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Direct observation of massless excitons and linear exciton dispersion

Nature Physics (2026)Cite this article

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Abstract

Excitons—elementary excitations formed by bound electron–hole pairs—govern the optical properties and excited-state dynamics of materials. In two dimensions, excitons are theoretically predicted to have a linear energy–momentum relation with a non-analytic discontinuity in the long wavelength limit, which mimics the dispersion of a photon. This results in an exciton with a dispersion resembling a massless particle, despite it being a composite boson composed of massive constituents. However, direct experimental observation of massless excitons has not been achieved. Here we experimentally demonstrate the linear exciton dispersion in free-standing monolayer hBN using momentum-resolved electron energy-loss spectroscopy. The observation is consistent with our theoretical prediction based on ab initio many-body perturbation theory. Additionally, we identify the lowest dipole-allowed transition in monolayer hBN to be at 6.6 eV, which illuminates a long-standing debate about the bandgap of monolayer hBN. These findings provide critical insights into two-dimensional excitonic physics and show potential pathways for exciton-mediated superconductivity, Bose–Einstein condensation and high-efficiency optoelectronic applications.

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Fig. 1: Q-EELS spectrum for free-standing monolayer hBN.
Fig. 2: Electronic and excitonic band structures of monolayer hBN from first-principles calculations.
Fig. 3: Experimental and theoretical Q-EELS spectra.

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Data availability

The theoretical and experimental data supporting the findings of this study are available via Figshare at https://doi.org/10.6084/m9.figshare.30960242 (ref. 56). Other data are available from the corresponding authors upon reasonable request. Source data are provided with this paper.

Code availability

Code associated with exciton–phonon calculations are available from the corresponding authors by request. All other code is part of the open source QUANTUM ESPRESSO47,48 and BerkeleyGW24 software packages.

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Acknowledgements

This work (L.Y.L., J.W., B.H. and D.Y.Q.) was primarily supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (Early Career Award No. DE-SC0021965). Excited-state code development was supported by the Center for Computational Study of Excited-State Phenomena in Energy Materials at the Lawrence Berkeley National Laboratory, funded by the US DOE, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division (Contract No. DE-C02-05CH11231 to D.Y.Q.). The calculations used resources of the National Energy Research Scientific Computing, a DOE Office of Science User Facility operated under Contract No. DE-AC02-05CH11231, and the Texas Advanced Computing Center at the University of Texas at Austin. L.Y.L. acknowledges the support of the Enrico Fermi Fellowships (https://cstq.org/eff/) led by the Center for Spacetime and the Quantum and the support of the John Templeton Foundation (Grant No. 63132). The opinions expressed in this publication are those of the authors and do not necessarily reflect the views of the John Templeton Foundation or those of the Center for Spacetime and the Quantum. Experimental Q-EELS research conducted as part of a user project was supported by the Center for Nanophase Materials Sciences, which is a US DOE, Office of Science User Facility at Oak Ridge National Laboratory. This research was conducted, in part, using instrumentation within ORNL’s Materials Characterization Core provided by UT-Battelle, LLC (Contract No. DE-AC05-00OR22725 with the US DOE). We acknowledge helpful comments from E. Hoglund, T. Wang, Y. He, D. Ma and D. Muller.

Author information

Authors and Affiliations

  1. Department of Applied Physics, Yale University, New Haven, CT, USA

    Luna Y. Liu & Cong Su

  2. Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA

    Steffi Y. Woo

  3. Department of Materials Science, Yale University, New Haven, CT, USA

    Jinyuan Wu, Bowen Hou, Cong Su & Diana Y. Qiu

  4. Energy Science Institute, Yale University, West Haven, CT, USA

    Diana Y. Qiu

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Contributions

D.Y.Q. and C.S. conceived the project. L.Y.L. prepared the samples. S.Y.W. designed the experiment and performed the measurements. L.Y.L. performed the experimental data analysis and first-principles calculations. S.Y.W. and C.S. supervised the analysis of the experimental data. D.Y.Q. supervised the calculations and the theoretical analyses. J.W. and B.H. contributed to the theoretical analysis and assisted with preparing figures. L.Y.L. wrote the initial draft of the paper; all authors reviewed and revised the paper. D.Y.Q. and C.S. supervised the project and acquired funding.

Corresponding authors

Correspondence to Steffi Y. Woo, Cong Su or Diana Y. Qiu.

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

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Supplementary Figs. 1–11, Discussion and Tables 1 and 2.

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Data for plotting the QP band structure, exciton band structure and exciton wavefunction.

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Theoretical and experimental data for plotting the EELS figures.

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Liu, L.Y., Woo, S.Y., Wu, J. et al. Direct observation of massless excitons and linear exciton dispersion. Nat. Phys. (2026). https://doi.org/10.1038/s41567-026-03193-8

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