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Induction of p-wave and d-wave order parameters in s-wave superconductors with light pulses

Hennadii Yerzhakov1,* and Alexander Balatsky1,2,†

  • *Contact author: yerzhako@ualberta.ca
  • †Contact author: alexander.balatsky@uconn.edu

Phys. Rev. B 114, 254509 – Published 9 November, 2026

DOI: https://doi.org/10.1103/gmxq-m8b4

Abstract

We construct a generalized time-dependent Ginzburg-Landau model to demonstrate the possibility of inducing p- and d-wave components in an originally pure s-wave centrosymmetric superconductor via microwave radiation. In this framework, specializing to Oh point-group symmetry, we introduce gradient terms that couple the s-wave superconducting order parameter with other symmetry-allowed components. The singlet-to-singlet gradient terms are quadratic in spatial derivatives, while, in the presence of spin-orbit coupling, linear-in-derivatives terms coupling singlet and triplet order parameters are also permitted. Through the minimal substitution procedure, these terms enable coupling between different superconducting order parameters via the vector potential, thereby leading to the generation of p-wave, d-wave, and other symmetry-allowed components. Such a manipulation of the superconducting state locally via a microwave beam could be considered as one more facet of the concept of quantum printing.

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References (71)

  1. A. F. G. Wyatt, V. M. Dmitriev, W. S. Moore, and F. W. Sheard, Microwave-enhanced critical supercurrents in constricted tin films, Phys. Rev. Lett. 16, 1166 (1966).
  2. A. H. Dayem and J. J. Wiegand, Behavior of thin-film superconducting bridges in a microwave field, Phys. Rev. 155, 419 (1967).
  3. G. M. Eliashberg, Film superconductivity stimulated by a high-frequency field, ZhETF Pis. Red. 11, 186 (1970) [Sov. JETP Lett. 11, 114 (1970)].
  4. G. M. Eliashberg and B. I. Ivlev, Theory of superconductivity stimulation, in Nonequilibrium Superconductivity, Modern Problems in Condensed Matter Sciences, edited by D. N. Langenberg and A. I. Larkin (North-Holland, Amsterdam, 1986), Chap. 6, Vol. 12, pp. 211–251.
  5. T. Klapwijk and J. Mooij, Microwave-enhanced superconductivity in aluminium films, Phys. B+C 81, 132 (1976).
  6. J. A. Pals and J. Dobben, Measurements of microwave-enhanced superconductivity in aluminum strips, Phys. Rev. B 20, 935 (1979).
  7. D. Fausti, R. I. Tobey, N. Dean, S. Kaiser, A. Dienst, M. C. Hoffmann, S. Pyon, T. Takayama, H. Takagi, and A. Cavalleri, Light-induced superconductivity in a stripe-ordered cuprate, Science 331, 189 (2011).
  8. S. Kaiser, C. R. Hunt, D. Nicoletti, W. Hu, I. Gierz, H. Y. Liu, M. Le Tacon, T. Loew, D. Haug, B. Keimer, and A. Cavalleri, Optically induced coherent transport far above Tc in underdoped YBa2Cu3O6+δ, Phys. Rev. B 89, 184516 (2014).
  9. M. Mitrano, A. Cantaluppi, D. Nicoletti, S. Kaiser, A. Perucchi, S. Lupi, P. Di Pietro, D. Pontiroli, M. Riccò, S. R. Clark, D. Jaksch, and A. Cavalleri, Possible light-induced superconductivity in K3C60 at high temperature, Nature (London) 530, 461 (2016).
  10. D. Nicoletti and A. Cavalleri, Nonlinear light–matter interaction at terahertz frequencies, Adv. Opt. Photonics 8, 401 (2016).
  11. M. Buzzi, D. Nicoletti, S. Fava, G. Jotzu, K. Miyagawa, K. Kanoda, A. Henderson, T. Siegrist, J. A. Schlueter, M.-S. Nam, A. Ardavan, and A. Cavalleri, Phase diagram for light-induced superconductivity in κ−(ET)2−X, Phys. Rev. Lett. 127, 197002 (2021).
  12. A. Komnik and M. Thorwart, BCS theory of driven superconductivity, Eur. Phys. J. B 89, 244 (2016).
  13. M. A. Sentef, A. F. Kemper, A. Georges, and C. Kollath, Theory of light-enhanced phonon-mediated superconductivity, Phys. Rev. B 93, 144506 (2016).
  14. 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).
  15. M. Babadi, M. Knap, I. Martin, G. Refael, and E. Demler, Theory of parametrically amplified electron-phonon superconductivity, Phys. Rev. B 96, 014512 (2017).
  16. Y. Murakami, N. Tsuji, M. Eckstein, and P. Werner, Nonequilibrium steady states and transient dynamics of conventional superconductors under phonon driving, Phys. Rev. B 96, 045125 (2017).
  17. R. Shimano and N. Tsuji, Higgs mode in superconductors, Annu. Rev. Condens. Matter Phys. 11, 103 (2020).
  18. T. Mizushima and M. Sato, Imprinting spiral Higgs waves onto superconductors with vortex beams, Phys. Rev. Res. 5, L042004 (2023).
  19. D. Kang, S. Kitamura, and T. Morimoto, Quantum optical spanner: Twisting superconductors with vortex beam via Higgs mode, Phys. Rev. B 112, 214315 (2025).
  20. D. Kang, T.-T. Yeh, T. Morimoto, and A. V. Balatsky, Kapitza-Dirac interference of Higgs waves in superconductors, arXiv:2511.10954.
  21. S. Gassner, C. S. Weber, and M. Claassen, Light-induced switching between singlet and triplet superconducting states, Nat. Commun. 15, 1776 (2024).
  22. T. Yokoyama, Creation of superconducting vortices by angular momentum of light, J. Phys. Soc. Jpn. 89, 103703 (2020).
  23. V. D. Plastovets, I. D . Tokman, B. Lounis, A. S. Mel'nikov, and A. I. Buzdin, All-optical generation of Abrikosov vortices by the inverse Faraday effect, Phys. Rev. B 106, 174504 (2022).
  24. T.-T. Yeh, H. Yerzhakov, L. Bishop-Van Horn, S. Raghu, and A. Balatsky, Quantum printing and induced vorticity in superconductors I: Linearly polarized light, Phys. Rev. Res. 7, 043111 (2025).
  25. T.-T. Yeh, H. Yerzhakov, L. B.-V. Horn, S. Raghu, and A. Balatsky, Quantum printing and induced vorticity in superconductors II: Laguerre-Gaussian beam, Phys. Rev. Res. 7, 043112 (2025).
  26. T.-T. Yeh, E. Wilson, M. Fogelström, and A. Balatsky, Light induced Berezinskii-Kosterlitz-Thouless transition in superconducting films, arXiv:2510.22645.
  27. H. Dehghani, M. Hafezi, and P. Ghaemi, Light-induced topological superconductivity via Floquet interaction engineering, Phys. Rev. Res. 3, 023039 (2021).
  28. S. Kitamura and H. Aoki, Floquet topological superconductivity induced by chiral many-body interaction, Commun. Phys. 5, 174 (2022).
  29. Z. Shen, C. Xie, W.-C. Chen, and Y. Wang, Light control of triplet pairing in correlated electrons with mixed-sign interactions, Commun. Phys. 8, 475 (2025).
  30. T. Yokoyama, Floquet engineering triplet superconductivity in superconductors with spin-orbit coupling or altermagnetism, Phys. Rev. B 112, 024512 (2025).
  31. P.-H. Fu, S. Mondal, J.-F. Liu, Y. Tanaka, and J. Cayao, Floquet engineering spin triplet states in unconventional magnets, Phys. Rev. Lett. 136, 066703 (2026).
  32. C. L. Kane and E. J. Mele, Quantum spin Hall effect in graphene, Phys. Rev. Lett. 95, 226801 (2005).
  33. L. D. Landau and E. M. Lifshitz, Statistical Physics, Course of Theoretical Physics (Pergamon Press, Oxford, 1969), Vol. 5.
  34. G. Aeppli, A. V. Balatsky, S. Bonetti, G. Cardoso, S. Raghu, E. Syljuåsen, T.-T. Yeh, S.-Z. Lin, Y. Liu, J. Weissenrieder, and P. J. Wong, Quantum printing, arXiv:2509.16792.
  35. V. V. Kabanov, Triplet pairing and upper critical field in the mixed state of d-wave superconductors, Phys. Rev. B 76, 172501 (2007).
  36. E. Persky, A. V. Bjørlig, I. Feldman, A. Almoalem, E. Altman, E. Berg, I. Kimchi, J. Ruhman, A. Kanigel, and B. Kalisky, Magnetic memory and spontaneous vortices in a van der Waals superconductor, Nature (London) 607, 692 (2022).
  37. S. Mandal and C.-X. Liu, Pair-mixing induced time-reversal-breaking superconductivity, Phys. Rev. B 114, 094511 (2026).
  38. M. Sigrist and K. Ueda, Phenomenological theory of unconventional superconductivity, Rev. Mod. Phys. 63, 239 (1991).
  39. J. F. Annett, Symmetry of the order parameter for high-temperature superconductivity, Adv. Phys. 39, 83 (1990).
  40. M. Sigrist, Introduction to unconventional superconductivity, AIP Conf. Proc. 789, 165 (2005).
  41. B. Normand, H. Kohno, and H. Fukuyama, Properties of a mixed-symmetry superconductor, Phys. C 235–240, 2275 (1994).
  42. C. O'Donovan and J. Carbotte, Mixed order parameter symmetry in the BCS model, Phys. C 252, 87 (1995).
  43. M. P. Sörensen, T. Schneider, and M. Frick, Nonlinear properties of the BCS gap equation, in Microscopic Aspects of Nonlinearity in Condensed Matter, edited by A. R. Bishop, V. L. Pokrovsky, and V. Tognetti (Springer, Boston, 1991), pp. 315–327.
  44. J. Hutchinson and F. Marsiglio, Mixed temperature-dependent order parameters in the extended Hubbard model, J. Phys.: Condens. Matter 33, 065603 (2021).
  45. P. Senarath Yapa, X. Guo, J. Maciejko, and F. Marsiglio, Mixed-symmetry superconductivity and the energy gap, Phys. C 633, 1354719 (2025).
  46. V. P. Mineev and K. V. Samokhin, Helical phases in superconductors, Zh. Eksp. Teor. Fiz. 105, 747 (1994) [Sov. Phys. JETP 78, 401 (1994)].
  47. K. V. Samokhin, E. S. Zijlstra, and S. K. Bose, CePt3Si: An unconventional superconductor without inversion center, Phys. Rev. B 69, 094514 (2004).
  48. V. P. Mineev and K. V. Samokhin, Nonuniform states in noncentrosymmetric superconductors: Derivation of Lifshitz invariants from microscopic theory, Phys. Rev. B 78, 144503 (2008).
  49. K. V. Samokhin, Gradient energy of superconductors without inversion symmetry, Phys. C 489, 19 (2013).
  50. A. Kapustin and L. Radzihovsky, Piezosuperconductivity: Novel effects in noncentrosymmetric superconductors, Phys. Rev. B 105, 134514 (2022).
  51. T. Kamatani, S. Kitamura, N. Tsuji, R. Shimano, and T. Morimoto, Optical response of the Leggett mode in multiband superconductors in the linear response regime, Phys. Rev. B 105, 094520 (2022).
  52. R. Nagashima, S. Tian, R. Haenel, N. Tsuji, and D. Manske, Classification of Lifshitz invariant in multiband superconductors: An application to Leggett modes in the linear response regime in Kagome lattice models, Phys. Rev. Res. 6, 013120 (2024).
  53. A. Dunbrack, P. Virtanen, and T. T. Heikkilä, Quantum geometry of time-reversal symmetry breaking in flat-band superconductivity, Phys. Rev. B 113, 174525 (2026).
  54. P. W. Atkins, M. S. Child, and C. S. G. Phillips, Tables for Group Theory (Oxford University Press, Oxford, 1970).
  55. G. Katzer, Character table for the Oh point group, http://gernot-katzers-spice-pages.com/character_tables/Oh.html.
  56. L. Landau and E. Lifshitz, Quantum Mechanics: Non-Relativistic Theory, Course of Theoretical Physics (Butterworth-Heinemann, Oxford, 1981).
  57. A. Talkachov, P. Leask, and E. Babaev, Multiple correlation lengths and type-1.5 superconductivity in U(1) superconductors due to hidden competition between irreducible representations of nonlocal pairing, Phys. Rev. B 113, 224520 (2026).
  58. N. B. Kopnin, Theory of Nonequilibrium Superconductivity (Oxford University Press, Oxford, 2001), Vol. 110.
  59. L. Kramer and R. J. Watts-Tobin, Theory of dissipative current-carrying states in superconducting filaments, Phys. Rev. Lett. 40, 1041 (1978).
  60. R. J. Watts-Tobin, Y. Kröhenböhl, and L. Kramer, Nonequilibrium theory of dirty, current-carrying superconductors: Phase-slip oscillators in narrow filaments near Tc, J. Low Temp. Phys. 42, 459 (1981).
  61. L. Landau and E. Lifshitz, Mechanics (Elsevier, Amsterdam, 1982), Vol. 1.
  62. A. Samoilenka and E. Babaev, Microscopic derivation of superconductor-insulator boundary conditions for Ginzburg-Landau theory revisited: Enhanced superconductivity at boundaries with and without magnetic field, Phys. Rev. B 103, 224516 (2021).
  63. P.-G. D. Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 2018).
  64. C. Caroli, P. G. de Gennes, and J. Matricon, Sur certaines propriétés des alliages supraconducteurs non magnétiques, J. Phys. Radium 23, 707 (1962).
  65. A. A. Abrikosov, Concerning surface superconductivity in strong magnetic fields, Zh. Eksp. Teor. Fiz. 47, 720 (1964) [Sov. Phys. JETP 20, 480 (1965)].
  66. A. Sergeev and V. Mitin, Electron-phonon interaction in disordered conductors: Static and vibrating scattering potentials, Phys. Rev. B 61, 6041 (2000).
  67. M. Sidorova, A. Semenov, H.-W. Hübers, K. Ilin, M. Siegel, I. Charaev, M. Moshkova, N. Kaurova, G. N. Goltsman, X. Zhang, and A. Schilling, Electron energy relaxation in disordered superconducting NbN films, Phys. Rev. B 102, 054501 (2020).
  68. J.-X. Zhu, W. Kim, C. S. Ting, and C.-R. Hu, Time-dependent Ginzburg-Landau equations for mixed d− and s-wave superconductors, Phys. Rev. B 58, 15020 (1998).
  69. S. Gassner (private communication).
  70. H. Yerzhakov, T.-T. Yeh, and A. Balatsky, Induction of orbital currents and Kapitza stabilization in superconducting circuits with Laguerre-Gaussian microwave beams, Phys. Rev. B 110, 144519 (2024).
  71. https://github.com/hennadii-phys/GeneralizedTDGL_Oh.

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