An exciton condensate is a Bose–Einstein condensate of electron and hole pairs bound by the Coulomb interaction1,2. In an electronic double layer (EDL) subject to strong magnetic fields, filled Landau states in one layer bind with empty states of the other layer to form an exciton condensate3,4,5,6,7,8,9. Here we report exciton condensation in a bilayer graphene EDL separated by hexagonal boron nitride. Driving current in one graphene layer generates a near-quantized Hall voltage in the other layer, resulting in coherent exciton transport4,6. Owing to the strong Coulomb coupling across the atomically thin dielectric, quantum Hall drag in graphene appears at a temperature ten times higher than previously observed in a GaAs EDL. The wide-range tunability of densities and displacement fields enables exploration of a rich phase diagram of Bose–Einstein condensates across Landau levels with different filling factors and internal quantum degrees of freedom. The observed robust exciton condensation opens up opportunities to investigate various many-body exciton phases.
Subscribe to Journal
Get full journal access for 1 year
only $15.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
Littlewood, P. B. et al. Models of coherent exciton condensation. J. Phys. Condens. Matter 16, S3597–S3620 (2004).
Snoke, D. et al. Spontaneous Bose coherence of excitons and polaritons. Science 298, 1368–1372 (2002).
Eisenstein, J. & MacDonald, A. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 691–694 (2004).
Eisenstein, J. P. Exciton condensation in bilayer quantum Hall systems. Annu. Rev. Condens. Matter Phys. 5, 159–181 (2014).
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).
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).
Kellogg, M., Eisenstein, J. P., 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, 36801 (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, 36802 (2004).
Nandi, D., Finck, A. D. K., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Exciton condensation and perfect Coulomb drag. Nature 488, 481–484 (2012).
Kasprzak, J. et al. Bose–Einstein condensation of exciton polaritons. Nature 443, 409–414 (2006).
Byrnes, T., Kim, N. Y. & Yamamoto, Y. Exciton–polariton condensates. Nat. Phys. 10, 803–813 (2014).
Deng, H., Weihs, G., Santori, C., Bloch, J. & Yamamoto, Y. Condensation of semiconductor microcavity exciton polaritons. Science 298 (2002).
Balili, R., Hartwell, V., Snoke, D., Pfeiffer, L. & West, K. Bose–Einstein condensation of microcavity polaritons in a trap. Science 316 (2007).
High, A. A. et al. Spontaneous coherence in a cold exciton gas. Nature 483, 584–588 (2012).
Seamons, J. A., Morath, C. P., Reno, J. L. & Lilly, M. P. Coulomb drag in the exciton regime in electron–hole bilayers. Phys. Rev. Lett. 102, 26804 (2009).
Yang, K. et al. Quantum ferromagnetism and phase transitions in double-layer quantum Hall systems. Phys. Rev. Lett. 72, 732–735 (1994).
Moon, K. et al. Spontaneous interlayer coherence in double-layer quantum Hall systems: charged vortices and Kosterlitz–Thouless phase transitions. Phys. Rev. B 51, 5138–5170 (1995).
Gorbachev, R. V. et al. Strong Coulomb drag and broken symmetry in double-layer graphene. Nat. Phys. 8, 896–901 (2012).
Liu, X. et al. Coulomb drag in graphene quantum Hall double-layers. Preprint at http://arxiv.org/abs/1612.08308 (2016).
Li, J. I. A. et al. Negative Coulomb drag in double bilayer graphene. Phys. Rev. Lett. 117, 46802 (2016).
Lee, K. et al. Giant frictional drag in double bilayer graphene heterostructures. Phys. Rev. Lett. 117, 46803 (2016).
Min, H., Bistritzer, R., Su, J.-J. & MacDonald, A. Room-temperature superfluidity in graphene bilayers. Phys. Rev. B 78, 121401 (2008).
Kharitonov, M. & Efetov, K. Electron screening and excitonic condensation in double-layer graphene systems. Phys. Rev. B 78, 241401 (2008).
Perali, A., Neilson, D. & Hamilton, A. R. High-temperature superfluidity in double-bilayer graphene. Phys. Rev. Lett. 110, 146803 (2013).
Skinner, B. Interlayer excitons with tunable dispersion relation. Phys. Rev. B 93, 2 (2016).
Lee, G. H. Electron tunneling through atomically flat and ultrathin hexagonal boron nitride. Appl. Phys. Lett. 99, 243114 (2011).
Narozhny, B. N. & Levchenko, A. Coulomb drag. Rev. Mod. Phys. 88, 25003 (2016).
Wen, X.-G. & Zee, A. Neutral superfluid modes and ‘magnetic’ monopoles in multilayered quantum Hall systems. Phys. Rev. Lett. 69, 1811–1814 (1992).
Champagne, A. R., Finck, A. D. K., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Charge imbalance and bilayer two-dimensional electron systems at νT = 1. Phys. Rev. B 78, 205310 (2008).
Kou, A. et al. Electron–hole asymmetric integer and fractional quantum Hall effect in bilayer graphene. Science 345, 55–57 (2014).
Lambert, J. & Côté, R. Quantum Hall ferromagnetic phases in the Landau level N = 0 of a graphene bilayer. Phys. Rev. B 87, 115415 (2013).
Maher, P. et al. Bilayer graphene. Tunable fractional quantum Hall phases in bilayer graphene. Science 345, 61–64 (2014).
Lee, K. et al. Chemical potential and quantum Hall ferromagnetism in bilayer graphene. Science 345, 58–61 (2014).
Hunt, B. M. et al. Competing valley, spin, and orbital symmetry breaking in bilayer graphene. Preprint at http://arxiv.org/abs/1607.06461 (2016).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
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).
Kellogg, M. Evidence for Excitonic Superfluidity in a Bilayer Two-Dimensional Electron System thesis (2005).
We thank A. Yacoby, A. Macdonald, A. Young and L. Anderson for helpful discussions. 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 the MEXT, Japan. T.T. acknowledges support from a Grant-in-Aid for Scientific Research on Grant262480621 and on Innovative Areas ‘Nano Informatics’ (Grant 25106006) from JSPS. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by 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 an NSF NNIN award ECS-00335765.
The authors declare no competing financial interests.
About this article
Cite this article
Liu, X., Watanabe, K., Taniguchi, T. et al. Quantum Hall drag of exciton condensate in graphene. Nature Phys 13, 746–750 (2017) doi:10.1038/nphys4116
Physical Review Letters (2019)
Physical Review Letters (2019)
Nature Communications (2019)
Physical Review B (2019)
Nature Physics (2019)