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Dynamical Breaking of Inversion Symmetry, Strong Second Harmonic Generation, and Nonequilibrium Ferroelectricity with Nonlinear Phonons

Egor I. Kiselev

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Phys. Rev. Lett. 137, 106903 – Published 4 September, 2026

DOI: https://doi.org/10.1103/lwpl-brrr

Abstract

We show how crystalline inversion symmetry can be dynamically broken by optical phonons with generic, hardening Kerr-like nonlinearities. The symmetry-broken state is reached through a parametric instability that can be accessed by driving close to half the phonon frequency. The system then settles to a steady state with inversion symmetry breaking phonon trajectories and strong second harmonic generation. The time averaged positions of the atoms are displaced relative to equilibrium, resulting in a ferroelectric rectification of the driving signal. For circularly polarized phonons, complex Lissajous-like trajectories, resulting in structured magnetic fields within a unit cell, can be achieved.

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References (60)

  1. D. Basov, R. Averitt, and D. Hsieh, Towards properties on demand in quantum materials, Nat. Mater. 16, 1077 (2017).
  2. J. Bloch, A. Cavalleri, V. Galitski, M. Hafezi, and A. Rubio, Strongly correlated electron–photon systems, Nature (London) 606, 41 (2022).
  3. M. S. Rudner and N. H. Lindner, Band structure engineering and non-equilibrium dynamics in floquet topological insulators, Nat. Rev. Phys. 2, 229 (2020).
  4. M. Först, C. Manzoni, S. Kaiser, Y. Tomioka, Y. Tokura, R. Merlin, and A. Cavalleri, Nonlinear phononics as an ultrafast route to lattice control, Nat. Phys. 7, 854 (2011).
  5. R. Mankowsky, M. Först, and A. Cavalleri, Non-equilibrium control of complex solids by nonlinear phononics, Rep. Prog. Phys. 79, 064503 (2016).
  6. R. Mankowsky, A. Subedi, M. Först, S. O. Mariager, M. Chollet, H. Lemke, J. S. Robinson, J. M. Glownia, M. P. Minitti, A. Frano et al., Nonlinear lattice dynamics as a basis for enhanced superconductivity in YBa2Cu3O6.5, Nature (London) 516, 71 (2014).
  7. M. Knap, M. Babadi, G. Refael, I. Martin, and E. Demler, Dynamical cooper pairing in nonequilibrium electron-phonon systems, Phys. Rev. B 94, 214504 (2016).
  8. M. Babadi, M. Knap, I. Martin, G. Refael, and E. Demler, Theory of parametrically amplified electron-phonon superconductivity, Phys. Rev. B 96, 014512 (2017).
  9. A. Cavalleri, Photo-induced superconductivity, Contemp. Phys. 59, 31 (2018).
  10. B. Liu, M. Först, M. Fechner, D. Nicoletti, J. Porras, T. Loew, B. Keimer, and A. Cavalleri, Pump frequency resonances for light-induced incipient superconductivity in YbA2Cu3O6.5, Phys. Rev. X 10, 011053 (2020).
  11. M. Fechner, A. Sukhov, L. Chotorlishvili, C. Kenel, J. Berakdar, and N. Spaldin, Magnetophononics: Ultrafast spin control through the lattice, Phys. Rev. Mater. 2, 064401 (2018).
  12. D. Afanasiev, J. Hortensius, B. Ivanov, A. Sasani, E. Bousquet, Y. Blanter, R. Mikhaylovskiy, A. Kimel, and A. Caviglia, Ultrafast control of magnetic interactions via light-driven phonons, Nat. Mater. 20, 607 (2021).
  13. A. Disa, J. Curtis, M. Fechner, A. Liu, A. Von Hoegen, M. Först, T. Nova, P. Narang, A. Maljuk, A. Boris et al., Photo-induced high-temperature ferromagnetism in YTiO3, Nature (London) 617, 73 (2023).
  14. T. Luo, H. Ning, B. Ilyas, A. von Hoegen, E. Viñas Boström, J. Park, J. Kim, J.-G. Park, D. M. Juraschek, A. Rubio et al., Terahertz control of linear and nonlinear magno-phononics, Nat. Commun. 16, 6863 (2025).
  15. H. Ning, O. Mehio, X. Li, M. Buchhold, M. Driesse, H. Zhao, G. Cao, and D. Hsieh, A coherent phonon-induced hidden quadrupolar ordered state in Ca2RuO4, Nat. Commun. 14, 8258 (2023).
  16. D. Kaplan, P. A. Volkov, A. Chakraborty, Z. Zhuang, and P. Chandra, Tunable spatiotemporal orders in driven insulators, Phys. Rev. Lett. 134, 066902 (2025).
  17. D. Kaplan, P. A. Volkov, J. Coulter, S. Zhang, and P. Chandra, Spatiotemporal order and parametric instabilities from first-principles, npj Quantum Mater. 11, 50 (2026).
  18. T. Nova, A. Disa, M. Fechner, and A. Cavalleri, Metastable ferroelectricity in optically strained SrTiO3, Science 364, 1075 (2019).
  19. X. Li, T. Qiu, J. Zhang, E. Baldini, J. Lu, A. M. Rappe, and K. A. Nelson, Terahertz field–induced ferroelectricity in quantum paraelectric SrTiO3, Science 364, 1079 (2019).
  20. E. I. Kiselev, M. S. Rudner, and N. H. Lindner, Inducing exceptional points, enhancing plasmon quality and creating correlated plasmon states with modulated floquet parametric driving, Nat. Commun. 15, 9914 (2024).
  21. E. I. Kiselev, Y. Pan, and N. H. Lindner, Light-controlled terahertz plasmonic time-varying media: Momentum gaps, entangled plasmon pairs, and pulse-induced time reversal, Phys. Rev. B 110, L241411 (2024).
  22. E. I. Kiselev, J. F. Karcher, M. S. Rudner, R. Duine, and N. H. Lindner, Exciting terahertz magnons with amplitude modulated light: Spin pumping, squeezed states, symmetry breaking and pattern formation, arXiv:2507.08147.
  23. M. Wanic, C. Jasiukiewicz, Z. Toklikishvili, V. Jandieri, M. Trybus, E. Jartych, S. Mishra, and L. Chotorlishvili, Entanglement properties of photon–magnon crystal from nonlinear perspective, Physica D (Amsterdam) 476, 134699 (2025).
  24. D. Kaplan, P. A. Volkov, A. Cavalleri, and P. Chandra, Optically-induced faraday-goldstone waves, arXiv:2511.07320.
  25. M. Wanic, Z. Toklikishvili, S. Mishra, M. Trybus, and L. Chotorlishvili, Magnetoelectric fractals, magnetoelectric parametric resonance and hopf bifurcation, Physica D (Amsterdam) 467, 134257 (2024).
  26. A. Cartella, T. F. Nova, M. Fechner, R. Merlin, and A. Cavalleri, Parametric amplification of optical phonons, Proc. Natl. Acad. Sci. U.S.A. 115, 12148 (2018).
  27. M. Buzzi, G. Jotzu, A. Cavalleri, J. I. Cirac, E. A. Demler, B. I. Halperin, M. D. Lukin, T. Shi, Y. Wang, and D. Podolsky, Higgs-mediated optical amplification in a nonequilibrium superconductor, Phys. Rev. X 11, 011055 (2021).
  28. M. H. Michael, S. R. U. Haque, L. Windgaetter, S. Latini, Y. Zhang, A. Rubio, R. D. Averitt, and E. Demler, Photonic time-crystalline behaviour mediated by phonon squeezing in Ta2NiSe5, Nat. Commun. 15, 3638 (2024).
  29. R. W. Boyd, Nonlinear Optics (Academic Press, New York, 2008).
  30. A. S. Disa, M. Fechner, T. F. Nova, B. Liu, M. Först, D. Prabhakaran, P. G. Radaelli, and A. Cavalleri, Polarizing an antiferromagnet by optical engineering of the crystal field, Nat. Phys. 16, 937 (2020).
  31. D. M. Juraschek, R. M. Geilhufe, H. Zhu, M. Basini, P. Baum, A. Baydin, S. Chaudhary, M. Fechner, B. Flebus, G. Grissonnanche et al., Chiral phonons, Nat. Phys. 21, 1532 (2025).
  32. T. Kahana, D. A. Bustamante Lopez, and D. M. Juraschek, Light-induced magnetization from magnonic rectification, Sci. Adv. 10, eado0722 (2024).
  33. J. Luo, T. Lin, J. Zhang, X. Chen, E. R. Blackert, R. Xu, B. I. Yakobson, and H. Zhu, Large effective magnetic fields from chiral phonons in rare-Earth halides, Science 382, 698 (2023).
  34. D. M. Juraschek, T. Neuman, and P. Narang, Giant effective magnetic fields from optically driven chiral phonons in 4 F paramagnets, Phys. Rev. Res. 4, 013129 (2022).
  35. G. Xiong, H. Chen, D. Ma, and L. Zhang, Effective magnetic fields induced by chiral phonons, Phys. Rev. B 106, 144302 (2022).
  36. O. Yaniv and D. M. Juraschek, Multicolor phonon excitation in terahertz cavities, Phys. Rev. Lett. 135, 246901 (2025).
  37. L. Turyn, The damped Mathieu equation, Q. Appl. Math. 51, 389 (1993).
  38. L. D. Landau and E. M. Lifshitz, Mechanics (Butterworth-Heinemann, Oxford, 1976).

  39. The equations on page 390 of this reference contain a typo.

  40. A. von Hoegen, R. Mankowsky, M. Fechner, M. Först, and A. Cavalleri, Probing the interatomic potential of solids with strong-field nonlinear phononics, Nature (London) 555, 79 (2018).
  41. C. Olson and M. Olsson, Dynamical symmetry breaking and chaos in Duffing’s equation, Am. J. Phys. 59, 907 (1991).
  42. B. Xu, C. Paillard, B. Dkhil, and L. Bellaiche, Pinched hysteresis loop in defect-free ferroelectric materials, Phys. Rev. B 94, 140101 (2016).
  43. V. A. Abalmasov, Ultrafast reversal of the ferroelectric polarization by a midinfrared pulse, Phys. Rev. B 101, 014102 (2020).
  44. V. A. Abalmasov, Ferroelectric polarization reversal versus pump spot shape, Phys. Rev. B 104, L140102 (2021).
  45. B. Cheng, T. Schumann, Y. Wang, X. Zhang, D. Barbalas, S. Stemmer, and N. Armitage, A large effective phonon magnetic moment in a dirac semimetal, Nano Lett. 20, 5991 (2020).
  46. H. Mustafa, C. Nnokwe, G. Ye, M. Fang, S. Chaudhary, J.-A. Yan, K. Wu, C. J. Cunningham, C. M. Hemesath, A. J. Stollenwerk et al., Origin of large effective phonon magnetic moments in monolayer MoS2, ACS Nano 19, 11241 (2025).
  47. L. Zhang and Q. Niu, Chiral phonons at high-symmetry points in monolayer hexagonal lattices, Phys. Rev. Lett. 115, 115502 (2015).
  48. H. Zhu, J. Yi, M.-Y. Li, J. Xiao, L. Zhang, C.-W. Yang, R. A. Kaindl, L.-J. Li, Y. Wang, and X. Zhang, Observation of chiral phonons, Science 359, 579 (2018).
  49. K. Ishito, H. Mao, Y. Kousaka, Y. Togawa, S. Iwasaki, T. Zhang, S. Murakami, J.-i. Kishine, and T. Satoh, Truly chiral phonons in α-HgS, Nat. Phys. 19, 35 (2023).
  50. H. Ueda, M. Garcia-Fernandez, S. Agrestini, C. P. Romao, J. van den Brink, N. A. Spaldin, K.-J. Zhou, and U. Staub, Chiral phonons in quartz probed by x-rays, Nature (London) 618, 946 (2023).
  51. J. Bonini, S. Ren, D. Vanderbilt, M. Stengel, C. E. Dreyer, and S. Coh, Frequency splitting of chiral phonons from broken time-reversal symmetry in CrI3, Phys. Rev. Lett. 130, 086701 (2023).
  52. H. Chen, W. Zhang, Q. Niu, and L. Zhang, Chiral phonons in two-dimensional materials, 2D Mater. 6, 012002 (2019).
  53. V. Ginzburg, Theory of ferroelectric phenomena, Usp. Fiz. Nauk 38, 490 (1949).
  54. W. Cochran, Crystal stability and the theory of ferroelectricity, Phys. Rev. Lett. 3, 412 (1959).
  55. W. Cochran, Crystal stability and the theory of ferroelectricity, Adv. Phys. 9, 387 (1960).
  56. J. Scott, Soft-mode spectroscopy: Experimental studies of structural phase transitions, Rev. Mod. Phys. 46, 83 (1974).
  57. S. Pal, N. Strkalj, C.-J. Yang, M. C. Weber, M. Trassin, M. Woerner, and M. Fiebig, Origin of terahertz soft-mode nonlinearities in ferroelectric perovskites, Phys. Rev. X 11, 021023 (2021).
  58. L. N. Alyabyeva, A. S. Prokhorov, D. Vinnik, V. B. Anzin, A. Ahmed, A. Mikheykin, P. Bednyakov, C. Kadlec, F. Kadlec, E. de Prado et al., Lead-substituted barium hexaferrite for tunable terahertz optoelectronics, NPG Asia Mater. 13, 63 (2021).
  59. E. Kiselev, A. Averkin, M. Fistul, V. Koshelets, and A. Ustinov, Two-tone spectroscopy of a squid metamaterial in the nonlinear regime, Phys. Rev. Res. 1, 033096 (2019).

  60. We note that this must not necessarily be the case for other less generic types of nonlinearities than the one considered here.

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Phys. Rev. Lett. 137, 106903– Published 4 September, 2026
  • Received 24 October 2025
  • Revised 12 March 2026
  • Accepted 9 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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