Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

High-resolution tunnelling spectroscopy of a graphene quartet

Nature volume 467, pages 185–189 (2010)Cite this article

Subjects

Abstract

Electrons in a single sheet of graphene behave quite differently from those in traditional two-dimensional electron systems. Like massless relativistic particles, they have linear dispersion and chiral eigenstates. Furthermore, two sets of electrons centred at different points in reciprocal space (‘valleys’) have this dispersion, giving rise to valley degeneracy. The symmetry between valleys, together with spin symmetry, leads to a fourfold quartet degeneracy of the Landau levels, observed as peaks in the density of states produced by an applied magnetic field. Recent electron transport measurements have observed the lifting of the fourfold degeneracy in very large applied magnetic fields, separating the quartet into integer1,2,3,4 and, more recently, fractional5,6 levels. The exact nature of the broken-symmetry states that form within the Landau levels and lift these degeneracies is unclear at present and is a topic of intense theoretical debate7,8,9,10,11. Here we study the detailed features of the four quantum states that make up a degenerate graphene Landau level. We use high-resolution scanning tunnelling spectroscopy at temperatures as low as 10 mK in an applied magnetic field to study the top layer of multilayer epitaxial graphene. When the Fermi level lies inside the fourfold Landau manifold, significant electron correlation effects result in an enhanced valley splitting for even filling factors, and an enhanced electron spin splitting for odd filling factors. Most unexpectedly, we observe states with Landau level filling factors of 7/2, 9/2 and 11/2, suggestive of new many-body states in graphene.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Landau level spectroscopy of epitaxial graphene on SiC.
Figure 2: Landau levels of epitaxial graphene on SiC as a function of magnetic field.
Figure 3: Electron density and filling-factor variation as a function of magnetic field in epitaxial graphene.
Figure 4: High-resolution Landau level spectroscopy of the fourfold states that make up the N = 1 Landau level.
Figure 5: Energies in the epitaxial graphene N = 1 Landau level.

References

  1. Zhang, Y. et al. Landau-level splitting in graphene in high magnetic fields. Phys. Rev. Lett. 96, 1–4 (2006)

    Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  3. Abanin, D. A. et al. Dissipative quantum Hall effect in graphene near the Dirac point. Phys. Rev. Lett. 98, 196806 (2007)

    Article  ADS  Google Scholar 

  4. Gusynin, V. P. & Sharapov, S. G. Unconventional integer quantum Hall effect in graphene. Phys. Rev. Lett. 95, 146801 (2005)

    Article  ADS  CAS  Google Scholar 

  5. 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  CAS  Google Scholar 

  6. 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  CAS  Google Scholar 

  7. Nomura, K. & MacDonald, A. Quantum Hall ferromagnetism in graphene. Phys. Rev. Lett. 96, 256602 (2006)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  9. Yang, K., Das Sarma, S. & MacDonald, A. Collective modes and skyrmion excitations in graphene SU(4) quantum Hall ferromagnets. Phys. Rev. B 74, 1–8 (2006)

    Google Scholar 

  10. Goerbig, M. O., Moessner, R. & Doucot, B. Electron interactions in graphene in a strong magnetic field. Phys. Rev. B 74, 161407 (2006)

    Article  ADS  Google Scholar 

  11. Abanin, D., Lee, P. & Levitov, L. Randomness-induced XY ordering in a graphene quantum Hall ferromagnet. Phys. Rev. Lett. 98, 1–4 (2007)

    Google Scholar 

  12. Kamerlingh Onnes, H. The resistance of pure mercury at helium temperatures. Comm. Phys. Lab. Univ. Leiden. 120b, (1911)

  13. Klitzing, K. V., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980)

    Article  ADS  Google Scholar 

  14. Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  16. Li, G., Luican, A. & Andrei, E. Scanning tunneling spectroscopy of graphene on graphite. Phys. Rev. Lett. 102, 1–4 (2009)

    Google Scholar 

  17. Dial, O. E., Ashoori, R. C., Pfeiffer, L. N. & West, K. W. Anomalous structure in the single particle spectrum of the fractional quantum Hall effect. Nature 464, 566–570 (2010)

    Article  ADS  CAS  Google Scholar 

  18. Hass, J. et al. Why multilayer graphene on 4H-SiC(0001-bar) behaves like a single sheet of graphene. Phys. Rev. Lett. 100, 125504 (2008)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Ando, T. & Uemura, Y. Theory of oscillatory g factor in an MOS inversion layer under strong magnetic fields. J. Phys. Soc. Jpn 37, 1044–1052 (1974)

    Article  ADS  CAS  Google Scholar 

  22. Smith, A. P., MacDonald, A. H. & Gumbs, G. Quasiparticle effective mass and enhanced g factor for a two-dimensional electron gas at intermediate magnetic fields. Phys. Rev. B 45, 8829–8832 (1992)

    Article  ADS  CAS  Google Scholar 

  23. Dial, O. E., Ashoori, R. C., Pfeiffer, L. N. & West, K. W. High-resolution spectroscopy of two-dimensional electron systems. Nature 448, 176–179 (2007)

    Article  ADS  CAS  Google Scholar 

  24. Zhang, C. & Joglekar, Y. Wigner crystal and bubble phases in graphene in the quantum Hall regime. Phys. Rev. B 75, 1–6 (2007)

    Google Scholar 

  25. Wang, H., Sheng, D., Sheng, L. & Haldane, F. Broken-symmetry states of Dirac fermions in graphene with a partially filled high Landau level. Phys. Rev. Lett. 100, 1–4 (2008)

    Google Scholar 

  26. Rezayi, E., Haldane, F. & Yang, K. Charge-density-wave ordering in half-filled high Landau levels. Phys. Rev. Lett. 83, 1219–1222 (1999)

    Article  ADS  CAS  Google Scholar 

  27. Lilly, M., Cooper, K., Eisenstein, J., Pfeiffer, L. & West, K. Evidence for an anisotropic state of two-dimensional electrons in high Landau levels. Phys. Rev. Lett. 82, 394–397 (1999)

    Article  ADS  CAS  Google Scholar 

  28. Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  29. Eisenstein, J. P. & MacDonald, A. H. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004)

    Article  ADS  CAS  Google Scholar 

  30. 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  CAS  Google Scholar 

Download references

Acknowledgements

We thank N. Zhitenev for discussions, S. Blankenship, A. Band and F. Hess for their technical contributions to the construction of the millikelvin scanning probe microscopy system, V. Shvarts for his advice on cryogenics and U. D. Ham for instructions on making silver probe tips. This work was supported in part by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF- 2006-214-C00022), the NSF (DMR-0820382 [MRSEC], DMR-0804908, DMR-0606489), the Welch Foundation and the Semiconductor Research Corporation (NRI-INDEX programme).

Author information

Authors and Affiliations

  1. Center for Nanoscale Science and Technology, NIST, Gaithersburg, 20899, Maryland, USA

    Young Jae Song, Alexander F. Otte, Hongki Min, Shaffique Adam, Mark D. Stiles & Joseph A. Stroscio

  2. Maryland NanoCenter, University of Maryland, College Park, 20742, Maryland, USA

    Young Jae Song, Alexander F. Otte & Hongki Min

  3. Department of Physics and Astronomy, Seoul National University, Seoul, 151-7474, South Korea

    Young Kuk

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

    Yike Hu, David B. Torrance, Phillip N. First & Walt A. de Heer

  5. Department of Physics, University of Texas at Austin, Austin, 78712, Texas, USA

    Allan H. MacDonald

Authors
  1. Young Jae Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander F. Otte
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Young Kuk
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yike Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. David B. Torrance
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Phillip N. First
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Walt A. de Heer
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Hongki Min
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Shaffique Adam
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Mark D. Stiles
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Allan H. MacDonald
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Joseph A. Stroscio
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Y.J.S, A.F.O, Y.K. and J.A.S designed and constructed the millikelvin scanning probe microscopy system. The graphene scanning tunnelling microscopy/scanning tunnelling spectroscopy measurements were performed by Y.J.S, A.F.O and J.A.S. The graphene sample was grown by Y.H and W.A.d.H., and the surface was prepared and characterized by D.B.T and P.N.F. A theoretical analysis of the epitaxial graphene multilayer system was performed by H.M., S.A., M.D.S and A.H.M.

Corresponding author

Correspondence to Joseph A. Stroscio.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Figures

The file contains Supplementary Figures 1-2 with legends. (PDF 365 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Song, Y., Otte, A., Kuk, Y. et al. High-resolution tunnelling spectroscopy of a graphene quartet. Nature 467, 185–189 (2010). https://doi.org/10.1038/nature09330

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature09330

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing