Atoms start behaving as waves rather than classical particles if confined in spaces commensurate with their de Broglie wavelength. At room temperature this length is only about one ångström even for the lightest atom, hydrogen. This restricts quantum-confinement phenomena for atomic species to the realm of very low temperatures1,2,3,4,5. Here, we show that van der Waals gaps between atomic planes of layered crystals provide ångström-size channels that make quantum confinement of protons apparent even at room temperature. Our transport measurements show that thermal protons experience a notably higher barrier than deuterons when entering van der Waals gaps in hexagonal boron nitride and molybdenum disulfide. This is attributed to the difference in the de Broglie wavelengths of the isotopes. Once inside the crystals, transport of both isotopes can be described by classical diffusion, albeit with unexpectedly fast rates comparable to that of protons in water. The demonstrated ångström-size channels can be exploited for further studies of atomistic quantum confinement and, if the technology can be scaled up, for sieving hydrogen isotopes.

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  1. 1.

    Cronin, A. D., Schmiedmayer, J. & Pritchard, D. E. Optics and interferometry with atoms and molecules. Rev. Mod. Phys. 81, 1051–1129 (2009).

  2. 2.

    Davis, K. B. et al. Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995).

  3. 3.

    Bradley, C. C., Sackett, C. A., Tollett, J. J. & Hulet, R. G. Evidence of Bose-Einstein condensation in an atomic gas with attractive interactions. Phys. Rev. Lett. 75, 1687–1690 (1995).

  4. 4.

    Beenakker, J. J. M., Borman, V. D. & Krylov, S. Y. Molecular transport in subnanometer pores: zero-point energy, reduced dimensionality and quantum sieving. Chem. Phys. Lett. 232, 379–382 (1995).

  5. 5.

    Cai, J., Xing, Y. & Zhao, X. Quantum sieving: feasibility and challenges for the separation of hydrogen isotopes in nanoporous materials. RSC Adv. 2, 8579 (2012).

  6. 6.

    Oh, H., Savchenko, I., Mavrandonakis, A., Heine, T. & Hirscher, M. Highly effective hydrogen isotope separation in nanoporous metal-organic frameworks with open metal sites: direct measurement and theoretical analysis. ACS Nano 8, 761–770 (2014).

  7. 7.

    Tanaka, H., Kanoh, H., Yudasaka, M., Iijima, S. & Kaneko, K. Quantum effects on hydrogen isotope adsorption on single-wall carbon nanohorns. J. Am. Chem. Soc. 127, 7511–7516 (2005).

  8. 8.

    Chen, B. et al. Surface interactions and quantum kinetic molecular sieving for H2 and D2 adsorption on a mixed metal−organic framework material. J. Am. Chem. Soc. 130, 6411–6423 (2008).

  9. 9.

    Chu, X. Z. et al. Adsorption of hydrogen isotopes on micro- and mesoporous adsorbents with orderly structure. J. Phys. Chem. B 110, 22596–22600 (2006).

  10. 10.

    Nguyen, T. X., Jobic, H. & Bhatia, S. K. Microscopic observation of kinetic molecular sieving of hydrogen isotopes in a nanoporous material. Phys. Rev. Lett. 105, 1–4 (2010).

  11. 11.

    Zhao, X., Villar-Rodil, S., Fletcher, A. J. & Thomas, K. M. Kinetic isotope effect for H2 and D2 quantum molecular sieving in adsorption/desorption on porous carbon materials. J. Phys. Chem. B 110, 9947–9955 (2006).

  12. 12.

    Wolfsberg, M., Van Hook, W. A., Paneth, P. & Rebelo, L. P. N. Isotope Effects in the Chemical, Geological and Biosciences (Springer, Dordrecht, 2010).

  13. 13.

    Levy, F. Intercalated Layered Materials (D. Reidel, Dordrecht, 1979).

  14. 14.

    Elman, B. S. et al. Channeling studies in graphite. J. Appl. Phys. 56, 2114–2119 (1984).

  15. 15.

    Hamilton, G. F. & Quinton, A. R. The observation of proton channeling in mica. Phys. Lett. 22, 312–313 (1966).

  16. 16.

    Devanathan, M. A. V. & Stachurski, Z. The adsorption and diffusion of electrolytic hydrogen in palladium. Proc. R. Soc. A 270, 90–102 (1962).

  17. 17.

    Schuldiner, S., Castellan, G. W. & Hoare, J. P. Electrochemical behavior of the palladium-hydrogen system. I. Potential-determining mechanisms. J. Chem. Phys. 28, 16 (1958).

  18. 18.

    Mauritz, K. & Moore, R. State of understanding of Nafion. Chem. Rev. 104, 4535–4585 (2004).

  19. 19.

    Burch, B. Y. R. Theoretical aspects of the absorption of hydrogen by palladium and its alloys. Part 1. A reassessment and comparison of the various proton models. Trans. Faraday Soc. 66, 736–748 (1970).

  20. 20.

    Ebisuzaki, Y. & Keeffe, M. O. The solubility of hydrogen in transition metals and alloys. Prog. Solid State Chem. 4, 187–211 (1967).

  21. 21.

    Hu, S. et al. Proton transport through one-atom-thick crystals. Nature 516, 227–230 (2014).

  22. 22.

    Lozada-Hidalgo, M. et al. Sieving hydrogen isotopes through two-dimensional crystals. Science 351, 68–70 (2016).

  23. 23.

    Hornekær, L. et al. Clustering of chemisorbed H(D) atoms on the graphite (0001) surface due to preferential sticking. Phys. Rev. Lett. 97, 186102 (2006).

  24. 24.

    Herrero, C. P. & Ramírez, R. Diffusion of hydrogen in graphite: a molecular dynamics simulation. J. Phys. D 43, 255402 (2010).

  25. 25.

    Keong Koh, E. W., Chiu, C. H., Lim, Y. K., Zhang, Y. W. & Pan, H. Hydrogen adsorption on and diffusion through MoS2 monolayer: First-principles study. Int. J. Hydrog. Energy 37, 14323–14328 (2012).

  26. 26.

    Persson, K. et al. Lithium diffusion in graphitic carbon. J. Phys. Chem. Lett. 1, 1176–1180 (2010).

  27. 27.

    Cussler, E. L. Diffusion: Mass Transfer in Fluid Systems (Cambridge Univ. Press, New York, 1984).

  28. 28.

    Flanagan, T. B. & Oates, W. A. The palladium-hydrogen system. Annu. Rev. Mater. Sci. 21, 269–304 (1991).

  29. 29.

    Ke, X. & Kramer, G. J. Absorption and diffusion of hydrogen in palladium-silver alloys by density functional theory. Phys. Rev. B 66, 184304 (2002).

  30. 30.

    Marx, D. Proton transfer 200 years after Von Grotthuss: Insights from ab initio simulations. ChemPhysChem 7, 1849–1870 (2006).

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The authors acknowledge support from the Lloyd’s Register Foundation, EPSRC - EP/N010345/1, the European Research Council ARTIMATTER project - ERC-2012-ADG and from Graphene Flagship. M.L.-H. acknowledges a Leverhulme Early Career Fellowship.

Author information


  1. National Graphene Institute, The University of Manchester, Manchester, UK

    • S. Hu
    • , M. Neek-Amal
    • , A. K. Geim
    •  & M. Lozada-Hidalgo
  2. School of Physics and Astronomy, The University of Manchester, Manchester, UK

    • K. Gopinadhan
    • , I. V. Grigorieva
    • , A. K. Geim
    •  & M. Lozada-Hidalgo
  3. School of Materials, The University of Manchester, Manchester, UK

    • A. Rakowski
    •  & S. J. Haigh
  4. Departement Fysica, Universiteit Antwerpen, Antwerpen, Belgium

    • M. Neek-Amal
    •  & F. M. Peeters
  5. Department of Physics, Shahid Rajaee Teacher Training University, Tehran, Iran

    • M. Neek-Amal
  6. Wilhelm-Ostwald-Institut für Physikalische und Theoretische Chemie, Universität Leipzig, Leipzig, Germany

    • T. Heine


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A.K.G. designed the project and directed it with help of S.H. and M.L.-H. S.H. fabricated devices, K.G. performed transport measurements. M.L.-H. and S.H. carried out data analyses. A.R. and S.J.H. performed TEM and SEM measurements. F.M.P., M.N.-A. and T.H. provided theoretical support. M.L.-H., I.V.G., S.H. and A.K.G. wrote the manuscript. All co-authors took part in discussing results.

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The authors declare no competing interests.

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Correspondence to S. Hu or A. K. Geim or M. Lozada-Hidalgo.

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    Supplementary Text and Supplementary Figures 1–3.

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