Emergence of superlattice Dirac points in graphene on hexagonal boron nitride

Article metrics


The Schrödinger equation dictates that the propagation of nearly free electrons through a weak periodic potential results in the opening of bandgaps near points of the reciprocal lattice known as Brillouin zone boundaries1. However, in the case of massless Dirac fermions, it has been predicted that the chirality of the charge carriers prevents the opening of a bandgap and instead new Dirac points appear in the electronic structure of the material2,3. Graphene on hexagonal boron nitride exhibits a rotation-dependent moiré pattern4,5. Here, we show experimentally and theoretically that this moiré pattern acts as a weak periodic potential and thereby leads to the emergence of a new set of Dirac points at an energy determined by its wavelength. The new massless Dirac fermions generated at these superlattice Dirac points are characterized by a significantly reduced Fermi velocity. Furthermore, the local density of states near these Dirac cones exhibits hexagonal modulation due to the influence of the periodic potential.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Graphene device schematic and STM moiré images.
Figure 2: Density of states of graphene on hBN showing new superlattice Dirac points.
Figure 3: Gate dependence of graphene density of states near the superlattice Dirac points for a 13.4 nm moiré pattern.
Figure 4: Experimental and theoretical images of LDOS for a long wavelength moiré pattern.


  1. 1

    Ashcroft, N. W. & Mermin, N.D. Solid State Physics (Brooks Cole, 1976).

  2. 2

    Park, C-H., Yang, L., Son, Y-W., Cohen, M. L. & Louie, S. G. Anisotropic behaviours of massless Dirac fermions in graphene under periodic potentials. Nature Phys. 4, 213–217 (2008).

  3. 3

    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).

  4. 4

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

  5. 5

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

  6. 6

    Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).

  7. 7

    Katsnelson, M. I., Novoselov, K. S. & Geim, A. K. Chiral tunnelling and the Klein paradox in graphene. Nature Phys. 2, 620–625 (2006).

  8. 8

    Klein, O. Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac. Z. Phys. 53, 157–165 (1929).

  9. 9

    Stander, N., Huard, B. & Goldhaber-Gordon, D. Evidence for Klein tunneling in graphene p–n junctions. Phys. Rev. Lett. 102, 026807 (2009).

  10. 10

    Young, A. F. & Kim, P. Quantum interference and Klein tunnelling in graphene heterojunctions. Nature Phys. 5, 222–226 (2009).

  11. 11

    Barbier, M., Peeters, F. M., Vasilopoulos, P. & Pereira, J. M. Dirac and Klein-Gordon particles in one-dimensional periodic potentials. Phys. Rev. B 77, 115446 (2008).

  12. 12

    Brey, L. & Fertig, H. A. Emerging zero modes for graphene in a periodic potential. Phys. Rev. Lett. 103, 046809 (2009).

  13. 13

    Sun, J., Fertig, H. A. & Brey, L. Effective magnetic fields in graphene superlattices. Phys. Rev. Lett. 105, 156801 (2010).

  14. 14

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

  15. 15

    Ortix, C., Yang, L. & van den Brink, J. Graphene on incommensurate substrates: trigonal warping and emerging Dirac cone replicas with halved group velocity. Preprint at http://arxiv.org/abs/1111.0399 (2011).

  16. 16

    Marchini, S., Günther, S. & Wintterlin, J. Scanning tunneling microscopy of graphene on Ru(0001). Phys. Rev. B 76, 075429 (2007).

  17. 17

    Vásquez de Parga, A. L. et al. Periodically rippled graphene: Growth and spatially resolved electronic structure. Phys. Rev. Lett. 100, 056807 (2008).

  18. 18

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

  19. 19

    Dagotto, E. Correlated electrons in high-temperature superconductors. Rev. Mod. Phys. 66, 763–840 (1994).

  20. 20

    Brar, V. W. et al. Observation of carrier-density-dependent many-body effects in graphene via tunneling spectroscopy. Phys. Rev. Lett. 104, 036805 (2010).

Download references


The work at Arizona was partially supported by the US Army Research Laboratory and the US Army Research Office under contract/grant number W911NF-09-1-0333 and the National Science Foundation CAREER award DMR-0953784, EECS-0925152 and DMR-0706319. J.D.S-Y. and P.J-H. were primarily supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award DE-SC0001819 and partly by the 2009 US Office of Naval Research Multi University Research Initiative (MURI) on Graphene Advanced Terahertz Engineering (Gate) at MIT, Harvard and Boston University. P.J. acknowledges the support of the Swiss Center of Excellence MANEP.

Author information

M.Y., J.X., D.C. and B.J.L. performed the STM experiments of the graphene on hBN. M.Y. and D.C. fabricated the CVD graphene devices. J.D.S-Y. fabricated the devices on single crystal hBN. K.W. and T.T. provided the single crystal hBN. P.J. performed the theoretical calculations. P.J-H. and B.J.L. conceived and provided advice on the experiments. All authors participated in the data discussion and writing of the manuscript.

Correspondence to Brian J. LeRoy.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 997 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Yankowitz, M., Xue, J., Cormode, D. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nature Phys 8, 382–386 (2012) doi:10.1038/nphys2272

Download citation

Further reading