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Cloning of Dirac fermions in graphene superlattices

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.

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Figure 1: Transport properties of Dirac fermions in moiré superlattices.
Figure 2: Quantization in graphene superlattices.
Figure 3: Zak-type cloning of third-generation Dirac points.

References

  1. Weiss, D., Klitzing, K. V., Ploog, K. & Weimann, G. Magnetoresistance oscillations in a two-dimensional electron gas induced by a submicrometer periodic potential. Europhys. Lett. 8, 179–184 (1989)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  6. Schlösser, T., Ensslin, K., Kotthaus, J. P. & Holland, M. Internal structure of a Landau band induced by a lateral superlattice: a glimpse of Hofstadter’s butterfly. Europhys. Lett. 33, 683–688 (1996)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  13. Park, C. H., Yang, L., Son, Y. W., Cohen, M. L. & Louie, S. G. New generation of massless Dirac fermions in graphene under external periodic potentials. Phys. Rev. Lett. 101, 126804 (2008)

    ADS  Article  Google Scholar 

  14. Bliokh, Y. P., Freilikher, V., Savel’ev, S. & Nori, F. Transport and localization in periodic and disordered graphene superlattices. Phys. Rev. B 79, 075123 (2009)

    ADS  Article  Google Scholar 

  15. Tiwari, R. P. & Stroud, D. Tunable band gap in graphene with a noncentrosymmetric superlattice potential. Phys. Rev. B 79, 205435 (2009)

    ADS  Article  Google Scholar 

  16. Barbier, M., Vasilopoulos, P. & Peeters, F. M. Extra Dirac points in the energy spectrum for superlattices on single-layer graphene. Phys. Rev. B 81, 075438 (2010)

    ADS  Article  Google Scholar 

  17. Burset, P., Yeyati, A. L., Brey, L. & Fertig, H. A. Transport in superlattices on single-layer graphene. Phys. Rev. B 83, 195434 (2011)

    ADS  Article  Google Scholar 

  18. Wu, S., Killi, M. & Paramekanti, A. Graphene under spatially varying external potentials: Landau levels, magnetotransport, and topological modes. Phys. Rev. B 85, 195404 (2012)

    ADS  Article  Google Scholar 

  19. Ortix, C., Yang, L. & van den Brink, J. Graphene on incommensurate substrates: trigonal warping and emerging Dirac cone replicas with halved group velocity. Phys. Rev. B 86, 081405 (2012)

    ADS  Article  Google Scholar 

  20. Zarenia, M., Leenaerts, O., Partoens, B. & Peeters, F. M. Substrate-induced chiral states in graphene. Phys. Rev. B 86, 085451 (2012)

    ADS  Article  Google Scholar 

  21. Kindermann, M. M., Uchoa, B. & Miller, D. L. Zero energy modes and gate-tunable gap in graphene on hexagonal boron nitride. Phys. Rev. B 86, 115415 (2012)

    ADS  Article  Google Scholar 

  22. Wallbank, J. R., Patel, A. A., Mucha-Kruczynski, M., Geim, A. K. & Fal’ko, V. I. Generic miniband structure of graphene on a hexagonal substrate. Preprint at http://arxiv.org/abs/1211.4711 (2012)

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

    ADS  Article  Google Scholar 

  24. Bistritzer, R. & MacDonald, A. H. Moire butterflies. Phys. Rev. B 84, 035440 (2011)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  26. Li, G., Luican, A. & Andrei, E. Y. Scanning tunneling spectroscopy of graphene on graphite. Phys. Rev. Lett. 102, 176804 (2009)

    ADS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  30. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183–191 (2007)

    ADS  CAS  Article  Google Scholar 

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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.

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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.

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Correspondence to R. V. Gorbachev.

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The authors declare no competing financial interests.

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Ponomarenko, L., Gorbachev, R., Yu, G. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013). https://doi.org/10.1038/nature12187

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