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