[1] Coullet, P., Gil, L. & Rocca, F. Optical Vortices. Opt. Commun. 73, 403-408 (1989)
[2] Bliokh, K. Y., Rodríguez-Fortuño, F. J., Nori, F. & Zayats, A. V. Spin–orbit interactions of light. Nat. Photon. 9, 796–808 (2015)
[3] Grier, D. G. A revolution in optical manipulation. Nature 424, 810-816 (2003)
[4] Padgett, M. & Bowman, R. Tweezers with a twist. Nat. Photon. 5, 343-348 (2011)
[5] Schmiegelow, C. T., et. al. Transfer of optical orbital angular momentum to a bound electron. Nature Commun. 7, 12998 (2016)
[6] Bozinovic, N. et. al. Terabit-scale orbital angular momentum mode division multiplexing in fibers. Science 340, 1545-1548 (2013)
[7] Nicolas, A. et. al. A quantum memory for orbital angular momentum photonic qubits. Nat. Photon. 8, 234-238 (2014)
[8] Weber, M. et. al. MINSTED fluorescence localization and nanoscopy. Nat. Photon. 15, 361–366 (2021)
[9] Beijersbergen, M. W. Helical-wavefront laser beams produced with a spiral phaseplate. Opt. Commun. 112, 321-327 (1994)
[10] Yu. N. et. al. Light propagation with phase discontinuities: generalized laws of reflection and refraction. Science 334, 333-337 (2011)
[11] Chong, K. E. et. al. Polarization-independent silicon metadevices for efficient optical wavefront control. Nano Lett. 15, 5369-5374 (2015)
[12] Deng, Z.-L. et. al. Observation of localized magnetic plasmon skyrmions. Nat. Commun. 13 8 (2022)
[13] Uhlíř, V. et. al. Dynamic switching of the spin circulation in tapered magnetic nanodisks. Nat. Nanotechnol. 8, 341-346 (2013)
[14] Jenkins, A. S. et. al. Spin-torque resonant expulsion of the vortex core for an efficient radiofrequency detection scheme. Nat. Nanotechnol. 11, 360-364 (2016)
[15] Kwon, W. J. et. al. Sound emission and annihilations in a programmable quantum vortex collider. Nature 600, 64-69 (2021)
[16] Veshchunov, I. S. et. al. Optical manipulation of single flux quanta. Nature Commun. 7, 12801 (2016)
[17] Dobrovoloskiy, O. V. et. al. Ultra-fast vortex motion in a direct-write Nb-C superconductor. Nature Commun. 11, 3291 (2020)
[18] Mermin, N. D. The topological theory of defects in ordered media. Rev. Mod. Phys. 51 591 (1979)
[19] Blatter, G., et. al. Vortices in high-temperature superconductors. Rev. Mod. Phys. 66, 1125 (1994)
[20] Shinjo, T. et. al. Magnetic vortex core observation in circular dots of permalloy. Science 289, 930-932 (2000)
[21] Chmiel, F. P. et. al. Observation of magnetic vortex pairs at room temperature in a planar α-Fe2O3/Co heterostructure. Nat. Mater. 17, 581-585 (2018)
[22] Lagoudakis, K. G. et. al. Quantized vortices in an exciton-polariton condensate. Nat. Phys. 4, 706-710 (2008)
[23] Ma, X. et. al. Realization of all-optical vortex switching in exciton-polariton condensates. Nat. Commun. 11, 897 (2020)
[24] Indenbom, M. V. et. al. Magneto-optical observation of twisted vortices in type-II superconductors. Nature 385, 702-705 (1997)
[25] Reimann, T. et. al. Visualizing the morphology of vortex lattice domains in a bulk type-II superconductor. Nat. Commun. 6, 8813 (2015)
[26] Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C: Solid State Phys. 6, 1181 (1973)
[27] Christodoulou, P. et. al. Observation of first and second sound in a BKT superfluid. Nature 594, 191–194 (2021)
[28] Allen, L. et. al. Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes. Phys. Rev. A 45, 8185 (1992)
[29] Gorodetski, A. et. al. Observation of the spin-based plasmonic effect in nanoscale structures. Phys. Rev. Lett. 101, 043903 (2008)
[30] Jin, J. et. al. Topologically enabled ultrahigh-Q guided resonances robust to out-of-plane scattering. Nature 574, 501-504 (2019)
[31] Wang, B. et. al. Generating optical vortex beams by momentum-space polarization vortices centred at bound states in the continuum. Nat. Photon. 14, 623-628 (2020)
[32] Situ, G. & Fleischer, J. W. Dynamics of the Berezinskii–Kosterlitz–Thouless transition in a photon fluid. Nat. Photon. 14, 517-522 (2020)
[33] Bruno, P., Dugaev, V. K., & Tailefumier, M. Topological Hall Effect and Berry Phase in Magnetic Nanostructures. Phys. Rev. Lett. 93, 096806 (2004)
[34] Jiang, W. et. al. Direct observation of the skyrmion Hall effect. Nat. Phys. 13, 162-169 (2017)
[35] Heinze, S. et. al. Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions. Nat. Phys. 7, 713-718 (2011)
[36] Zheng, G. et. al. Tailoring Dzyaloshinskii–Moriya interaction in a transition metal dichalcogenide by dual-intercalation. Nat. Commun. 12, 3639 (2021)
[37] Xu, S-. Y. et. al. Topological Phase Transition and Texture Inversion in a Tunable Topological Insulator. Science 332, 560-564 (2011)
[38] Sie, E. J. et. al. An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61-66 (2019)
[39] Carcia, P. F. Perpendicular magnetic anisotropy in Pd/Co and Pt/Co thin-film layered structures. J. Appl. Phys. 63, 5066 (1988)
[40] Kim, D. et. al. Extreme anti-reflection enhanced magneto-optic Kerr effect microscopy. Nat. Commun. 11, 5937 (2020)
[41] Huang, B. et. al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017)
[42] Hu, Y. et. al. On-chip electro-optic frequency shifters and beam splitters. Nature 599, 587-593 (2021)
[43] Kita, D. M. et. al. High-performance and scalable on-chip digital Fourier transform spectroscopy. Nat. Commun. 9, 4405 (2018)
[44] Li, G., Zhang, S. & Zentgraf, T. Nonlinear photonic metasurfaces. Nat. Rev. Mater. 2, 17010 (2017)
[45] Yu, J. et. al. Electrically tunable nonlinear polaritonic metasurface. Nat. Photon. 16, 72-78 (2022)
[46] Li, J. I. A. et. al. Excitonic superfluid phase in double bilayer graphene. Nat. Phys. 13, 751-755 (2017)
[47] Kwon, W. J. et. al. Sound emission and annihilations in a programmable quantum vortex collider. Nature 600, 64-69 (2021)
[48] Sroor, H. et. al. High-purity orbital angular momentum states from a visible metasurface laser. Nat. Photon. 14, 498-503 (2020)
[49] Bahari, B. et. al. Photonic quantum Hall effect and multiplexed light sources of large orbital angular momenta. Nat. Phys. 17, 700-703 (2021)
[50] Zdagkas, A., Shen, Y., Papasimakis, N. & Zheludev, N. I. Observation of Toroidal Pulses of Light. arXiv:2102.03636
[51] Shen, Y., Hou, Y., Papasimakis, N. & Zheludev, N. I., Supertoroidal light pulses as electromagnetic skyrmions propagating in free space. Nat. Commun. 12, 5891 (2021)
[52] Larocque, H. et. al. Reconstructing the topology of optical polarization knots. Nat. Phys. 14, 1079-1082 (2018)
[53] Dennis, M. R. et. al. Isolated optical vortex knots. Nat. Phys. 6, 118-121 (2010)
[54] Wang, K., Dutt, A., Wojcik, C. C. & Fan, S. Topological complex-energy braiding of non-Hermitian bands. Nature 598, 59-64 (2021)