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.

Observation of the fractional quantum Hall effect in graphene

A Corrigendum to this article was published on 15 June 2011

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

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.

References

  1. 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)

    ADS  CAS  Article  Google Scholar 

  2. 2

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

    Book  Google Scholar 

  3. 3

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

    ADS  CAS  Article  Google Scholar 

  4. 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)

    ADS  CAS  Article  Google Scholar 

  5. 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)

    ADS  CAS  Article  Google Scholar 

  6. 6

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

    ADS  CAS  Article  Google Scholar 

  7. 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)

    ADS  Article  Google Scholar 

  8. 8

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

    ADS  Article  Google Scholar 

  9. 9

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

    ADS  Article  Google Scholar 

  10. 10

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

    ADS  Article  Google Scholar 

  11. 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)

    ADS  Article  Google Scholar 

  12. 12

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

    ADS  Article  Google Scholar 

  13. 13

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

    ADS  Article  Google Scholar 

  14. 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)

    ADS  Article  Google Scholar 

  15. 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)

    ADS  Article  Google Scholar 

  16. 16

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

    ADS  Article  Google Scholar 

  17. 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)

    ADS  Article  Google Scholar 

  18. 18

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

    Google Scholar 

  19. 19

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

    ADS  CAS  Article  Google Scholar 

  20. 20

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

    ADS  CAS  Article  Google Scholar 

  21. 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)

    ADS  CAS  Article  Google Scholar 

  22. 22

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

    ADS  Article  Google Scholar 

  23. 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)

    ADS  CAS  Article  Google Scholar 

  24. 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.

    ADS  CAS  Article  Google Scholar 

  25. 25

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

    ADS  Article  Google Scholar 

  26. 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)

    ADS  CAS  Article  Google Scholar 

  27. 27

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

    ADS  Article  Google Scholar 

  28. 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)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

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.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Philip Kim.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Figures S1-S4 with Legends, Supplementary Data and Supplementary References. (PDF 873 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bolotin, K., Ghahari, F., Shulman, M. et al. Observation of the fractional quantum Hall effect in graphene . Nature 462, 196–199 (2009). https://doi.org/10.1038/nature08582

Download citation

Further reading

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

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