Evidence of high-temperature exciton condensation in two-dimensional atomic double layers

Abstract

A Bose–Einstein condensate is the ground state of a dilute gas of bosons, such as atoms cooled to temperatures close to absolute zero1. With much smaller mass, excitons (bound electron–hole pairs) are expected to condense at considerably higher temperatures2,3,4,5,6,7. Two-dimensional van der Waals semiconductors with very strong exciton binding are ideal systems for the study of high-temperature exciton condensation. Here we study electrically generated interlayer excitons in MoSe2–WSe2 atomic double layers with a density of up to 1012 excitons per square centimetre. The interlayer tunnelling current depends only on the exciton density, which is indicative of correlated electron–hole pair tunnelling8. Strong electroluminescence arises when a hole tunnels from WSe2 to recombine with an electron in MoSe2. We observe a critical threshold dependence of the electroluminescence intensity on exciton density, accompanied by super-Poissonian photon statistics near the threshold, and a large electroluminescence enhancement with a narrow peak at equal electron and hole densities. The phenomenon persists above 100 kelvin, which is consistent with the predicted critical condensation temperature9,10,11,12. Our study provides evidence for interlayer exciton condensation in two-dimensional atomic double layers and opens up opportunities for exploring condensate-based optoelectronics and exciton-mediated high-temperature superconductivity13.

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Fig. 1: Electrical generation of high-density exciton gases.
Fig. 2: Tunnelling characteristics and correlated pair tunnelling.
Fig. 3: Threshold dependence of electroluminescence on exciton density at 3.5 K.
Fig. 4: Effect of electron–hole density imbalance.
Fig. 5: Temperature dependence of electroluminescence.

Data availability

The data shown in the figures and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. 1.

    Cornell, E. A. & Wieman, C. E. Nobel lecture: Bose–Einstein condensation in a dilute gas, the first 70 years and some recent experiments. Rev. Mod. Phys. 74, 875–893 (2002).

    ADS  CAS  Article  Google Scholar 

  2. 2.

    Snoke, D. Spontaneous Bose coherence of excitons and polaritons. Science 298, 1368–1372 (2002).

    ADS  CAS  Article  Google Scholar 

  3. 3.

    Eisenstein, J. P. & MacDonald, A. H. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004).

    ADS  CAS  Article  Google Scholar 

  4. 4.

    Butov, L. V. Condensation and pattern formation in cold exciton gases in coupled quantum wells. J. Phys. Condens. Matter 16, R1577–R1613 (2004).

    ADS  CAS  Article  Google Scholar 

  5. 5.

    Butov, L. V. Cold exciton gases in coupled quantum well structures. J. Phys. Condens. Matter 19, 295202 (2007).

    CAS  Article  Google Scholar 

  6. 6.

    Snoke, D. & Littlewood, P. Polariton condensates. Phys. Today 63, 42–47 (2010).

    CAS  Article  Google Scholar 

  7. 7.

    Deng, H., Haug, H. & Yamamoto, Y. Exciton–polariton Bose–Einstein condensation. Rev. Mod. Phys. 82, 1489–1537 (2010).

    ADS  CAS  Article  Google Scholar 

  8. 8.

    Xie, M. & MacDonald, A. H. Electrical reservoirs for bilayer excitons. Phys. Rev. Lett. 121, 067702 (2018).

    ADS  CAS  Article  Google Scholar 

  9. 9.

    Fogler, M. M., Butov, L. V. & Novoselov, K. S. High-temperature superfluidity with indirect excitons in van der Waals heterostructures. Nat. Commun. 5, 4555 (2014).

    ADS  CAS  Article  Google Scholar 

  10. 10.

    Wu, F.-C., Xue, F. & MacDonald, A. H. Theory of two-dimensional spatially indirect equilibrium exciton condensates. Phys. Rev. B 92, 165121 (2015).

    ADS  Article  Google Scholar 

  11. 11.

    Berman, O. L. & Kezerashvili, R. Y. High-temperature superfluidity of the two-component Bose gas in a transition metal dichalcogenide bilayer. Phys. Rev. B 93, 245410 (2016).

    ADS  Article  Google Scholar 

  12. 12.

    Debnath, B., Barlas, Y., Wickramaratne, D., Neupane, M. R. & Lake, R. K. Exciton condensate in bilayer transition metal dichalcogenides: strong coupling regime. Phys. Rev. B 96, 174504 (2017).

    ADS  Article  Google Scholar 

  13. 13.

    Lozovik, Yu. E. & Yudson, V. I. A new mechanism for superconductivity: pairing between spatially separated electrons and holes. Zh. Eksp. Teor. Fiz. 71, 738–753 (1976).

    Google Scholar 

  14. 14.

    Li, J. I. A., Taniguchi, T., Watanabe, K., Hone, J. & Dean, C. R. Excitonic superfluid phase in double bilayer graphene. Nat. Phys. 13, 751–755 (2017).

    CAS  Article  Google Scholar 

  15. 15.

    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).

    CAS  Article  Google Scholar 

  16. 16.

    Burg, G. W. et al. Strongly enhanced tunneling at total charge neutrality in double-bilayer graphene–WSe2 heterostructures. Phys. Rev. Lett. 120, 177702 (2018).

    ADS  CAS  Article  Google Scholar 

  17. 17.

    Kogar, A. et al. Signatures of exciton condensation in a transition metal dichalcogenide. Science 358, 1314–1317 (2017).

    ADS  CAS  Article  Google Scholar 

  18. 18.

    Mak, K. F. & Shan, J. Photonics and optoelectronics of 2D semiconductor transition metal dichalcogenides. Nat. Photon. 10, 216–226 (2016).

    ADS  CAS  Article  Google Scholar 

  19. 19.

    Keldysh, L. V. The electron–hole liquid in semiconductors. Contemp. Phys. 27, 395–428 (1986).

    ADS  CAS  Article  Google Scholar 

  20. 20.

    Rivera, P. et al. Interlayer valley excitons in heterobilayers of transition metal dichalcogenides. Nat. Nanotechnol. 13, 1004–1015 (2018).

    ADS  CAS  Article  Google Scholar 

  21. 21.

    Wang, Z., Shan, J. & Mak, K. F. Valley- and spin-polarized Landau levels in monolayer WSe2. Nat. Nanotechnol. 12, 144–149 (2017).

    ADS  CAS  Article  Google Scholar 

  22. 22.

    Fang, H. et al. Strong interlayer coupling in van der Waals heterostructures built from single-layer chalcogenides. Proc. Natl Acad. Sci. USA 111, 6198–6202 (2014).

    ADS  CAS  Article  Google Scholar 

  23. 23.

    Hanamura, E. Superradiance from p–n junction of hole- and electron-superconductors. Phys. Status Solidi B 234, 166–171 (2002).

    ADS  CAS  Article  Google Scholar 

  24. 24.

    Hayashi, Y. et al. Superconductor-based light emitting diode: demonstration of role of Cooper pairs in radiative recombination processes. Appl. Phys. Express 1, 011701 (2008).

    ADS  Article  Google Scholar 

  25. 25.

    Van der Donck, M. & Peeters, F. M. Interlayer excitons in transition metal dichalcogenide heterostructures. Phys. Rev. B 98, 115104 (2018).

    ADS  Article  Google Scholar 

  26. 26.

    DeGiorgio, V. & Scully, M. O. Analogy between the laser threshold region and a second-order phase transition. Phys. Rev. A 2, 1170–1177 (1970).

    ADS  Article  Google Scholar 

  27. 27.

    Graham, R. & Haken, H. Laserlight — first example of a second-order phase transition far away from thermal equilibrium. Z. Phys. 237, 31–46 (1970).

    ADS  CAS  Article  Google Scholar 

  28. 28.

    Hu, B. Y.-K. Prospecting for the superfluid transition in electron–hole coupled quantum wells using Coulomb drag. Phys. Rev. Lett. 85, 820–823 (2000).

    ADS  CAS  Article  Google Scholar 

  29. 29.

    Morath, C. P., Seamons, J. A., Reno, J. L. & Lilly, M. P. Density imbalance effect on the Coulomb drag upturn in an undoped electron–hole bilayer. Phys. Rev. B 79, 041305 (2009).

    ADS  Article  Google Scholar 

  30. 30.

    Efimkin, D. K. & Galitski, V. Anomalous Coulomb drag in electron–hole bilayers due to the formation of excitons. Phys. Rev. Lett. 116, 046801 (2016).

    ADS  Article  Google Scholar 

  31. 31.

    High, A. A. et al. Spontaneous coherence in a cold exciton gas. Nature 483, 584–588 (2012).

    ADS  CAS  Article  Google Scholar 

  32. 32.

    Anankine, R. et al. Quantized vortices and four-component superfluidity of semiconductor excitons. Phys. Rev. Lett. 118, 127402 (2017).

    ADS  Article  Google Scholar 

  33. 33.

    Dang, S. et al. Defect proliferation at the quasicondensate crossover of two-dimensional dipolar excitons trapped in coupled GaAs quantum wells. Phys. Rev. Lett. 122, 117402 (2019).

    ADS  CAS  Article  Google Scholar 

  34. 34.

    Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    ADS  CAS  Article  Google Scholar 

  35. 35.

    Gustafsson, M. V. et al. Ambipolar Landau levels and strong band-selective carrier interactions in monolayer WSe2. Nat. Mater. 17, 411–415 (2018).

    ADS  CAS  Article  Google Scholar 

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Acknowledgements

We thank A. H. MacDonald, M. Gilbert, H. Deng and D. W. Snoke for discussions. Research was primarily supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under award number DE-SC0019481 (optical spectroscopy) and DE-SC0013883 (device fabrication). Synthesis of WSe2 and MoSe2 bulk crystals was supported by the National Science Foundation Materials Research Science and Engineering Centers programme through the Center for Precision Assembly of Superstratic and Superatomic Solids of Columbia University (DMR-1420634). The growth of hBN crystals was supported by the Elemental Strategy Initiative of MEXT, Japan and CREST (JPMJCR15F3), JST. K.F.M. also acknowledges support from a David and Lucille Packard Fellowship and a Sloan Fellowship.

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Contributions

Z.W. fabricated the devices, developed the experimental setup and performed the measurements. D.A.R. and J.C.H. grew the bulk TMD crystals, and K.W. and T.T. grew the bulk hBN crystals. K.F.M., J.S. and Z.W. designed the study, performed the analysis and co-wrote the manuscript. All authors discussed the results and commented on the manuscript.

Corresponding authors

Correspondence to Jie Shan or Kin Fai Mak.

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The authors declare no competing interests.

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Peer review information Nature thanks Andrey Chaves, Francois Dubin and Galan Moody for their contribution to the peer review of this work.

Extended data figures and tables

Extended Data Fig. 1 Electroluminescence image.

Optical reflection image (left) and electroluminescence image (right) of device 1. The latter was measured at a fixed exciton density above threshold (N = 0.79 × 102 cm−2). The colour bar shows the number of electroluminescence photons.

Extended Data Fig. 2 Analysis of electroluminescence spectra.

a, Electroluminescence (EL) spectra at different charge imbalance values. The total density is fixed at 1.34 × 1012 cm−2. b, c, Energy-averaged electroluminescence peak energy (b) and linewidth (c) as a function of normalized density imbalance, (n – p)/(n + p), for three fixed total charge densities. The linewidth is minimum at charge balance. d, e, Energy-averaged electroluminescence peak energy (d) and linewidth (e) as a function of exciton density N at charge balance. The dashed lines mark Nth. Although both the electroluminescence peak energy and linewidth depend on N, no clear threshold behaviour is seen.

Extended Data Fig. 3 Effect of charge imbalance on g(2)(0).

Electroluminescence intensity (upper panel, left axis), intensity correlation at zero delay time g(2)(0) (upper panel, right axis) and normalized neutral exciton reflection contrast of the double layer (lower panel) as a function of charge imbalance near the threshold. The total charge density is fixed at 0.51 × 1012 cm−2. Photon bunching can only be observed near charge balance.

Extended Data Fig. 4 Additional results for device 1 (basic characterization).

a, Normalized neutral exciton reflection contrast of the double layer as a function of charge imbalance at different total densities. b, The corresponding electroluminescence intensity (left) and tunnelling current (right) as a function of charge imbalance.

Extended Data Fig. 5 Additional results for device 1 (electroluminescence).

a, Intensity correlation function g(2)(τ) at various exciton densities. Curves are displaced vertically for clarity. Clear non-Poissonian statistics is seen near the threshold. Correlation with a longer decay time and extra oscillations are observed in this device compared to device 2. Further investigations are required to understand the microscopic mechanism responsible for these differences. b, Dependence of electroluminescence intensity and g(2)(0) on exciton density. c, Density imbalance dependence of the electroluminescence intensity and g(2)(0) (upper panel) and the normalized neutral exciton reflection contrast (lower panel) near the threshold. The total density is fixed at 1.18 × 1012 cm−2. Photon bunching is observed only near charge balance.

Extended Data Fig. 6 Comparison between experiment and electrostatic model.

a, Dependence of the normalized reflection contrast of the neutral exciton resonance in MoSe2 (dashed lines) and WSe2 (solid lines) monolayers on gate voltage for different bias voltages. When the TMDs are doped, the reflection contrast decreases like a broadened step function, reflecting the reduced oscillation strength of the neutral excitons. b, Bias and gate voltage combinations corresponding to n = p (grey symbols), p = 0 (red symbols) and n = 0 (blue symbols). The solid lines are a guide to the eye. The dashed lines are predictions of the electrostatic model (see equations (3)–(5)).

Extended Data Fig. 7 Photoluminescence.

a, Contour plot of photoluminescence (PL) spectra versus gate voltage in a double-layer device with a three-layer hBN barrier (the photoluminescence intensity is shown on a logarithmic scale). Interlayer exciton photoluminescence (around 1.4 eV) is absent owing to the negligible oscillator strength. b, Photoluminescence spectra at three representative gate voltages.

Extended Data Fig. 8 Dependence of electroluminescence on MoSe2–WSe2 alignment angle.

a, b, Dependence of electroluminescence intensity on exciton density (a) and on temperature (b) at charge balance for two different types of devices, one with a small (2°–5°) misalignment and the other with a large (20°) misalignment. The temperature in a is 4 K and the exciton density in b is about 0.74 × 1012 cm−2.

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Wang, Z., Rhodes, D.A., Watanabe, K. et al. Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nature 574, 76–80 (2019). https://doi.org/10.1038/s41586-019-1591-7

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