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Real-space mapping of magnetically quantized graphene states

Nature Physics volume 6, pages 811–817 (2010)Cite this article

Abstract

The symmetry of graphene’s two carbon sublattices underlies its unique electronic structure and half-integer quantum Hall effect. Quantized Hall resistance requires confinement of cyclotron orbits (Landau levels) in the sample interior. Such magnetic localization may be unique in graphene, especially for the fourfold-degenerate Landau level (LL0) straddling graphene’s charge-neutrality energy. Here we map the two-dimensional spatial distribution of LL0, using cryogenic scanning tunnelling spectroscopy to measure the local density of states (LDOS) on electronically decoupled multilayer epitaxial graphene. Unlike disordered LDOS patterns found in conventional quantum Hall systems, we find an organized pattern of localized states and extended states that emerge above a threshold magnetic field. In distinct regions, an energy gap associated with lattice-scale variations of the LDOS suggests the sublattice (and LL0 valley) degeneracy is locally lifted. We propose this occurs when cyclotron orbits become small enough to sample regions of small symmetry-breaking potential originating from a graphene-on-graphene moiré.

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Figure 1: Topographic STM images of the multilayer epitaxial graphene sample grown on SiC.
Figure 2: STS dI/dV maps showing an extended state at the LL0av peak energy (E0av) and localized states at energies above and below E0av.
Figure 3: Spatial variation of the LL0 energy and the local lifting of valley degeneracy.
Figure 4: Magnetic-field dependence of the spatially varying LL0 peak energy.
Figure 5: Energy-gap map and proposed model of the local valley splitting.

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References

  1. Davies, J. H. The Physics of Low-dimensional Semiconductors: An Introduction (Cambridge Univ. Press, 1998).

    Google Scholar 

  2. Ando, T. Electron localization in a two-dimensional system in strong magnetic fields. II: Long-range scatterers and response functions. J. Phys. Soc. Jpn 53, 3101–3111 (1984).

    Article  ADS  Google Scholar 

  3. Huckestein, B. Scaling theory of the integer quantum Hall effect. Rev. Mod. Phys. 67, 357–396 (1995).

    ADS  Google Scholar 

  4. Zhang, Y., Tan, Y-W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature 438, 201–204 (2005).

    Article  ADS  Google Scholar 

  5. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).

    ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  7. Pereira, A. L. C. & Schulz, P. A. Valley polarization effects on localization in graphene Landau levels. Phys. Rev. B 77, 075416 (2008).

    Article  ADS  Google Scholar 

  8. Beenakker, C. W. J. Colloquium: Andreev reflection and Klein tunneling in graphene. Rev. Mod. Phys. 80, 1337–1354 (2008).

    Article  ADS  Google Scholar 

  9. Pereira, A. L. C. Splitting of critical energies in the n=0 Landau level of graphene. New J. Phys. 11, 095019 (2009).

    Article  ADS  Google Scholar 

  10. Wu, X. et al. Half integer quantum Hall effect in high mobility single layer epitaxial graphene. Appl. Phys. Lett. 95, 223108 (2009).

    Article  ADS  Google Scholar 

  11. Checkelsky, J. G., Li, L. & Ong, N. P. Divergent resistance at the Dirac point in graphene: Evidence for a transition in a high magnetic field. Phys. Rev. B 79, 115434 (2009).

    Article  ADS  Google Scholar 

  12. Checkelsky, J. G., Li, L. & Ong, N. P. Zero-energy state in graphene in a high magnetic field. Phys. Rev. Lett. 100, 206801 (2008).

    Article  ADS  Google Scholar 

  13. Jiang, Z., Zhang, Y., Stormer, H. L. & Kim, P. Quantum Hall states near the charge-neutral Dirac point in graphene. Phys. Rev. Lett. 99, 106802 (2007).

    Article  ADS  Google Scholar 

  14. Zhang, Y. et al. Landau-level splitting in graphene in high magnetic fields. Phys. Rev. Lett. 96, 136806 (2006).

    Article  ADS  Google Scholar 

  15. Feldman, B. E., Martin, J. & Yacoby, A. Broken-symmetry states and divergent resistance in suspended bilayer graphene. Nature Phys. 5, 889–893 (2009).

    Article  ADS  Google Scholar 

  16. Zhao, Y., Cadden-Zimansky, P., Jiang, Z. & Kim, P. Symmetry breaking in the zero-energy Landau level in bilayer graphene. Phys. Rev. Lett. 104, 066801 (2010).

    Article  ADS  Google Scholar 

  17. Du, X., Skachko, I., Duerr, F., Luican, A. & Andrei, E. Y. Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene. Nature 462, 192–195 (2009).

    Article  ADS  Google Scholar 

  18. Bolotin, K. I., Ghahari, F., Shulman, M. D., Stormer, H. L. & Kim, P. Observation of the fractional quantum Hall effect in graphene. Nature 462, 196–199 (2009).

    Article  ADS  Google Scholar 

  19. Miller, D. L. et al. Observing the quantization of zero mass carriers in graphene. Science 324, 924–927 (2009).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. de Heer, W. A. et al. Epitaxial graphene. Solid State Commun. 143, 92–100 (2007).

    Article  ADS  Google Scholar 

  22. First, P. N. et al. Epitaxial graphenes on silicon carbide. MRS Bull. 35, 296–305 (2010).

    Article  Google Scholar 

  23. Hass, J. et al. Why multilayer graphene on behaves like a single sheet of graphene. Phys. Rev. Lett. 100, 125504 (2008).

    Article  ADS  Google Scholar 

  24. Martin, J. et al. The nature of localization in graphene under quantum Hall conditions. Nature Phys. 5, 669–674 (2009).

    Article  ADS  Google Scholar 

  25. Morgenstern, M., Klijn, J., Meyer, C., Haude, D. & Wiesendanger, R. in Scanning Tunneling Microscopy/Spectroscopy and Related Techniques: 12th International Conference (eds Koenraad, P. M. & Kemerink, M.) 11–19 (AIP Conference Proceedings, Vol. 696, AIP, 2003) http://link.aip.org/link/?APC/696/11/1.

    Google Scholar 

  26. Morgenstern, M., Klijn, J., Meyer, C. & Wiesendanger, R. Real-space observation of drift states in a two-dimensional electron system at high magnetic fields. Phys. Rev. Lett. 90, 056804 (2003).

    Article  ADS  Google Scholar 

  27. Hashimoto, K. et al. Quantum Hall transition in real space: From localized to extended states. Phys. Rev. Lett. 101, 256802 (2008).

    Article  ADS  Google Scholar 

  28. Niimi, Y., Kambara, H. & Fukuyama, H. Localized distributions of quasi-two-dimensional electronic states near defects artificially created at graphite surfaces in magnetic fields. Phys. Rev. Lett. 102, 026803 (2009).

    Article  ADS  Google Scholar 

  29. Pan, S. H. et al. Microscopic electronic inhomogeneity in the high-Tc superconductor Bi2Sr2CaCu2O8+x . Nature 413, 282–285 (2001).

    Article  ADS  Google Scholar 

  30. Poplavskyy, O., Goerbig, M. O. & Smith, C. M. Local density of states of electron-crystal phases in graphene in the quantum Hall regime. Phys. Rev. B 80, 195414 (2009).

    Article  ADS  Google Scholar 

  31. Nomura, K., Ryu, S. & Lee, D-H. Field-induced Kosterlitz–Thouless transition in the n=0 Landau level of graphene. Phys. Rev. Lett. 103, 216801 (2009).

    Article  ADS  Google Scholar 

  32. Luk’yanchuk, I. A. & Bratkovsky, A. M. Lattice-induced double-valley degeneracy lifting in graphene by a magnetic field. Phys. Rev. Lett. 100, 176404 (2008).

    Article  ADS  Google Scholar 

  33. Hass, J., de Heer, W. A. & Conrad, E. H. The growth and morphology of epitaxial multilayer graphene. J. Phys. Condens. Matter 20, 323202 (2008).

    Article  Google Scholar 

  34. Sprinkle, M. et al. First direct observation of a nearly ideal graphene band structure. Phys. Rev. Lett. 103, 226803 (2009).

    Article  ADS  Google Scholar 

  35. Latil, S., Meunier, V. & Henrard, L. Massless fermions in multilayer graphitic systems with misoriented layers: Ab initio calculations and experimental fingerprints. Phys. Rev. B 76, 201402 (2007).

    Article  ADS  Google Scholar 

  36. Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Graphene bilayer with a twist: Electronic structure. Phys. Rev. Lett. 99, 256802–256804 (2007).

    Article  ADS  Google Scholar 

  37. Mele, E. J. Commensuration and interlayer coherence in twisted bilayer graphene. Phys. Rev. B 81, 161405(R) (2010).

    Article  ADS  Google Scholar 

  38. Li, G. et al. Observation of van Hove singularities in twisted graphene layers. Nature Phys. 6, 109–113 (2010).

    Article  ADS  Google Scholar 

  39. Miller, D. L. et al. Structural analysis of multilayer graphene via atomic moiré interferometry. Phys. Rev. B 81, 125427 (2010).

    Article  ADS  Google Scholar 

  40. Fuchs, J-N. & Lederer, P. Spontaneous parity breaking of graphene in the quantum Hall regime. Phys. Rev. Lett. 98, 016803 (2007).

    Article  ADS  Google Scholar 

  41. Alicea, J. & Fisher, M. P. A. Graphene integer quantum Hall effect in the ferromagnetic and paramagnetic regimes. Phys. Rev. B 74, 075422 (2006).

    Article  ADS  Google Scholar 

  42. Khveshchenko, D. V. Magnetic-field-induced insulating behavior in highly oriented pyrolitic graphite. Phys. Rev. Lett. 87, 206401 (2001).

    Article  ADS  Google Scholar 

  43. Partoens, B. & Peeters, F. M. From graphene to graphite: Electronic structure around the K point. Phys. Rev. B 74, 075404 (2006).

    Article  ADS  Google Scholar 

  44. Dresselhaus, M. S. & Dresselhaus, G. Intercalation compounds of graphite. Adv. Phys. 51, 1–186 (2002).

    Article  ADS  Google Scholar 

  45. Berger, C. et al. Electronic confinement and coherence in patterned epitaxial graphene. Science 312, 1191–1196 (2006).

    Article  ADS  Google Scholar 

  46. Berger, C. et al. Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics. J. Phys. Chem. B 108, 19912–19916 (2004).

    Article  Google Scholar 

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Acknowledgements

We thank C. Berger, M. Sprinkle, N. Sharma, S. Blankenship, A. Band and F. Hess for their technical contributions to this work. Financial support from NSF (DMR-0804908), the Semiconductor Research Corporation Nanoelectronics Research Initiative (NRI-INDEX) and the W. M. Keck Foundation are gratefully acknowledged. Graphene production facilities of the Georgia Tech MRSEC (NSF DMR-0820382) were employed.

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Authors and Affiliations

  1. School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA

    David L. Miller, Kevin D. Kubista, Ming Ruan, Walt A. de Heer, Markus Kindermann & Phillip N. First

  2. Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA

    Gregory M. Rutter & Joseph A. Stroscio

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Contributions

D.L.M., K.D.K., G.M.R., P.N.F. and J.A.S. carried out the measurements in the 4 K UHV STM facility in the CNST at NIST. The graphene sample was grown by M.R. and W.A.dH at Georgia Tech, and the surface prepared/characterized by D.L.M. and P.N.F. A theoretical analysis of the epitaxial graphene multilayer system was carried out by M.K.

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Correspondence to Phillip N. First or Joseph A. Stroscio.

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Miller, D., Kubista, K., Rutter, G. et al. Real-space mapping of magnetically quantized graphene states. Nature Phys 6, 811–817 (2010). https://doi.org/10.1038/nphys1736

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