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Cloning of Dirac fermions in graphene superlattices


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.


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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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Authors and Affiliations



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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Ponomarenko, L., Gorbachev, R., Yu, G. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).

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