Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Self-induced Berry flux and spontaneous non-equilibrium magnetism


When a physical system is governed by statistical or dynamical equations possessing certain symmetries, its stationary states can be classified into phases according to which of those symmetries are preserved, and which are broken1,2. Near equilibrium, the properties of the system’s collective excitations reflect the symmetries of the underlying phase and thereby provide means for detecting these phases3,4. Here, we show that, in driven systems, the collective modes may take on a separate life, exhibiting their own spontaneous symmetry-breaking phenomena independent of the underlying equilibrium phase. We illustrate this principle by demonstrating a mechanism through which a non-magnetic interacting metal subjected to a linearly polarized driving field can spontaneously magnetize. The strong internal a.c. fields of the metal driven close to its plasmonic resonance5,6 enable Berryogenesis: the spontaneous generation of a self-induced Bloch band Berry flux. The self-induced Berry flux supports and is sustained by a chiral circulating plasmonic motion that breaks the mirror symmetry of the system. This non-equilibrium phase transition may be of either continuous or discontinuous type. Berryogenesis can occur in a wide variety of multiband metals with high-quality plasmons, as available in present-day graphene devices7,8,9.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Prices vary by article type



Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Spontaneous generation of Berry flux via plasmonic internal fields.
Fig. 2: Berry flux generation and nonlinear plasmon dynamics.
Fig. 3: Spontaneous magnetization in the presence of a linearly polarized drive.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.


  1. Chaikin, P. M. & Lubensky, T. C. Principles of Condensed Matter Physics (Cambridge University Press, 1995).

  2. Haken, H. Cooperative phenomena in systems far from thermal equilibrium and in nonphysical systems. Rev. Mod. Phys. 47, 67–121 (1975).

    Article  ADS  MathSciNet  Google Scholar 

  3. Goldstone, J., Salam, A. & Weinberg, S. Broken symmetries. Phys. Rev. 127, 965–970 (1962).

    Article  ADS  MathSciNet  Google Scholar 

  4. Basov, D. N., Fogler, M. M. & García de Abajo, F. J. Polaritons in van der Waals materials. Science 354, aag1992 (2016).

    Article  Google Scholar 

  5. Atwater, H. A. & Polman, A. Plasmonics for improved photovoltaic devices. Nat. Mater. 9, 205–213 (2010).

    Article  ADS  Google Scholar 

  6. Koppens, F. H. L., Chang, D. E. & Garcia de Abajo, F. J. Graphene plasmonics: a platform for strong light–matter interactions. Nano Lett. 11, 3370–3377 (2011).

    Article  ADS  Google Scholar 

  7. Woessner, A. et al. Highly confined low-loss plasmons in graphene-boron nitride heterostructures. Nat. Mater. 14, 421–425 (2015).

    Article  ADS  Google Scholar 

  8. Ni, G. X. et al. Fundamental limits to graphene plasmonics. Nature 557, 530–533 (2018).

    Article  ADS  Google Scholar 

  9. Iranzo, D. A. et al. Probing the ultimate plasmon confinement limits with a van der Waals heterostructure. Science 360, 291–295 (2018).

    Article  Google Scholar 

  10. Yao, W., MacDonald, A. H. & Niu, Q. Optical control of topological quantum transport in semiconductors. Phys. Rev. Lett. 99, 047401 (2007).

    Article  ADS  Google Scholar 

  11. Sie, E. J. et al. Valley-selective optical Stark effect in monolayer WS2. Nat. Mater. 14, 290–294 (2015).

    Article  ADS  Google Scholar 

  12. Basov, D. N., Averitt, R. D. & Hsieh, D. Towards properties on demand in quantum materials. Nat. Mater. 16, 1077–1088 (2017).

    Article  ADS  Google Scholar 

  13. Fausti, D. et al. Light-induced superconductivity in a stripe-ordered cuprate. Science 331, 189–191 (2011).

    Article  ADS  Google Scholar 

  14. Wang, Y. H., Steinberg, H., Jarillo-Herrero, P. & Gedik, N. Observation of Floquet–Bloch states on the surface of a topological insulator. Science 342, 453–457 (2013).

    Article  ADS  Google Scholar 

  15. Oka, T. & Aoki, H. Photovoltaic Hall effect in graphene. Phys. Rev. B 79, 081406 (2009).

    Article  ADS  Google Scholar 

  16. Kitagawa, T., Berg, E., Rudner, M. & Demler, E. Topological characterization of periodically driven quantum systems. Phys. Rev. B 82, 235114 (2010).

    Article  ADS  Google Scholar 

  17. Kitagawa, T., Oka, T., Brataas, A., Fu, L. & Demler, E. Transport properties of nonequilibrium systems under the application of light: photoinduced quantum Hall insulators without Landau levels. Phys. Rev. B 84, 235108 (2011).

    Article  ADS  Google Scholar 

  18. Lindner, N. H., Refael, G. & Galitski, V. Floquet topological insulator in semiconductor quantum wells. Nat. Phys. 7, 490–495 (2011).

    Article  Google Scholar 

  19. Gu, Z., Fertig, H. A., Arovas, D. P. & Auerbach, A. Floquet spectrum and transport through an irradiated graphene ribbon. Phys. Rev. Lett. 107, 216601 (2011).

    Article  ADS  Google Scholar 

  20. Usaj, G., Perez-Piskunow, P. M., Foa Torres, L. E. F. & Balseiro, C. A. Irradiated graphene as a tunable Floquet topological insulator. Phys. Rev. B 90, 115423 (2014).

    Article  ADS  Google Scholar 

  21. Yudin, D., Eriksson, O. & Katsnelson, M. I. Dynamics of quasiparticles in graphene under intense circularly polarized light. Phys. Rev. B 91, 075419 (2015).

    Article  ADS  Google Scholar 

  22. Grushin, A. G., Gómez-León, A. & Neupert, T. Floquet fractional Chern insulators. Phys. Rev. Lett. 112, 156801 (2014).

    Article  ADS  Google Scholar 

  23. Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).

    Article  ADS  Google Scholar 

  24. You, J.-S., Fang, S., Xu, S.-Y., Kaxiras, E. & Low, T. Berry curvature dipole current in the transition metal dichalcogenides family. Phys. Rev. B 98, 121109(R) (2018).

    Article  ADS  Google Scholar 

  25. Son, D. T. & Yamamoto, N. Berry curvature, triangle anomalies, and the chiral magnetic effect in Fermi liquids. Phys. Rev. Lett. 109, 181602 (2012).

    Article  ADS  Google Scholar 

  26. Son, D. T. & Spivak, B. Z. Chiral anomaly and classical negative magnetoresistance of Weyl metals. Phys. Rev. B 88, 104412 (2013).

    Article  ADS  Google Scholar 

  27. Song, J. C. W. & Rudner, M. S. Chiral plasmons without magnetic field. Proc. Natl Acad. Sci. USA 113, 4658–4663 (2016).

    Article  ADS  Google Scholar 

  28. Dykman, M. I. & Krivoglaz, M. A. Fluctuations in nonlinear systems near bifurcations corresponding to the appearance of new stable states. Physica 104A, 480–494 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  29. Dykman, M. I. Theory of optical polarization bistability. Sov. Phys. JETP 64, 927–933 (1986).

    Google Scholar 

  30. Vasyukov, D. et al. A scanning superconducting quantum interference device with single electron spin sensitivity. Nat. Nanotechnol. 8, 639–644 (2013).

    Article  ADS  Google Scholar 

  31. Degen, C. L. Scanning magnetic field microscope with a diamond single-spin sensor. Appl. Phys. Lett. 92, 243111 (2008).

    Article  ADS  Google Scholar 

  32. Xia, J., Beyersdorf, P. T., Fejer, M. M. & Kapitulnik, A. Modified Sagnac interferometer for high-sensitivity magneto-optic measurements at cryogenic temperatures. Appl. Phys. Lett. 89, 062508 (2006).

    Article  ADS  Google Scholar 

  33. Foster, M. S., Gurarie, V., Dzero, M. & Yuzbashyan, E. A. Quench-induced Floquet topological p-wave superfluids. Phys. Rev. Lett. 113, 076403 (2014).

    Article  ADS  Google Scholar 

  34. Alicea, J., Balents, L., Fisher, M. P. A., Paramekanti, A. & Radzihovsky, L. Transition to zero resistance in a two-dimensional electron gas driven with microwaves. Phys. Rev. B 71, 235322 (2005).

    Article  ADS  Google Scholar 

  35. Shirley, J. H. Solution of the Schrödinger equation with a Hamiltonian periodic in time. Phys. Rev. 138, B979–B987 (1965).

    Article  ADS  Google Scholar 

  36. Sambe, H. Steady states and quasienergies of a quantum mechanical system in an oscillating field. Phys. Rev. A 7, 2203–2213 (1973).

    Article  ADS  Google Scholar 

  37. Haldane, F. D. M. Berry curvature on the Fermi surface: anomalous Hall effect as a topological Fermi-liquid property. Phys. Rev. Lett. 93, 206602 (2004).

    Article  ADS  Google Scholar 

Download references


We thank D. Huse, M. Kats, M. Katsnelson, L. Levitov, R. Nandkishore, L. Radzihovsky and G. Refael for helpful discussions. M.S.R. gratefully acknowledges the support of the European Research Council under the European Union Horizon 2020 Research and Innovation Programme (grant agreement no. 678862), and the Villum Foundation. J.C.W.S. gratefully acknowledges the support of the Singapore National Research Foundation (NRF) under NRF fellowship award NRF-NRFF2016-05, and a start-up grant from the Nanyang Technological University.

Author information

Authors and Affiliations



M.S.R. and J.C.W.S. designed the research, performed the research and wrote the paper together.

Corresponding authors

Correspondence to Mark S. Rudner or Justin C. W. Song.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Additional theoretical details and refs. 1–15.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rudner, M.S., Song, J.C.W. Self-induced Berry flux and spontaneous non-equilibrium magnetism. Nat. Phys. 15, 1017–1021 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing