Abstract

Superlattices have attracted great interest because their use may make it possible to modify the spectra of two-dimensional electron systems and, ultimately, create materials with tailored electronic properties1,2,3,4,5,6,7,8. In previous studies (see, for example, refs 1, 2, 3, 4, 5, 6, 7, 8), it proved difficult to realize superlattices with short periodicities and weak disorder, and most of their observed features could be explained in terms of cyclotron orbits commensurate with the superlattice1,2,3,4. Evidence for the formation of superlattice minibands (forming a fractal spectrum known as Hofstadter’s butterfly9) has been limited to the observation of new low-field oscillations5 and an internal structure within Landau levels6,7,8. Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate’s moiré potential10,11,12 acts as a superlattice and leads to profound changes in the graphene’s electronic spectrum. Second-generation Dirac points13,14,15,16,17,18,19,20,21,22 appear as pronounced peaks in resistivity, accompanied by reversal of the Hall effect. The latter indicates that the effective sign of the charge carriers changes within graphene’s conduction and valence bands. Strong magnetic fields lead to Zak-type cloning23 of the third generation of Dirac points, which are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices such as this one provide a way of studying the rich physics expected in incommensurable quantum systems7,8,9,22,23,24 and illustrate the possibility of controllably modifying the electronic spectra of two-dimensional atomic crystals by varying their crystallographic alignment within van der Waals heterostuctures25.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    , , & Magnetoresistance oscillations in a two-dimensional electron gas induced by a submicrometer periodic potential. Europhys. Lett. 8, 179–184 (1989)

  2. 2.

    et al. Electron pinball and commensurate orbits in a periodic array of scatterers. Phys. Rev. Lett. 66, 2790–2793 (1991)

  3. 3.

    & Theory of magnetotransport in two-dimensional electron systems subjected to weak two-dimensional superlattice potentials. Phys. Rev. B 46, 12606–12626 (1992)

  4. 4.

    Quantum magnetotransport in lateral surface superlattices. Prog. Quantum Electron. 16, 251–317 (1992)

  5. 5.

    et al. Fermiology of two-dimensional lateral superlattices. Phys. Rev. Lett. 83, 2234–2237 (1999)

  6. 6.

    , , & Internal structure of a Landau band induced by a lateral superlattice: a glimpse of Hofstadter’s butterfly. Europhys. Lett. 33, 683–688 (1996)

  7. 7.

    et al. Evidence of Hofstadter’s fractal energy spectrum in the quantized Hall conductance. Phys. Rev. Lett. 86, 147–150 (2001)

  8. 8.

    et al. Detection of a Landau band-coupling-induced rearrangement of the Hofstadter butterfly. Phys. Rev. Lett. 92, 256801 (2004)

  9. 9.

    Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields. Phys. Rev. B 14, 2239–2249 (1976)

  10. 10.

    et al. Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nature Mater. 10, 282–285 (2011)

  11. 11.

    et al. Local electronic properties of graphene on a BN substrate via scanning tunneling microscopy. Nano Lett. 11, 2291–2295 (2011)

  12. 12.

    et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nature Phys. 8, 382–386 (2012)

  13. 13.

    , , , & New generation of massless Dirac fermions in graphene under external periodic potentials. Phys. Rev. Lett. 101, 126804 (2008)

  14. 14.

    , , & Transport and localization in periodic and disordered graphene superlattices. Phys. Rev. B 79, 075123 (2009)

  15. 15.

    & Tunable band gap in graphene with a noncentrosymmetric superlattice potential. Phys. Rev. B 79, 205435 (2009)

  16. 16.

    , & Extra Dirac points in the energy spectrum for superlattices on single-layer graphene. Phys. Rev. B 81, 075438 (2010)

  17. 17.

    , , & Transport in superlattices on single-layer graphene. Phys. Rev. B 83, 195434 (2011)

  18. 18.

    , & Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes. Phys. Rev. B 85, 195404 (2012)

  19. 19.

    , & Graphene on incommensurate substrates: trigonal warping and emerging Dirac cone replicas with halved group velocity. Phys. Rev. B 86, 081405 (2012)

  20. 20.

    , , & Substrate-induced chiral states in graphene. Phys. Rev. B 86, 085451 (2012)

  21. 21.

    , & Zero energy modes and gate-tunable gap in graphene on hexagonal boron nitride. Phys. Rev. B 86, 115415 (2012)

  22. 22.

    , , , & Generic miniband structure of graphene on a hexagonal substrate. Preprint at (2012)

  23. 23.

    Magnetic translation group. Phys. Rev. 134, A1602–A1606 (1964)

  24. 24.

    & Moire butterflies. Phys. Rev. B 84, 035440 (2011)

  25. 25.

    et al. Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures and superlattices. Nature Mater. 11, 764–767 (2012)

  26. 26.

    , & Scanning tunneling spectroscopy of graphene on graphite. Phys. Rev. Lett. 102, 176804 (2009)

  27. 27.

    et al. Micrometer-scale ballistic transport in encapsulated graphene at room temperature. Nano Lett. 11, 2396–2399 (2011)

  28. 28.

    et al. Boron nitride substrates for high-quality graphene electronics. Nature Nanotechnol. 5, 722–726 (2010)

  29. 29.

    et al. How close can one approach the Dirac point in graphene experimentally? Nano Lett. 12, 4629–4634 (2012)

  30. 30.

    & The rise of graphene. Nature Mater. 6, 183–191 (2007)

Download references

Acknowledgements

We thank D. Weiss, A. MacDonald and F. Peeters for discussions. This work was supported by the European Research Council, the Körber Foundation, the Office of Naval Research, the Air Force Office of Scientific Research and the Royal Society.

Author information

Affiliations

  1. School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, UK

    • L. A. Ponomarenko
    • , G. L. Yu
    • , D. C. Elias
    • , A. Mishchenko
    • , A. S. Mayorov
    • , C. R. Woods
    • , I. V. Grigorieva
    • , K. S. Novoselov
    •  & A. K. Geim
  2. Centre for Mesoscience and Nanotechnology, University of Manchester, Manchester M13 9PL, UK

    • R. V. Gorbachev
    • , R. Jalil
    •  & A. K. Geim
  3. Physics Department, Lancaster University, Lancaster LA1 4YB, UK

    • A. A. Patel
    • , J. R. Wallbank
    • , M. Mucha-Kruczynski
    •  & V. I. Fal’ko
  4. Laboratoire National des Champs Magnétiques Intenses, CNRS-UJF-UPS-INSA, F-38042 Grenoble, France

    • B. A. Piot
    •  & M. Potemski
  5. Instituto de Ciencia de Materiales de Madrid, Sor Juana Inés de la Cruz 3, Madrid 28049, Spain

    • F. Guinea

Authors

  1. Search for L. A. Ponomarenko in:

  2. Search for R. V. Gorbachev in:

  3. Search for G. L. Yu in:

  4. Search for D. C. Elias in:

  5. Search for R. Jalil in:

  6. Search for A. A. Patel in:

  7. Search for A. Mishchenko in:

  8. Search for A. S. Mayorov in:

  9. Search for C. R. Woods in:

  10. Search for J. R. Wallbank in:

  11. Search for M. Mucha-Kruczynski in:

  12. Search for B. A. Piot in:

  13. Search for M. Potemski in:

  14. Search for I. V. Grigorieva in:

  15. Search for K. S. Novoselov in:

  16. Search for F. Guinea in:

  17. Search for V. I. Fal’ko in:

  18. Search for A. K. Geim in:

Contributions

R.V.G., L.A.P. and A.K.G. designed the project. R.V.G. and R.J. made the graphene devices. G.L.Y., D.C.E., L.A.P. and A.S.M. carried out the measurements. K.S.N., A.M., C.R.W., B.A.P., M.P. and I.V.G. provided experimental support. V.I.F., A.A.P., J.R.W., M.M.-K., A.K.G. and F.G. developed the theory. A.K.G. and V.I.F. wrote the manuscript with input from I.V.G., R.V.G., L.A.P., K.S.N. and F.G. All authors participated in discussions.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to R. V. Gorbachev.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    This file contains Supplementary Text, Supplementary Figures 1-10 and Supplementary References.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nature12187

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.