Abstract
When a strong magnetic field is applied to a two-dimensional electron system, interactions between the electrons can cause fractional quantum Hall (FQH) effects1,2. Bringing two two-dimensional conductors close to each other, a new set of correlated states can emerge due to interactions between electrons in the same and opposite layers3,4,5,6. Here we report interlayer-correlated FQH states in a device consisting of two parallel graphene layers separated by a thin insulator. Current flow in one layer generates different quantized Hall signals in the two layers. This result is interpreted using composite fermion (CF) theory7 with different intralayer and interlayer Chern–Simons gauge-field couplings. We observe FQH states corresponding to integer values of CF Landau level (LL) filling in both layers, as well as ‘semiquantized’ states, where a full CF LL couples to a continuously varying partially filled CF LL. We also find a quantized state between two coupled half-filled CF LLs and attribute it to an interlayer CF exciton condensate.
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Data availability
The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.
References
Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).
Laughlin, R. B. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395–1398 (1983).
Halperin, B. I. Theory of the quantized Hall conductance. Helv. Phys. Acta 56, 75–104 (1983).
Chakraborty, T. & Pietiläinen, P. Fractional quantum Hall effect at half-filled Landau level in a multiple-layer electron system. Phys. Rev. Lett. 59, 2784–2787 (1987).
Eisenstein, J. Exciton condensation in bilayer quantum Hall systems. Annu. Rev. Condens. Matter Phys. 5, 159–181 (2014).
Jain, J. Composite Fermions (Cambridge Univ. Press, 2007).
Jain, J. K. Composite-fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63, 199–202 (1989).
Halperin, B. I. Statistics of quasiparticles and the hierarchy of fractional quantized Hall states. Phys. Rev. Lett. 52, 1583–1586 (1984).
Suen, Y. W., Engel, L. W., Santos, M. B., Shayegan, M. & Tsui, D. C. Observation of a ν = 1/2 fractional quantum Hall state in a double-layer electron system. Phys. Rev. Lett. 68, 1379–1382 (1992).
Eisenstein, J. P., Boebinger, G. S., Pfeiffer, L. N., West, K. W. & He, S. New fractional quantum Hall state in double-layer two-dimensional electron systems. Phys. Rev. Lett. 68, 1383–1386 (1992).
Kellogg, M., Spielman, I. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Observation of quantized Hall drag in a strongly correlated bilayer electron system. Phys. Rev. Lett. 88, 126804 (2002).
Liu, X., Watanabe, K., Taniguchi, T., Halperin, B. I. & Kim, P. Quantum Hall drag of exciton condensate in graphene. Nat. Phys. 13, 746–750 (2017).
Li, J. I., Taniguchi, T., Watanabe, K., Hone, J. & Dean, C. R. Excitonic superfluid phase in double bilayer graphene. Nat. Phys. 13, 751–755 (2017).
Kellogg, M., Eisenstein, J. Pv, Pfeiffer, L. N. & West, K. W. Vanishing Hall resistance at high magnetic field in a double-layer two-dimensional electron system. Phys. Rev. Lett. 93, 036801 (2004).
Tutuc, E., Shayegan, M. & Huse, D. A. Counterflow measurements in strongly correlated GaAs hole bilayers: evidence for electron-hole pairing. Phys. Rev. Lett. 93, 036802 (2004).
Spielman, I. B., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Resonantly enhanced tunneling in a double layer quantum Hall ferromagnet. Phys. Rev. Lett. 84, 5808–5811 (2000).
Yoshioka, D., MacDonald, A. H. & Girvin, S. M. Fractional quantum Hall effect in two-layered systems. Phys. Rev. B 39, 1932–1935 (1989).
Scarola, V. W. & Jain, J. K. Phase diagram of bilayer composite fermion states. Phys. Rev. B 64, 085313 (2001).
Barkeshli, M. & Wen, X.-G. Non-Abelian two-component fractional quantum Hall states. Phys. Rev. B 82, 233301 (2010).
Geraedts, S., Zaletel, M. P., Papić, Z. & Mong, R. S. K. Competing Abelian and non-Abelian topological orders in ν = 1/3 + 1/3 quantum Hall bilayers. Phys. Rev. B 91, 205139 (2015).
He, S., Das Sarma, S. & Xie, X. C. Quantized Hall effect and quantum phase transitions in coupled two-layer electron systems. Phys. Rev. B 47, 4394–4412 (1993).
Zibrov, A. A. et al. Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level. Nature 549, 360–364 (2017).
Kellogg, M. J. Evidence for Excitonic Superfluidity in a Bilayer Two-Dimensional Electron System. PhD thesis, California Institute of Technology (2005).
Hill, N. P. R. et al. Frictional drag between parallel two-dimensional electron gases in a perpendicular magnetic field. J. Phys. Condens. Matter 8, L557–L562 (1996).
Acknowledgements
The major experimental work is supported by DOE (DE-SC0012260). The theoretical analysis was supported by the Science and Technology Center for Integrated Quantum Materials, NSF grant no. DMR-1231319. P.K. acknowledges partial support from the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant GBMF4543. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by MEXT, Japan, and CREST(JPMJCR15F3), JST. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement no. DMR-1157490* and the State of Florida. Nanofabrication was performed at the Center for Nanoscale Systems at Harvard, supported in part by NSF NNIN award ECS-00335765. In preparation of this manuscript, we are aware of related work done by J. I. A. Li et al. We thank B. Rosenow, J. I. A. Li and C. Dean for helpful discussions.
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X.L. and P.K. conceived the experiment. X.L. and Z.H. fabricated the samples and performed the measurements. X.L. analysed the data. B.H. conducted the theoretical analysis. X.L., B.I.H. and P.K. wrote the paper. K.W. and T.T. supplied hBN crystals.
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Additional theoretical details, Supplementary Figs. 1–4 and Supplementary references 1–12.
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Liu, X., Hao, Z., Watanabe, K. et al. Interlayer fractional quantum Hall effect in a coupled graphene double layer. Nat. Phys. 15, 893–897 (2019). https://doi.org/10.1038/s41567-019-0546-0
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DOI: https://doi.org/10.1038/s41567-019-0546-0
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