Skip to main content

Thank you for visiting nature.com. 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.

  • Article
  • Published:

Observation of Floquet–Bloch states in monolayer graphene

Nature Physics volume 21, pages 1100–1105 (2025)Cite this article

Subjects

Abstract

Floquet engineering enables the manipulation of quantum phases of matter through periodic driving. It has been implemented across different platforms, ranging from photonic systems to optical lattices of ultracold atoms. In solids, coherent light–matter interaction induced by periodic driving leads to hybridization of Bloch electrons with photons, resulting in the formation of replica bands known as Floquet–Bloch states. These states have been observed in several materials, and their properties have been linked to a range of predicted phase transitions. However, direct energy and momentum-resolved observation of these states remains limited to a few. Here we report the direct observation of Floquet–Bloch states in monolayer epitaxial graphene. By using time-resolved and angle-resolved photoemission spectroscopy with mid-infrared pump excitation, we detected replicas of the Dirac cone. The dependence of these replica bands on pump polarization shows that they originate from the scattering between Floquet–Bloch states and photon-dressed free-electron-like photoemission final states, known as Volkov states. Our method can potentially be used to directly observe Floquet–Bloch states at large momenta in other quantum materials.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to the full article PDF.

USD 39.95

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

Fig. 1: Generation of a replica band in graphene by means of 5 μm pump excitation.
Fig. 2: Evolution of photoemission intensity at constant energy as a function of pump-polarization angle θp.
Fig. 3: Intensity profiles and the angle of the maximum intensity (θk,max) as a function of pump-polarization angle (θp).

Similar content being viewed by others

Data availability

All the data in this study are available from the corresponding author upon reasonable request. Source data are provided with this paper.

References

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  3. Lindner, N. H., Bergman, D. L., Refael, G. & Galitski, V. Topological Floquet spectrum in three dimensions via a two-photon resonance. Phys. Rev. B 87, 235131 (2013).

    Article  ADS  Google Scholar 

  4. Mentink, J. H., Balzer, K. & Eckstein, M. Ultrafast and reversible control of the exchange interaction in Mott insulators. Nat. Commun. 6, 6708 (2015).

    Article  ADS  Google Scholar 

  5. Wang, R., Wang, B., Shen, R., Sheng, L. & Xing, D. Y. Floquet Weyl semimetal induced by off-resonant light. Europhys. Lett. 105, 17004 (2014).

    Article  ADS  Google Scholar 

  6. Ebihara, S., Fukushima, K. & Oka, T. Chiral pumping effect induced by rotating electric fields. Phys. Rev. B 93, 155107 (2016).

    Article  ADS  Google Scholar 

  7. Chan, C.-K., Oh, Y.-T., Han, J. H. & Lee, P. A. Type-II Weyl cone transitions in driven semimetals. Phys. Rev. B 94, 121106 (2016).

    Article  ADS  Google Scholar 

  8. Hübener, H., Sentef, M. A., De Giovannini, U., Kemper, A. F. & Rubio, A. Creating stable Floquet–Weyl semimetals by laser-driving of 3D Dirac materials. Nat. Commun. 8, 13940 (2017).

    Article  ADS  Google Scholar 

  9. Shin, D. et al. Phonon-driven spin-Floquet magneto-valleytronics in mos2. Nat. Commun. 9, 638 (2018).

    Article  ADS  Google Scholar 

  10. Topp, G. E. et al. Topological Floquet engineering of twisted bilayer graphene. Phys. Rev. Res. 1, 023031 (2019).

    Article  Google Scholar 

  11. Katz, O., Refael, G. & Lindner, N. H. Optically induced flat bands in twisted bilayer graphene. Phys. Rev. B 102, 155123 (2020).

    Article  ADS  Google Scholar 

  12. Rodriguez-Vega, M., Vogl, M. & Fiete, G. A. Low-frequency and Moiré–Floquet engineering: A review. Ann. Phys. 435, 168434 (2021).

    Article  Google Scholar 

  13. 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 

  14. Aeschlimann, S. et al. Survival of Floquet–Bloch states in the presence of scattering. Nano Lett. 21, 5028–5035 (2021).

    Article  ADS  Google Scholar 

  15. Shan, J.-Y. et al. Giant modulation of optical nonlinearity by Floquet engineering. Nature 600, 235–239 (2021).

    Article  ADS  Google Scholar 

  16. Zhou, S. et al. Pseudospin-selective Floquet band engineering in black phosphorus. Nature 614, 75–80 (2023).

    Article  ADS  Google Scholar 

  17. Zhou, S. et al. Floquet engineering of black Phosphorus upon below-gap pumping. Phys. Rev. Lett. 131, 116401 (2023).

    Article  ADS  Google Scholar 

  18. Zhang, X. et al. Light-induced electronic polarization in antiferromagnetic Cr2O3. Nat. Mater. 23, 790–795 (2024).

    Article  ADS  Google Scholar 

  19. McIver, J. W. et al. Light-induced anomalous Hall effect in graphene. Nat. Phys. 16, 38–41 (2020).

    Article  Google Scholar 

  20. Park, S. et al. Steady Floquet–Andreev states in graphene Josephson junctions. Nature 603, 421–426 (2022).

    Article  ADS  Google Scholar 

  21. Sentef, M. A. et al. Theory of Floquet band formation and local pseudospin textures in pump-probe photoemission of graphene. Nat. Commun. 6, 7047 (2015).

    Article  ADS  Google Scholar 

  22. Hübener, H., De Giovannini, U. & Rubio, A. Phonon driven Floquet matter. Nano Lett. 18, 1535–1542 (2018).

    Article  ADS  Google Scholar 

  23. Schüler, M. et al. Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials. Sci. Adv. 6, eaay2730 (2020).

    Article  ADS  Google Scholar 

  24. Schüler, M. et al. How circular dichroism in time-and angle-resolved photoemission can be used to spectroscopically detect transient topological states in graphene. Phys. Rev. X 10, 041013 (2020).

    Google Scholar 

  25. Sato, S. A. et al. Floquet states in dissipative open quantum systems. J. Phys. B: At., Mol. Opt. Phys. 53, 225601 (2020).

    Article  ADS  Google Scholar 

  26. Park, S. T. Interference in Floquet–Volkov transitions. Phys. Rev. A 90, 013420 (2014).

    Article  ADS  Google Scholar 

  27. Hwang, C. et al. Direct measurement of quantum phases in graphene via photoemission spectroscopy. Phys. Rev. B 84, 125422 (2011).

    Article  ADS  Google Scholar 

  28. Mahmood, F. et al. Selective scattering between Floquet–Bloch and Volkov states in a topological insulator. Nat. Phys. 12, 306–311 (2016).

    Article  Google Scholar 

  29. Syzranov, S. V., Fistul, M. V. & Efetov, K. B. Effect of radiation on transport in graphene. Phys. Rev. B 78, 045407 (2008).

    Article  ADS  Google Scholar 

  30. López-Rodríguez, F. J. & Naumis, G. G. Analytic solution for electrons and holes in graphene under electromagnetic waves: gap appearance and nonlinear effects. Phys. Rev. B 78, 201406 (2008).

    Article  ADS  Google Scholar 

  31. López-Rodríguez, F. J. & Naumis, G. G. Graphene under perpendicular incidence of electromagnetic waves: gaps and band structure. Philos. Mag. 90, 2977–2988 (2010).

    Article  Google Scholar 

  32. Zhou, Y. & Wu, M. W. Optical response of graphene under intense terahertz fields. Phys. Rev. B 83, 245436 (2011).

    Article  ADS  Google Scholar 

  33. Calvo, H. L., Pastawski, H. M., Roche, S. & Foa Torres, L. E. F. Tuning laser-induced band gaps in graphene. Appl. Phys. Lett. 98, 232103 (2011).

    Article  ADS  Google Scholar 

  34. Fregoso, B. M., Wang, Y. H., Gedik, N. & Galitski, V. Driven electronic states at the surface of a topological insulator. Phys. Rev. B 88, 155129 (2013).

    Article  ADS  Google Scholar 

  35. Ito, S. et al. Build-up and dephasing of Floquet–Bloch bands on subcycle timescales. Nature 616, 696–701 (2023).

    Article  ADS  Google Scholar 

  36. Keunecke, M. et al. Electromagnetic dressing of the electron energy spectrum of Au(111) at high momenta. Phys. Rev. B 102, 161403 (2020).

    Article  ADS  Google Scholar 

  37. Emtsev, K. V. et al. Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide. Nat. Mater. 8, 203–207 (2009).

    Article  ADS  Google Scholar 

  38. Sie, E. J., Rohwer, T., Lee, C. & Gedik, N. Time-resolved XUV ARPES with tunable 24–33 eV laser pulses at 30 meV resolution. Nat. Commun. 10, 3535 (2019).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We are grateful to M. Sentef, M. Eckstein, P. Werner, H. Ning and B. Ilyas for insightful discussions. We thank C. John for the detailed discussions regarding the sample, and also acknowledge Graphensic AB (Naveen Shetty) for providing sample characterization data. The work at MIT (D.C., M.M., D.A., B.L., Y.S. and N.G.) was supported by the US Department of Energy, BES DMSE (data acquisition, analysis and manuscript writing) and Gordon and Betty Moore Foundation’s EPiQS Initiative grant no. GBMF9459 (instrumentation). M.M. acknowledges the support from JST PRESTO (grant no. JPMJPR23HA). U.D.G., H.H. and A.R. acknowledge the support from HORIZON-MCSA-2022-DN ‘TIMES’ (project no. 101118915).

Author information

Author notes

  1. These authors contributed equally: Dongsung Choi, Masataka Mogi.

Authors and Affiliations

  1. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA

    Dongsung Choi

  2. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Masataka Mogi, Doron Azoury, Baiqing Lv, Yifan Su & Nuh Gedik

  3. Department of Applied Physics, University of Tokyo, Tokyo, Japan

    Masataka Mogi

  4. Max Planck Institute for the Structure and Dynamics of Matter and Center for Free Electron Laser Science, Hamburg, Germany

    Umberto De Giovannini, Hannes Hübener & Angel Rubio

  5. Dipartimento di Fisica e Chimica - Emilio Segrè, Università degli Studi di Palermo, Palermo, Italy

    Umberto De Giovannini

  6. Tsung-Dao Lee Institute, School of Physics and Astronomy, and Zhangjiang Institute for Advanced Study, Shanghai Jiao Tong University, Shanghai, China

    Baiqing Lv

  7. Center for Computational Quantum Physics (CCQ), The Flatiron Institute, New York, NY, USA

    Angel Rubio

Authors
  1. Dongsung Choi
    View author publications

    Search author on:PubMed Google Scholar

  2. Masataka Mogi
    View author publications

    Search author on:PubMed Google Scholar

  3. Umberto De Giovannini
    View author publications

    Search author on:PubMed Google Scholar

  4. Doron Azoury
    View author publications

    Search author on:PubMed Google Scholar

  5. Baiqing Lv
    View author publications

    Search author on:PubMed Google Scholar

  6. Yifan Su
    View author publications

    Search author on:PubMed Google Scholar

  7. Hannes Hübener
    View author publications

    Search author on:PubMed Google Scholar

  8. Angel Rubio
    View author publications

    Search author on:PubMed Google Scholar

  9. Nuh Gedik
    View author publications

    Search author on:PubMed Google Scholar

Contributions

N.G. conceived the project. D.C. and M.M. conducted trARPES experiments and simulations. D.C., M.M., U.D.G, H.H., A.R. and N.G. engaged in discussions regarding the results, and analysed and interpreted them. D.C., M.M., D.A., B.L. and Y.S. carried out maintenance of the trARPES set-up and discussions on the results. D.C., M.M., U.D.G., H.H. and N.G. wrote the paper. All the authors contributed to the final version of the paper. N.G. supervised the entire project.

Corresponding author

Correspondence to Nuh Gedik.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Julien Madéo and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Discussion, Figs. 1–14 and Tables 1–2.

Source data

Source Data Fig. 1

Source data for Fig. 1.

Source Data Fig. 2

Source data for Fig. 2.

Source Data Fig. 3

Source data for Fig. 3.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Choi, D., Mogi, M., De Giovannini, U. et al. Observation of Floquet–Bloch states in monolayer graphene. Nat. Phys. 21, 1100–1105 (2025). https://doi.org/10.1038/s41567-025-02888-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Version of record:

  • Issue date:

  • DOI: https://doi.org/10.1038/s41567-025-02888-8

This article is cited by

Search

Advanced search

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