# Emergence of superlattice Dirac points in graphene on hexagonal boron nitride

## Abstract

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.

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## Acknowledgements

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)

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Reprints and Permissions

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

• #### DOI

https://doi.org/10.1038/nphys2272

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