Quantum Hall drag of exciton condensate in graphene

Journal name:
Nature Physics
Volume:
13,
Pages:
746–750
Year published:
DOI:
doi:10.1038/nphys4116
Received
Accepted
Published online

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.

At a glance

Figures

  1. Quantized Hall drag for [nu]tot = 1 state in bilayer graphene double layers.
    Figure 1: Quantized Hall drag for νtot = 1 state in bilayer graphene double layers.

    a, Schematic diagram of device and measurement set-up. b, Optical microscope image of the device. Metal leads on the left and right of the image (three on each side) contact the top layer graphene, while others contact the bottom layer graphene. The blue shaded area of graphene is under the top gate; white and green shaded regions are under the contact gate. The contact gates support highly transparent electrical contacts under high magnetic fields, providing reliable data away from the ν = 0 insulating state. cRxydrag, Rxxdrag, Rxydrive as a function of filling factors of both layers at B = 25T and T = 300mK. The exciton BEC can be recognized by near-quantized Hall drag (Rxydrag = h/e2, Rxxdrag = 0) with the simultaneous re-entrant quantum Hall in the drive layer. (Inset) Temperature dependence (T = 0.9, 2.29, 3.13, 4.35, 6, 8, 10K) of Rxydrag at B = 25T. df, Rxydrag, −Rxxdrag, Rxydrive, respectively, as a function of filling fractions νtop and νbot, computed from VTG and VBG. The exciton BEC region appears as a diagonal region satisfying νtop + νbot = 1. The white trace in d shows the value of Rxydrag (axis on the left) along the νtot = 1 line (dashed line in d). For further quantitative analysis, we also present several traces of the colour plot in Supplementary Fig. 11.

  2. Exciton BEC in various LL fillings.
    Figure 2: Exciton BEC in various LL fillings.

    a, Rxy drag as a function of the top and bottom layer filling factors at B = 25T, T = 300mK and Vint = −0.05V. Besides (νdrag, νdrive) = (0.5, 0.5), a different exciton BEC state is found near (0.5, 2.5). bd, Zoomed-in plot of Rxydrag, Rxxdrag, Rxydrive, respectively, around νtot = 3 at a higher field of B = 31T. e, Line-cuts of Rxydrag, Rxxdrag, Rxydrive along the dashed lines shown in bd, respectively. f, Rxydrag as function of filling factors at B = 25T, T = 300mK and Vint = 0.15V. Additional exciton BEC state in the hole–hole regime is identified around (νdrag, νdrive) = (−1.5, −1.5). gjRxydrag, Rxxdrag, Rxydrive, Rxxdrive, respectively, at the same condition as f. k, Line-cuts of Rxydrag, Rxxdrag, Rxydrive, Rxxdrive along the dashed lines shown in gj, respectively. The horizontal dashed lines in e and k indicate ±(h/3e2), to which Rxydrag and Rxydrive are expected to be quantized.

  3. Phase transition of [nu]tot = 1 exciton BEC induced by transverse electric field.
    Figure 3: Phase transition of νtot = 1 exciton BEC induced by transverse electric field.

    a, Schematic diagram of Landau levels sequence (left) and wavefunctions (right) of bilayer graphene QHFM states for the lowest LL corresponding to −4 < ν < 4. In the left diagram, the x direction represents the displacement field D and coloured lines denote QHFM Landau levels with different orbital (0/1), layer (+/−) and spin ( / ) quantum numbers, as noted next to the lines. Different colours are used for different orbital and layer quantum numbers. As the displacement field changes, the coloured lines cross each other, representing QHFM transitions induced by the displacement field. The horizontal black dashed line marks charge neutrality (ν = 0) and the horizontal white dashed line marks the Fermi level of the half-filled first LL (ν = 1/2). The diagram on the right depicts wavefunctions of different bilayer graphene QHFM states, with the same colour code as the lines in the left diagram. b (d), Longitudinal resistance of top (bottom) bilayer graphene as a function of displacement Dtop (Dbot) and density ntop (nbot) at B = 13T and T = 1.5K. The QHFM transitions are marked with arrows. The data in b is taken at a fixed VBG = −5.5V and the data in d is taken at VTG = −1.1V. c, Rxydrag (blue curve) as a function of Dtop (top axis of b) or Dbot (bottom axis of d) for νtot = 1 state at B = 13T and T = 1.5K. Each data point is taken at a different Vint, with VBG and VTG tuned around νtot = 1 to maximize Rxydrag (filling factor νtop, νbot calculated from the gate voltages are marked by the horizontal dashed line in b and d). The coloured bars on the top and bottom of the plot represent orbital and layer character of the half-filled LL (ν = 1/2) of the top and bottom bilayer graphene with the same colour code as a. The orange and green shaded regions of the main plot which signify N = 1 orbital states of the top and bottom layer coincide well with where the Hall drag vanishes, indicating the N = 1 orbit is incapable of forming the exciton BEC phase.

References

  1. Littlewood, P. B. et al. Models of coherent exciton condensation. J. Phys. Condens. Matter 16, S3597S3620 (2004).
  2. Snoke, D. et al. Spontaneous Bose coherence of excitons and polaritons. Science 298, 13681372 (2002).
  3. Eisenstein, J. & MacDonald, A. Bose–Einstein condensation of excitons in bilayer electron systems. Nature691694 (2004).
  4. Eisenstein, J. P. Exciton condensation in bilayer quantum Hall systems. Annu. Rev. Condens. Matter Phys. 5, 159181 (2014).
  5. 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, 58085811 (2000).
  6. 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).
  7. 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).
  8. 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).
  9. Nandi, D., Finck, A. D. K., Eisenstein, J. P., Pfeiffer, L. N. & West, K. W. Exciton condensation and perfect Coulomb drag. Nature 488, 481484 (2012).
  10. Kasprzak, J. et al. Bose–Einstein condensation of exciton polaritons. Nature 443, 409414 (2006).
  11. Byrnes, T., Kim, N. Y. & Yamamoto, Y. Exciton–polariton condensates. Nat. Phys. 10, 803813 (2014).
  12. Deng, H., Weihs, G., Santori, C., Bloch, J. & Yamamoto, Y. Condensation of semiconductor microcavity exciton polaritons. Science 298 (2002).
  13. Balili, R., Hartwell, V., Snoke, D., Pfeiffer, L. & West, K. Bose–Einstein condensation of microcavity polaritons in a trap. Science 316 (2007).
  14. High, A. A. et al. Spontaneous coherence in a cold exciton gas. Nature 483, 584588 (2012).
  15. 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).
  16. Yang, K. et al. Quantum ferromagnetism and phase transitions in double-layer quantum Hall systems. Phys. Rev. Lett. 72, 732735 (1994).
  17. Moon, K. et al. Spontaneous interlayer coherence in double-layer quantum Hall systems: charged vortices and Kosterlitz–Thouless phase transitions. Phys. Rev. B 51, 51385170 (1995).
  18. Gorbachev, R. V. et al. Strong Coulomb drag and broken symmetry in double-layer graphene. Nat. Phys. 8, 896901 (2012).
  19. Liu, X. et al. Coulomb drag in graphene quantum Hall double-layers. Preprint at http://arxiv.org/abs/1612.08308 (2016).
  20. Li, J. I. A. et al. Negative Coulomb drag in double bilayer graphene. Phys. Rev. Lett. 117, 46802 (2016).
  21. Lee, K. et al. Giant frictional drag in double bilayer graphene heterostructures. Phys. Rev. Lett. 117, 46803 (2016).
  22. Min, H., Bistritzer, R., Su, J.-J. & MacDonald, A. Room-temperature superfluidity in graphene bilayers. Phys. Rev. B 78, 121401 (2008).
  23. Kharitonov, M. & Efetov, K. Electron screening and excitonic condensation in double-layer graphene systems. Phys. Rev. B 78, 241401 (2008).
  24. Perali, A., Neilson, D. & Hamilton, A. R. High-temperature superfluidity in double-bilayer graphene. Phys. Rev. Lett. 110, 146803 (2013).
  25. Skinner, B. Interlayer excitons with tunable dispersion relation. Phys. Rev. B 93, 2 (2016).
  26. Lee, G. H. Electron tunneling through atomically flat and ultrathin hexagonal boron nitride. Appl. Phys. Lett. 99, 243114 (2011).
  27. Narozhny, B. N. & Levchenko, A. Coulomb drag. Rev. Mod. Phys. 88, 25003 (2016).
  28. Wen, X.-G. & Zee, A. Neutral superfluid modes and ‘magnetic’ monopoles in multilayered quantum Hall systems. Phys. Rev. Lett. 69, 18111814 (1992).
  29. 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).
  30. Kou, A. et al. Electron–hole asymmetric integer and fractional quantum Hall effect in bilayer graphene. Science 345, 5557 (2014).
  31. Lambert, J. & Côté, R. Quantum Hall ferromagnetic phases in the Landau level N = 0 of a graphene bilayer. Phys. Rev. B 87, 115415 (2013).
  32. Maher, P. et al. Bilayer graphene. Tunable fractional quantum Hall phases in bilayer graphene. Science 345, 6164 (2014).
  33. Lee, K. et al. Chemical potential and quantum Hall ferromagnetism in bilayer graphene. Science 345, 5861 (2014).
  34. Hunt, B. M. et al. Competing valley, spin, and orbital symmetry breaking in bilayer graphene. Preprint at http://arxiv.org/abs/1607.06461 (2016).
  35. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614617 (2013).
  36. Hill, N. P. R. et al. Frictional drag between parallel two-dimensional electron gases in a perpendicular magnetic field. J. Phys. Condens. Matter 8, L557L562 (1996).
  37. Kellogg, M. Evidence for Excitonic Superfluidity in a Bilayer Two-Dimensional Electron System thesis (2005).

Download references

Author information

Affiliations

  1. Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

    • Xiaomeng Liu,
    • Bertrand I. Halperin &
    • Philip Kim
  2. National Institute for Material Science, 1-1 Namiki, Tsukuba 305-0044, Japan

    • Kenji Watanabe &
    • Takashi Taniguchi

Contributions

X.L. performed the experiments and analysed the data. X.L. and P.K. conceived the experiment. X.L., B.I.H. and P.K. wrote the paper. K.W. and T.T. provided hBN crystals.

Competing financial interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to:

Author details

Supplementary information

PDF files

  1. Supplementary information (1,200 KB)

    Supplementary information

Additional data