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Observation of the fractional quantum Hall effect in graphene

A Corrigendum to this article was published on 15 June 2011


When electrons are confined in two dimensions and subject to strong magnetic fields, the Coulomb interactions between them can become very strong, leading to the formation of correlated states of matter, such as the fractional quantum Hall liquid1,2. In this strong quantum regime, electrons and magnetic flux quanta bind to form complex composite quasiparticles with fractional electronic charge; these are manifest in transport measurements of the Hall conductivity as rational fractions of the elementary conductance quantum. The experimental discovery of an anomalous integer quantum Hall effect in graphene has enabled the study of a correlated two-dimensional electronic system, in which the interacting electrons behave like massless chiral fermions3,4. However, owing to the prevailing disorder, graphene has so far exhibited only weak signatures of correlated electron phenomena5,6, despite intense experimental and theoretical efforts7,8,9,10,11,12,13,14. Here we report the observation of the fractional quantum Hall effect in ultraclean, suspended graphene. In addition, we show that at low carrier density graphene becomes an insulator with a magnetic-field-tunable energy gap. These newly discovered quantum states offer the opportunity to study correlated Dirac fermions in graphene in the presence of large magnetic fields.

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Figure 1: Electrical properties of suspended graphene at low magnetic field.
Figure 2: Magnetotransport at high magnetic fields.
Figure 3: Identifying additional fractional quantum Hall states.
Figure 4: The insulating state in graphene near zero density.


  1. 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 

  2. Jain, J. Composite Fermions (Cambridge Univ. Press, 2007)

    Book  Google Scholar 

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

    Article  ADS  CAS  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  CAS  Google Scholar 

  5. 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  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  7. Goerbig, M. O. & Regnault, N. Analysis of a SU(4) generalization of Halperin's wave function as an approach towards a SU(4) fractional quantum Hall effect in graphene sheets. Phys. Rev. B 75, 241405 (2007)

    Article  ADS  Google Scholar 

  8. Toke, C., Lammert, P. E., Crespi, V. H. & Jain, J. K. Fractional quantum Hall effect in graphene. Phys. Rev. B 74, 235417 (2006)

    Article  ADS  Google Scholar 

  9. Peres, N. M. R., Guinea, F. & Neto, A. H. C. Electronic properties of disordered two-dimensional carbon. Phys. Rev. B 73, 125411 (2006)

    Article  ADS  Google Scholar 

  10. Apalkov, V. M. & Chakraborty, T. Fractional quantum Hall states of Dirac electrons in graphene. Phys. Rev. Lett. 97, 126801 (2006)

    Article  ADS  Google Scholar 

  11. Yang, K., Sarma, S. D. & MacDonald, A. H. Collective modes and skyrmion excitations in graphene SU(4) quantum Hall ferromagnets. Phys. Rev. B 74, 075423 (2006)

    Article  ADS  Google Scholar 

  12. Khveshchenko, D. V. Composite Dirac fermions in graphene. Phys. Rev. B 75, 153405 (2007)

    Article  ADS  Google Scholar 

  13. Shibata, N. & Nomura, K. Coupled charge and valley excitations in graphene quantum Hall ferromagnets. Phys. Rev. B 77, 235426 (2008)

    Article  ADS  Google Scholar 

  14. Toke, C. & Jain, J. K. SU(4) composite fermions in graphene: fractional quantum Hall states without analog in GaAs. Phys. Rev. B 75, 245440 (2007)

    Article  ADS  Google Scholar 

  15. Neto, A. H. C., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–163 (2009)

    Article  ADS  Google Scholar 

  16. Yang, K. Spontaneous symmetry breaking and quantum Hall effect in graphene. Solid State Commun. 143, 27–32 (2007)

    Article  ADS  Google Scholar 

  17. 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 

  18. Sarma, S. D. & Pinczuk, A. Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-Dimensional Semiconductor Structures (Wiley, 1997)

    Google Scholar 

  19. Bolotin, K. I. et al. Ultrahigh electron mobility in suspended graphene. Solid State Commun. 146, 351–355 (2008)

    Article  ADS  CAS  Google Scholar 

  20. Du, X., Skachko, I., Barker, A. & Andrei, E. Y. Approaching ballistic transport in suspended graphene. Nature Nanotechnol. 3, 491–495 (2008)

    Article  ADS  CAS  Google Scholar 

  21. Bolotin, K. I., Sikes, K. J., Hone, J., Stormer, H. L. & Kim, P. Temperature-dependent transport in suspended graphene. Phys. Rev. Lett. 101, 096802 (2008)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Cobden, D. H., Barnes, C. H. W. & Ford, C. J. B. Fluctuations and evidence for charging in the quantum Hall effect. Phys. Rev. Lett. 82, 4695–4698 (1999)

    Article  ADS  CAS  Google Scholar 

  24. Martin, J., et al. The nature of localization in graphene under quantum Hall conditions. Nature Phys. 5, 669–674 (2009); published online 26 July 2009.

    Article  ADS  CAS  Google Scholar 

  25. Ozyilmaz, B. et al. Electronic transport and quantum Hall effect in bipolar graphene p-n-p junctions. Phys. Rev. Lett. 99, 166804 (2007)

    Article  ADS  Google Scholar 

  26. Williams, J. R., DiCarlo, L. & Marcus, C. M. Quantum Hall effect in a gate-controlled p-n junction of graphene. Science 317, 638–641 (2007)

    Article  ADS  CAS  Google Scholar 

  27. Abanin, D. A. & Levitov, L. S. Conformal invariance and shape-dependent conductance of graphene samples. Phys. Rev. B 78, 035416 (2008)

    Article  ADS  Google Scholar 

  28. Willett, R. L., West, K. W. & Pfeiffer, L. N. Transition in the correlated 2D electron system induced by a periodic density modulation. Phys. Rev. Lett. 78, 4478–4481 (1997)

    Article  ADS  CAS  Google Scholar 

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We thank D. Abanin, A. Pinczuk and B. Feldman for discussions. We acknowledge A. Young, P. Cadden-Zimansky and V. Deshpande for careful reading of the manuscript. We especially thank E. Andrei for discussing her results and sample fabrication before publication. This research was supported by the Microsoft Project Q, DARPA and the Department of Energy (DOE).

Author Contributions K.I.B. and F.G. performed the experiments and analysed the data. M.D.S. assisted with fabrication. H.L.S. and P.K. conceived the project. All authors contributed to writing the manuscript.

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Correspondence to Philip Kim.

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Bolotin, K., Ghahari, F., Shulman, M. et al. Observation of the fractional quantum Hall effect in graphene . Nature 462, 196–199 (2009).

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