Cloning of Dirac fermions in graphene superlattices

Nature

Volumn 497, Issue 7451, 2013, Pages 594-597

  Ponomarenko, L A ^a   Gorbachev, R V ^a   Yu, G L ^a   Elias, D C ^a   Jalil, R ^a   Patel, A A ^b   Mishchenko, A ^a   Mayorov, A S ^a   Woods, C R ^a   Wallbank, J R ^b   Mucha Kruczynski, M ^b   Piot, B A ^c   Potemski, M ^c   Grigorieva, I V ^a   Novoselov, K S ^a   Guinea, F ^d   Fal'Ko, V I ^b   Geim, A K ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b LANCASTER UNIVERSITY   (United Kingdom)

^c CNRS   (France)

^d INSTITUTO DE CIENCIA DE MATERIALES DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPHENE;

CARBON; CRYSTAL STRUCTURE; CRYSTALLOGRAPHY; ELECTRICAL RESISTIVITY; MAGNETIC FIELD; QUANTUM MECHANICS;

ARTICLE; CRYSTALLOGRAPHY; ELECTRIC CONDUCTIVITY; FERMION; MAGNETIC FIELD; MATERIALS; PRIORITY JOURNAL; SUPERLATTICE;

EID: 84878391708     PISSN: 00280836     EISSN: 14764687     Source Type: Journal    
DOI: 10.1038/nature12187     Document Type: Article

References (30)

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).
2. Weiss, D. et al. Electron pinball and commensurate orbits in a periodic array of scatterers. Phys. Rev. Lett. 66, 2790-2793 (1991).
3. Pfannkuche, D.& Gerhardts, R. R. Theory of magnetotransport in two-dimensional electron systemssubjected to weak two-dimensional superlattice potentials. Phys. Rev. B 46, 12606-12626 (1992).
4. Ferry, D. K. Quantum magnetotransport in lateral surface superlattices. Prog. Quantum Electron. 16, 251-317 (1992).
5. Albrecht, C. et al. Fermiology of two-dimensional lateral superlattices. Phys. Rev. Lett. 83, 2234-2237 (1999).
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).
7. Albrecht, C. et al. Evidence ofHofstadter's fractal energy spectrumin the quantized Hall conductance. Phys. Rev. Lett. 86, 147-150 (2001).
8. Geisler, M. C. et al. Detection of a Landau band-coupling-induced rearrangement of the Hofstadter butterfly. Phys. Rev. Lett. 92, 256801 (2004).
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).
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).
11. Decker, R. et al. Local electronic properties of graphene on a BN substrate via scanning tunneling microscopy. Nano Lett. 11, 2291-2295 (2011).
12. Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nature Phys. 8, 382-386 (2012).
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).
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).
15. Tiwari, R. P. & Stroud, D. Tunable band gap in graphene with a noncentrosymmetric superlattice potential. Phys. Rev. B 79, 205435 (2009).
16. Barbier,M., Vasilopoulos,P.&Peeters, F. M. ExtraDirac points inthe energy spectrum for superlattices on single-layer graphene. Phys. Rev. B 81, 075438 (2010).
17. Burset, P., Yeyati, A. L., Brey, L. & Fertig, H. A. Transport in superlattices on singlelayer graphene. Phys. Rev. B 83, 195434 (2011).
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).
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).
20. Zarenia, M., Leenaerts, O., Partoens, B. & Peeters, F. M. Substrate-induced chiral states in graphene. Phys. Rev. B 86, 085451 (2012).
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).
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).
24. Bistritzer, R.& MacDonald, A. H. Moire butterflies. Phys. Rev. B 84, 035440 (2011).
25. Haigh, S. J. et al. Cross-sectional imaging of individual layers and buried interfaces of graphene-based heterostructures andsuperlattices. NatureMater. 11, 764-767 (2012).
26. Li, G., Luican, A. & Andrei, E. Y. Scanning tunneling spectroscopy of graphene on graphite. Phys. Rev. Lett. 102, 176804 (2009).
27. Mayorov, A. S. et al. Micrometer-scale ballistic transport in encapsulated graphene at room temperature. Nano Lett. 11, 2396-2399 (2011).
28. Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nature Nanotechnol. 5, 722-726 (2010).
29. Mayorov, A. S. et al. How close can one approach the Dirac point in graphene experimentally? Nano Lett. 12, 4629-4634 (2012).
30. Geim,A.K.&Novoselov, K.S. The rise of graphene.NatureMater. 6,183-191(2007).