Landau, L. The theory of phase transitions. Nature 138, 840\u2013841 (1936).<\/p>\n
Article<\/a>\u00a0 Post, K. W. et al. Coexisting first- and second-order electronic phase transitions in a correlated oxide. Nat. Phys. 14, 1056\u20131061 (2018).<\/p>\n Article<\/a>\u00a0 Kosterlitz, J. M. & Thouless, D. J. Ordering, metastability and phase transitions in two-dimensional systems. J. Phys. C 6, 1181 (1973).<\/p>\n Article<\/a>\u00a0 Thouless, D. J. Long-range order in one-dimensional Ising systems. Phys. Rev. 187, 732 (1969).<\/p>\n Article<\/a>\u00a0 Kosterlitz, J. M. Nobel lecture: topological defects and phase transitions. Rev. Mod. Phys. 89, 040501 (2017).<\/p>\n Article<\/a>\u00a0 Sone, K. et al. Nonlinearity-induced topological phase transition characterized by the nonlinear Chern number. Nat. Phys. 20, 1164\u20131170 (2024).<\/p>\n Article<\/a>\u00a0 Qi, X. & Zhang, S. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057\u20131110 (2011).<\/p>\n Article<\/a>\u00a0 Wachowiak, A. et al. Direct observation of internal spin structure of magnetic vortex cores. Science 298, 577\u2013580 (2002).<\/p>\n Article<\/a>\u00a0 Naumov, I. I., Bellaiche, L. & Fu, H. Unusual phase transitions in ferroelectric nanodisks and nanorods. Nature 432, 737\u2013740 (2004).<\/p>\n Article<\/a>\u00a0 Tang, Y. L. et al. Observation of a periodic array of flux-closure quadrants in strained ferroelectric PbTiO3 films. Science 348, 547\u2013551 (2015).<\/p>\n Article<\/a>\u00a0 Yadav, A. et al. Observation of polar vortices in oxide superlattices. Nature 530, 198\u2013201 (2016).<\/p>\n Article<\/a>\u00a0 Das, S. et al. Observation of room-temperature polar skyrmions. Nature 568, 368\u2013372 (2019).<\/p>\n Article<\/a>\u00a0 Han, L. et al. High-density switchable skyrmion-like polar nanodomains integrated on silicon. Nature 603, 63\u201367 (2022).<\/p>\n Article<\/a>\u00a0 Wang, J. et al. Polar Solomon rings in ferroelectric nanocrystals. Nat. Commun. 14, 3941 (2023).<\/p>\n Article<\/a>\u00a0 S\u00e1nchez-Santolino, G. et al. A 2D ferroelectric vortex pattern in twisted BaTiO3 freestanding layers. Nature 626, 529\u2013534 (2024).<\/p>\n Article<\/a>\u00a0 Yadav, A. K. et al. Spatially resolved steady-state negative capacitance. Nature 565, 468\u2013471 (2019).<\/p>\n Article<\/a>\u00a0 Das, S. et al. Local negative permittivity and topological phase transition in polar skyrmions. Nat. Mater. 20, 194\u2013201 (2021).<\/p>\n Article<\/a>\u00a0 Shao, Y. T. et al. Emergent chirality in a polar meron to skyrmion phase transition. Nat. Commun. 14, 1355 (2023).<\/p>\n Article<\/a>\u00a0 Wang, S. et al. Giant electric field-induced second harmonic generation in polar skyrmions. Nat. Commun. 15, 1374 (2024).<\/p>\n Article<\/a>\u00a0 Li, Q. et al. Subterahertz collective dynamics of polar vortices. Nature 592, 376\u2013380 (2021).<\/p>\n Article<\/a>\u00a0 Geng, W. R. et al. Dipolar wavevector interference induces a polar skyrmion lattice in strained BiFeO3 films. Nat. Nanotechnol. 20, 366\u2013373 (2025).<\/p>\n Article<\/a>\u00a0 Tang, Y. Y. et al. Organic ferroelectric vortex-antivortex domain structure. J. Am. Chem. Soc. 142, 21932\u201321937 (2020).<\/p>\n Article<\/a>\u00a0 Guo, M. et al. Toroidal polar topology in strained ferroelectric polymer. Science 371, 1050\u20131056 (2021).<\/p>\n Article<\/a>\u00a0 Avron, J. E., Seiler, R. & Simon, B. Homotopy and quantization in condensed matter physics. Phys. Rev. Lett. 51, 51\u201353 (1983).<\/p>\n Article<\/a>\u00a0 Li, L. et al. Defect-induced hedgehog polarization states in multiferroics. Phys. Rev. Lett. 120, 137602 (2018).<\/p>\n Article<\/a>\u00a0 Luk\u2019yanchuk, I. et al. Hopfions emerge in ferroelectrics. Nat. Commun. 11, 2433 (2020).<\/p>\n Article<\/a>\u00a0 Wang, Y. J. et al. Polar meron lattice in strained oxide ferroelectrics. Nat. Mater. 19, 881\u2013886 (2020).<\/p>\n Article<\/a>\u00a0 Zhou, L. et al. Harness of room-temperature polar skyrmion bag in oxide superlattice. Nat. Commun. 16, 9911 (2025).<\/p>\n Article<\/a>\u00a0 Zheng, W. et al. Skyrmion nanodomains in ferroelectric\u2013antiferroelectric solid solutions. Nat. Mater. 24, 1424\u20131432 (2025).<\/p>\n Article<\/a>\u00a0 Catalan, G. et al. Domains in three-dimensional ferroelectric nanostructures: theory and experiment. J. Phys. Condens. Matter 19, 132201 (2007).<\/p>\n Article<\/a>\u00a0 Hong, Z. et al. Stability of polar vortex lattice in ferroelectric superlattices. Nano Lett. 17, 2246\u20132252 (2017).<\/p>\n Article<\/a>\u00a0 Hong, Z. & Chen, L. Blowing polar skyrmion bubbles in oxide superlattices. Acta Mater. 152, 155\u2013161 (2018).<\/p>\n Article<\/a>\u00a0 Stoica, V. A. et al. Optical creation of a supercrystal with three-dimensional nanoscale periodicity. Nat. Mater. 18, 377\u2013383 (2019).<\/p>\n Article<\/a>\u00a0 Wang, B., Gu, Y., Zhang, S. & Chen, L. Flexoelectricity in solids: progress, challenges and perspectives. Prog. Mater. Sci. 106, 100570 (2019).<\/p>\n Article<\/a>\u00a0 Li, Q. et al. Quantification of flexoelectricity in PbTiO3\/SrTiO3 superlattice polar vortices using machine learning and phase-field modeling. Nat. Commun. 8, 1468 (2017).<\/p>\n Article<\/a>\u00a0 Morozovska, A. et al. Chiral polarization textures induced by the flexoelectric effect in ferroelectric nanocylinders. Phys. Rev. B 104, 054118 (2021).<\/p>\n Article<\/a>\u00a0 Janquera, J. et al. Topologial phases in polar oxide nanostructures. Rev. Mod. Phys. 95, 025001 (2023).<\/p>\n Article<\/a>\u00a0 Chen, P. et al. Atomic imaging of mechanically induced topological transition of ferroelectric vortices. Nat. Commun. 11, 1840 (2020).<\/p>\n Article<\/a>\u00a0 Zhao, H. J. et al. Dzyaloshinskii\u2013Moriya-like interaction in ferroelectrics and antiferroelectrics. Nat. Mater. 20, 341\u2013345 (2021).<\/p>\n Article<\/a>\u00a0 Prosandeev, S. & Bellaiche, L. Characteristics and signatures of dipole vortices in ferroelectric nanodots: first-principles-based simulations and analytical expressions. Phys. Rev. B 75, 094102 (2007).<\/p>\n Article<\/a>\u00a0 Nahas, Y. et al. Inverse transition of labyrinthine domain patterns in ferroelectric thin films. Nature 577, 47\u201351 (2020).<\/p>\n Article<\/a>\u00a0 Tong, P. et al. Thermal triggering for multi-state switching of polar topologies. Nat. Phys. 21, 464\u2013470 (2025).<\/p>\n Article<\/a>\u00a0 Wang, Y. J., Tang, Y. L., Zhu, Y. L. & Ma, X. L. Meron-antimeron annihilation induced by the electric field in a polar meron lattice. J. Appl. Phys. 131, 224102 (2022).<\/p>\n Article<\/a>\u00a0 Prokhorenko, S. et al. Motion and teleportation of polar bubbles in low-dimensional ferroelectrics. Nat. Commun. 15, 412 (2024).<\/p>\n Article<\/a>\u00a0 Hu, L., Wu, Y., Huang, Y., Tian, H. & Hong, Z. Dynamic motion of polar skyrmions in oxide heterostructures. Nano Lett. 23, 11353\u201311359 (2023).<\/p>\n Article<\/a>\u00a0 Margaret, M. R. et al. Structural chirality of polar skyrmions probed by resonant elastic X-ray scattering. Phys. Rev. Lett. 129, 247601 (2022).<\/p>\n Article<\/a>\u00a0 Shafer, P. et al. Emergent chirality in the electric polarization texture of titanate superlattices. Proc. Natl Acad. Sci. USA 115, 915\u2013920 (2018).<\/p>\n Article<\/a>\u00a0 Li, W. et al. Terahertz excitation of collective dynamics of polar skyrmions over a broad temperature range. Nat. Phys. 21, 1965\u20131972 (2025).<\/p>\n Article<\/a>\u00a0 Behera, P. et al. Electric field control of chirality. Sci. Adv. 8, eabj8030 (2022).<\/p>\n Article<\/a>\u00a0 Salahuddin, S. & Datta, S. Use of negative capacitance to provide voltage amplification for low power nanoscale devices. Nano Lett. 8, 405\u2013410 (2008).<\/p>\n Article<\/a>\u00a0 Wang, Y. et al. Polar Bloch points in strained ferroelectric films. Nat. Commun. 15, 3949 (2024).<\/p>\n Article<\/a>\u00a0 Huang, P. et al. Melting of a skyrmion lattice to a skyrmion liquid via a hexatic phase. Nat. Nanotechnol. 15, 761\u2013767 (2020).<\/p>\n Article<\/a>\u00a0 Cugliandolo, L. F. Coarsening phenomena. C. R. Phys. 16, 257\u2013266 (2015).<\/p>\n Article<\/a>\u00a0 Kibble, T. W. B. Some implications of a cosmological phase transition. Phys. Rep. 67, 183\u2013199 (1980).<\/p>\n Article<\/a>\u00a0 Biroli, G., Cugliandolo, L. F. & Sicilia, A. Kibble-Zurek mechanism and infinitely slow annealing through critical points. Phys. Rev. E 81, 050101 (2010).<\/p>\n Article<\/a>\u00a0 Roychowdhury, K. et al. Dynamics and correlations at a quantum phase transition beyond Kibble-Zurek. Phys. Rev. B 104, 014406 (2021).<\/p>\n Article<\/a>\u00a0 Du, G. et al. Design of polar skyrmion-based nanoelectronic prototype devices with phase-field simulations. Adv. Funct. Mater. 34, 2405594 (2024).<\/p>\n Article<\/a>\u00a0 Chazal, F. & Michel, B. An introduction to topological data analysis: fundamental and practical aspects for data scientists. Front. Artif. Intell. 4, 667963 (2021).<\/p>\n Article<\/a>\u00a0 Du, G. et al. Topological data analysis assisted machine learning for polar topological structures in oxide superlattices. Acta Mater. 282, 120467 (2025).<\/p>\n Article<\/a>\u00a0 Kalinin, S. V. et al. Machine learning for automated experimentation in scanning transmission electron microscopy. npj Comput. Mater. 9, 227 (2023).<\/p>\n Article<\/a>\u00a0 Liu, Y. et al. Ferroelectric-based neuromorphic memory devices for bio-inspired computing. Nat. Rev. Electr. Eng. 2, 773\u2013787 (2025).<\/p>\n Article<\/a>\u00a0 Mermin, N. D. The topological theory of defects in ordered media. Rev. Mod. Phys. 51, 591\u2013648 (1979).<\/p>\n Article<\/a>\u00a0
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