended to higher dimensional cases.

    “(iii) diversity of topologies-the vector textures of skyrmions can be characterized by multiple topological numbers and extended to higher dimensional cases [69,70]”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [69] Loder, F., Kampf, A. P., Kopp, T. & Braak, D. Momentum-space spin texture in a topological superconductor. Phys. Rev. B 96, 024508 (2017). source
    • cites [70] Lin, M., Du, L. & Yuan, X. Photonic pseudospin skyrmion in momentum space. IEEE Photon. J. 15, 6500106 (2022).

      Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  • Probably not a substantial claim. The paper’s conclusions may not depend on it.

    Premisecitation

    In magnetic skyrmionic racetrack memory for high-density information storage, information is encoded in the presence and absence of skyrmions.

    “In magnetic skyrmionic racetrack memory for high-density information storage, the information is encoded in the presence and absence of skyrmions [98].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [98] Wan, Z., Wang, H., Liu, Q., Fu, X. & Shen, Y. Ultra-degree-of-freedom structured light for ultracapacity information carriers. ACS Photon. 10, 2149–2164 (2023). source

      Checked before — its earlier verdict is held back until a new check runs.

  • Probably not a substantial claim. It may be too vague to check against evidence. The paper’s conclusions may not depend on it. The paper may give no reason why it holds.

    Interpretationnone given

    The complex topology of skyrmions may provide great potential to explore higher-dimensional quantum states for quantum technologies which are difficult to reach otherwise.

    “The complex topology of skyrmions may provide great potential to explore higher-dimensional quantum states for quantum technologies which are difficult to reach otherwise.”
    Quote in the paperNot a substantial claim
64 of 64

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • The mapping from real-space to a given parameter space is preserved so long as the channel can be described as a smooth deformation of the map.

    “where the mapping from real-space to a given parameter space is preserved, so long as the channel can be described as a smooth deformation of the map.”

    From Topological robustness of optical skyrmions through a real-world free-space link (2026) · cites this paper as [52]

    The 'Skyrmions in free-space fields' section says that an optical skyrmion’s topology and skyrmion number remain invariant during propagation and are resilient to perturbations, except catastrophic events such as strong scattering. Box 1 discusses mappings between parameter space and real space. The copy does not state the claim’s specific condition that a channel preserves the mapping whenever it acts as a smooth deformation; it supports preservation of topology in the optical settings discussed, not that general criterion. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

  • Dissipative and entangling circuits have recently been shown to enable methods for preparing a wide range of ground states, facilitate representation of nontrivial thermal states with enhanced noise resilience, and eliminate the barren plateau effect in training quantum neural networks.

    “Such dissipative and entangling circuits have recently been shown to enable methods for preparing a wide range of ground states, facilitating the representation of nontrivial thermal states with significantly enhanced noise resilience 47 , and able to eliminate the barren plateau effect in the training of quantum neural networks 48 .”

    From Quantum skyrmions and high dimensional entanglement mediated by nanophotonics (2026) · cites this paper as [47]

    Split into 3 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 3 unverifiable. Expand the claim to see per-atom verdicts.

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Figure 4c is identified as both a meron and a skyrmion

    Minor

    The discussion identifies Figure 4c as a triplet-meron structure, whereas the figure caption calls it an optical spin-skyrmion.

  • Setting f to zero cannot produce the stated skyrmion

    Minor

    In the stated mapping, f = 0 makes all three sin f components zero and the cos f component one, regardless of position. The resulting constant vector cannot produce the 2D skyrmion claimed in the next statement.

  • Skyrmion-number derivation drops a minus sign

    Minor

    The radial integral of sin β(r) times dβ(r)/dr is minus the change in cos β(r), not plus the change shown. The stated equality therefore reverses the sign of the skyrmion number derived from the integral.

3 of 3

Citations

Cites

Flagged first, then by citations

Research works printed but not linked: 4

  1. Skyrme, T. H. R. A non-linear feld theory. Proc. R. Soc. A 260, 127–138 (1961).
  2. Shen, Y., Hou, Y., Papasimakis, N. & Zheludev, N. I. Supertoroidal light pulses as electromagnetic skyrmions propagating in free space. Nat. Commun. 12, 5891 (2021).
  3. Lin, M., Du, L. & Yuan, X. Photonic pseudospin skyrmion in momentum space. IEEE Photon. J. 15, 6500106 (2022).
  4. Shen, Y. et al. Topological transformation and freespace transport of photonic hopfons. Adv. Photon. 5, 015001 (2023).

Cited by

Sorted by citations

Related

Metadata

Authors
Shen, Y., Zhang, Q., Shi, P., Du, L., Yuan, X., & Zayats, A. V.
Affiliations
  • Nanyang Technological University (SG)
  • Shenzhen University (CN)
  • King's College London (GB)
Corresponding author
  • Shen, Yijie
  • Yuan, Xiaocong
  • Zayats, Anatoly V.
ORCID
Venue
Nature Photonics
Publisher
Springer Science and Business Media LLC
Published
2023-12-28
Volume
18
Issue
1
Pages
15-25
ISSN
  • 1749-4885 (ISSN-L)
  • 1749-4893
DOI
10.1038/s41566-023-01325-7
OpenAlex
W4390345325
Cited by
469
References
103
Citations by year
2026: 178 · 2025: 184 · 2024: 93 · 2023: 13
FWCI
49.19
Type
journal article
Language
en
Open access
Licence
Locations
  • Nature Photonics (publishedVersion)
  • arXiv (Cornell University) (submittedVersion, cc-by)
  • Figshare (submittedVersion, public-domain)
  • Research Portal (King's College London) (submittedVersion, other-oa)
  • arXiv (Cornell University) (cc-by)
Funders
  • National Natural Science Foundation of China (2020B0301030009, (U1701661), 12047540, 61935013, 12174266)
  • H2020 European Research Council (789340)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Orbital Angular Momentum in Optics
  • Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Topological Materials and Phenomena
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Non-Hermitian Physics
Keywords
optical skyrmions, topological quasiparticles, structured light, evanescent waves, optical forces, topological classification, optical imaging, optical metrology

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