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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Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982)
Jain, J. Composite Fermions (Cambridge Univ. Press, 2007)
Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005)
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)
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)
Zhang, Y. et al. Landau-level splitting in graphene in high magnetic fields. Phys. Rev. Lett. 96, 136806 (2006)
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)
Toke, C., Lammert, P. E., Crespi, V. H. & Jain, J. K. Fractional quantum Hall effect in graphene. Phys. Rev. B 74, 235417 (2006)
Peres, N. M. R., Guinea, F. & Neto, A. H. C. Electronic properties of disordered two-dimensional carbon. Phys. Rev. B 73, 125411 (2006)
Apalkov, V. M. & Chakraborty, T. Fractional quantum Hall states of Dirac electrons in graphene. Phys. Rev. Lett. 97, 126801 (2006)
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)
Khveshchenko, D. V. Composite Dirac fermions in graphene. Phys. Rev. B 75, 153405 (2007)
Shibata, N. & Nomura, K. Coupled charge and valley excitations in graphene quantum Hall ferromagnets. Phys. Rev. B 77, 235426 (2008)
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)
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)
Yang, K. Spontaneous symmetry breaking and quantum Hall effect in graphene. Solid State Commun. 143, 27–32 (2007)
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)
Sarma, S. D. & Pinczuk, A. Perspectives in Quantum Hall Effects: Novel Quantum Liquids in Low-Dimensional Semiconductor Structures (Wiley, 1997)
Bolotin, K. I. et al. Ultrahigh electron mobility in suspended graphene. Solid State Commun. 146, 351–355 (2008)
Du, X., Skachko, I., Barker, A. & Andrei, E. Y. Approaching ballistic transport in suspended graphene. Nature Nanotechnol. 3, 491–495 (2008)
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)
Nomura, K. & MacDonald, A. H. Quantum Hall ferromagnetism in graphene. Phys. Rev. Lett. 96, 256602 (2006)
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)
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.
Ozyilmaz, B. et al. Electronic transport and quantum Hall effect in bipolar graphene p-n-p junctions. Phys. Rev. Lett. 99, 166804 (2007)
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)
Abanin, D. A. & Levitov, L. S. Conformal invariance and shape-dependent conductance of graphene samples. Phys. Rev. B 78, 035416 (2008)
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)
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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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
npj Quantum Materials (2022)
npj Quantum Information (2022)
Scientific Reports (2022)
International Journal of Theoretical Physics (2022)
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