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Observation of Floquet-induced gap in graphene

Nature Materials (2026)Cite this article

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Abstract

Floquet engineering provides a powerful pathway for creating non-equilibrium phases of matter with tailored electronic structures and properties through time-periodic driving. As the original theoretical prototype, graphene established the framework in which the Floquet topological insulator with the light-induced anomalous Hall effect was proposed. However, the defining spectroscopic signature of Floquet engineering in graphene, light-induced hybridization (avoided-crossing) gap at Floquet band crossings, has remained experimentally elusive. Here we report the direct observation of a Floquet-induced hybridization gap in monolayer graphene under resonant driving by a strong light field. Time- and angle-resolved photoemission spectroscopy reveals a gap opening at Floquet band crossings, accompanied by coherent Floquet sidebands. The gap exhibits pronounced momentum anisotropy, featuring two Dirac nodes protected by spatiotemporal symmetry and tunable by light polarization. These results provide the long-sought experimental demonstration of Floquet band engineering in graphene, opening up opportunities for light-field-engineered quantum phases in graphene and related materials.

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Fig. 1: Schematic of Bloch states, Floquet–Bloch states and gap opening.
Fig. 2: Experimental observation of a light-induced gap in monolayer graphene.
Fig. 3: Evidence of Floquet-induced gap from time-dependent measurements.
Fig. 4: Momentum anisotropy of the Floquet-induced gap and the emergence of spatiotemporal-symmetry-protected Dirac nodes.

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All data supporting the results of this study are available within the Article. Additional data are available from the corresponding author upon request. Source data are provided with this paper.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (grant numbers 12421004 and 12234011), Tsinghua University Initiative Scientific Research Program (grant number 20251080106), National Key R&D Program of China (grant number 2021YFA1400100), the National Natural Science Foundation of China (grant numbers 12327805, 52388201) and New Cornerstone Science Foundation through the XPLORER PRIZE.

Author information

Author notes

  1. These authors contributed equally: Fei Wang, Xuanxi Cai.

Authors and Affiliations

  1. Department of Physics, Tsinghua University, Beijing, People’s Republic of China

    Fei Wang, Xuanxi Cai, Xiao Tang, Jinxi Lu, Wanying Chen, Tianshuang Sheng, Runfa Feng, Haoyuan Zhong, Hongyun Zhang, Pu Yu & Shuyun Zhou

  2. State Key Laboratory of Low-Dimensional Quantum Physics, Tsinghua University, Beijing, People’s Republic of China

    Fei Wang, Xuanxi Cai, Xiao Tang, Jinxi Lu, Wanying Chen, Tianshuang Sheng, Runfa Feng, Haoyuan Zhong, Hongyun Zhang, Pu Yu & Shuyun Zhou

  3. Frontier Science Center for Quantum Information, Beijing, People’s Republic of China

    Pu Yu & Shuyun Zhou

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Contributions

S.Z. conceived the research project. F.W. and X.C. performed the TrARPES measurements and analysed the data. R.F., X.T. and W.C. prepared the samples. X.C. and H. Zhong developed and optimized the HHG light source. F.W., X.C., J.L., T.S., H. Zhong, H. Zhang and P.Y. discussed the results. F.W., X.C. and S.Z. wrote the manuscript and all authors commented on the manuscript.

Corresponding author

Correspondence to Shuyun Zhou.

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Nature Materials thanks Stefan Mathias, Michael Sentef and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data

Extended Data Fig. 1 Calibration of the Fermi energy EF and negligible pump-induced band broadening at high binding energy.

a, Dispersion image measured before pumping. b, Extracted EDCs within the region marked by the red box and fitting using Fermi-Dirac distribution (red curve), from which EF is extracted. c, Dispersion image measured upon pumping. d, EDCs cut through black box at different delay times with fitting peaks appended.

Extended Data Fig. 2 Schematic illustration of the experimental geometry.

a, Schematic for the experimental geometry. The pump is incident on the monolayer graphene sample at near normal angle, therefore, electric fields for both p-pol. and s-pol. are dominantly confined within the sample plane, and there is negligible out-of-plane light field. b, Schematic illustration of the polarization with respect to the Dirac cone. The light field is along the kx (ky) direction for p-pol. (s-pol.) pump.

Extended Data Fig. 3 Dependence of Floquet-induced hybridization gap on the pump fluence.

a-e, Dispersion images measured before pumping (a) and at Δt = 0 fs upon driving at 490 meV with different pump fluence (b-e). f-j, EDCs for data shown in (a-e) at momentum of resonant points. k, Extracted Floquet-induced hybridization gap as a function of the pump fluence. Data in k are presented as fitting values at different pump fluence, with error bars representing the combination of statistical fitting error and estimated systematic contribution.

Extended Data Fig. 4 Floquet band engineering upon driving at different pump photon energies.

a, A schematic for the resonance points upon driving with different pump photon energies. b, TrARPES dispersion images measured at Δt = -300 fs. c, TrARPES dispersion images measured at Δt = 0 fs upon 490 meV pumping. The pump polarization is along the kx direction and the pump fluence is 4.1 mJ/cm2. d, TrARPES dispersion images measured at Δt = 0 fs upon 600 meV pumping. The pump polarization is along the kx direction and the pump fluence is 6.4 mJ/cm2. e, EDCs for data shown in (b-d) at momentum resonance point.

Extended Data Fig. 5 Floquet band engineering upon driving at different pump polarizations.

a, A schematic of the experimental geometry for the p-pol. and s-pol. pumps. b-d, TrARPES dispersion images measured at Δt = -300 fs (b) and Δt = 0 fs with p-pol. pump (c) and s-pol. pump (d). The pump photon energy is 490 meV and the pump fluence is 4.1 mJ/cm2. e, EDCs for data shown in (b-d) at momentum resonance points with fitting peaks appended.

Extended Data Fig. 6 Fitting residuals to show the quality of the fitting.

a, Dispersion image at Δt = 0, with the momentum integration window marked by lines. b, EDCs obtained by integrating over the indicated momentum range. c, Residuals from the EDC fitting, shown on the same scale as (b).

Extended Data Fig. 7 Variation of the extracted gap by using different choices of integration momentum windows.

a-c, Dispersion images, where dashed boxes indicate the momentum integration windows used for EDCs shown in (d-f). The values are also labeled on the top of each panel. d-f, Extracted gap values obtained from EDC fittings.

Extended Data Fig. 8 TrARPES dispersion image and simulation.

a, Dispersion image at Δt = 0 with simulated dispersion overplotted. b, Simulated TrARPES spectrum upon pumping.

Extended Data Table 1 Comparison of our experimental parameters with those in the literature
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Wang, F., Cai, X., Tang, X. et al. Observation of Floquet-induced gap in graphene. Nat. Mater. (2026). https://doi.org/10.1038/s41563-026-02549-y

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