Two-component exciton condensates in an electron–hole bilayer

Abstract Macroscopic quantum coherence emerges when bosons condense into a Bose–Einstein condensate (BEC)1,2,3,4,5. Excitons are a long-sought solid-state route to high-temperature BECs with strong interactions, electrical tunability and potentially multicomponent spinor order, but conclusive evidence for equilibrium condensation has remained elusive. Here we report evidence for two-component exciton BECs in MoSe2/hBN/WSe2 electron–hole bilayers6,7,8,9 by probing the spin–valley susceptibility of constituent electrons and holes. This heterostructure hosts equilibrium exciton fluids with four spin–valley flavours. Magneto-optical spectroscopy in a dilution refrigerator reveals three exciton condensate phases with distinct flavour polarizations. At zero magnetic field, the many-body ground state is a coherent superposition of two condensed intravalley exciton flavours. Under a magnetic field, the intravalley exciton condensate first switches to a two-component intervalley condensate through a first-order quantum phase transition at a weak critical field and then turns into a fully polarized single-component condensate at high fields. The condensate signatures form a dome in density–temperature space, persisting up to approximately 1.8 K. Our results establish van der Waals electron–hole bilayers as a versatile platform for strongly interacting, multicomponent exciton BECs. This is a preview of subscription content, access via your institution Access options Access Nature and 54 other Nature Portfolio journals Get Nature+, our best-value online-access subscription £17.99 / 30 days cancel any time Subscribe to this journal Receive 52 print issues and online access £199.00 per year only £3.83 per issue Buy this article - Purchase on SpringerLink - Instant access to the full article PDF. £ 29.95 Prices may be subject to local taxes which are calculated during checkout Data availability Datasets that support the findings of this study are available from the corresponding authors upon request. Source data are provided with this paper. Code availability The custom code used for minimizing the interacting boson model Hamiltonian is available at https://github.com/ruishiqi/InteractingBosonModel. References Stamper-Kurn, D. M. & Ueda, M. Spinor Bose gases: symmetries, magnetism, and quantum dynamics. Rev. Mod. Phys. 85, 1191–1244 (2013). Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E. & Cornell, E. A. Observation of Bose-Einstein condensation in a dilute atomic vapor. Science 269, 198–201 (1995). Davis, K. B. et al. Bose-Einstein condensation in a gas of sodium atoms. Phys. Rev. Lett. 75, 3969–3973 (1995). Kapitza, P. Viscosity of liquid helium below the λ-point. Nature 141, 74 (1938). Allen, J. F. & Misener, A. D. Flow of liquid helium II. Nature 141, 75 (1938). Ma, L. et al. Strongly correlated excitonic insulator in atomic double layers. Nature 598, 585–589 (2021). Qi, R. et al. Thermodynamic behavior of correlated electron-hole fluids in van der Waals heterostructures. Nat. Commun. 14, 8264 (2023). Qi, R. et al. Perfect Coulomb drag and exciton transport in an excitonic insulator. Science 388, 278–283 (2025). Nguyen, P. X. et al. Perfect Coulomb drag in a dipolar excitonic insulator. Science 388, 274–278 (2025). Keldysh, L. V. & Kopaev, Y. V. Possible instability of the semimetallic state toward Coulomb interaction. Fiz. Tverd. Tela 6, 2791–2798 (1964). Zhu, X., Littlewood, P. B., Hybertsen, M. S. & Rice, T. M. Exciton condensate in semiconductor quantum well structures. Phys. Rev. Lett. 74, 1633–1636 (1995). 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). Wu, F.-C., Xue, F. & MacDonald, A. H. Theory of two-dimensional spatially indirect equilibrium exciton condensates. Phys. Rev. B 92, 165121 (2015). Fernández-Rossier, J. Spin degree of freedom in two dimensional exciton condensates. Phys. Rev. Lett. 78, 4809–4812 (1997). Moon, B. H., Mondal, A., Efimkin, D. K. & Lee, Y. H. Exciton condensate in van der Waals layered materials. Nat. Rev. Phys. 7, 388–401 (2025). Osheroff, D. D., Gully, W. J., Richardson, R. C. & Lee, D. M. New magnetic phenomena in liquid He3 below 3 mK. Phys. Rev. Lett. 29, 920–923 (1972). Osheroff, D. D., Richardson, R. C. & Lee, D. M. Evidence for a new phase of solid He3. Phys. Rev. Lett. 28, 885–888 (1972). O’Hara, K. E. Strong nonradiative recombination of excitons in Cu2O and its impact on Bose-Einstein statistics. Phys. Rev. B 60, 10565–10568 (1999). Butov, L. V., Lai, C. W., Ivanov, A. L., Gossard, A. C. & Chemla, D. S. Towards Bose–Einstein condensation of excitons in potential traps. Nature 417, 47–52 (2002). Kaneko, T. & Ohta, Y. A new era of excitonic insulators. J. Phys. Soc. Jpn. 94, 012001 (2025). Sun, B. et al. Evidence for equilibrium exciton condensation in monolayer WTe2. Nat. Phys. 18, 94–99 (2022). Jia, Y. et al. Evidence for a monolayer excitonic insulator. Nat. Phys. 18, 87–93 (2022). 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. A., Taniguchi, T., Watanabe, K., Hone, J. & Dean, C. R. Excitonic superfluid phase in double bilayer graphene. Nat. Phys. 13, 751–755 (2017). Eisenstein, J. P. Exciton condensation in bilayer quantum Hall systems. Annu. Rev. Condens. Matter Phys. 5, 159–181 (2014). Eisenstein, J. P. & MacDonald, A. H. Bose–Einstein condensation of excitons in bilayer electron systems. Nature 432, 691–694 (2004). 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, 036801 (2004). Zeng, Y. & MacDonald, A. H. Electrically controlled two-dimensional electron-hole fluids. Phys. Rev. B 102, 085154 (2020). Nguyen, P. X. et al. Quantum oscillations in a dipolar excitonic insulator. Nat. Mater. 25, 42–48 (2026). Qi, R. et al. Competition between excitonic insulators and quantum Hall states in correlated electron–hole bilayers. Nat. Mater. 25, 35–41 (2026). Qi, R. et al. Electrically controlled interlayer trion fluid in electron-hole bilayers. Science 390, 299–303 (2025). Nguyen, P. X. et al. An equilibrium trion liquid in atomic double layers. Science 390, 304–307 (2025). Neilson, D., Perali, A. & Hamilton, A. R. Excitonic superfluidity and screening in electron-hole bilayer systems. Phys. Rev. B 89, 060502 (2014). Xu, X., Yao, W., Xiao, D. & Heinz, T. F. Spin and pseudospins in layered transition metal dichalcogenides. Nat. Phys. 10, 343–350 (2014). Xiao, D., Liu, G.-B., Feng, W., Xu, X. & Yao, W. Coupled spin and valley physics in monolayers of MoS2 and other group-VI dichalcogenides. Phys. Rev. Lett. 108, 196802 (2012). Kittel, C. Introduction to Solid State Physics (Wiley, 2018). Blundell, S. Magnetism in Condensed Matter (Oxford Univ. Press, 2001). Smoleński, T. et al. Signatures of Wigner crystal of electrons in a monolayer semiconductor. Nature 595, 53–57 (2021). Sung, J. et al. An electronic microemulsion phase emerging from a quantum crystal-to-liquid transition. Nat. Phys. 21, 437–443 (2025). Maezono, R., López Ríos, P., Ogawa, T. & Needs, R. J. Excitons and biexcitons in symmetric electron-hole bilayers. Phys. Rev. Lett. 110, 216407 (2013). Fisher, D. S. & Hohenberg, P. C. Dilute Bose gas in two dimensions. Phys. Rev. B 37, 4936–4943 (1988). Prokof’ev, N., Ruebenacker, O. & Svistunov, B. Critical point of a weakly interacting two-dimensional Bose gas. Phys. Rev. Lett. 87, 270402 (2001). Filinov, A., Prokof’ev, N. V. & Bonitz, M. Berezinskii-Kosterlitz-Thouless transition in two-dimensional dipole systems. Phys. Rev. Lett. 105, 070401 (2010). Combescot, M., Combescot, R., Alloing, M. & Dubin, F. Effects of fermion exchange on the polarization of exciton condensates. Phys. Rev. Lett. 114, 090401 (2015). Edelberg, D. et al. Approaching the intrinsic limit in transition metal diselenides via point defect control. Nano Lett. 19, 4371–4379 (2019). Kobayashi, M. Berezinskii-Kosterlitz-Thouless transition of two-component Bose mixtures with intercomponent Josephson coupling. Phys. Rev. Lett. 123, 075303 (2019). 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). Robert, C. et al. Measurement of conduction and valence bands g-factors in a transition metal dichalcogenide monolayer. Phys. Rev. Lett. 126, 067403 (2021). Deilmann, T., Krüger, P. & Rohlfing, M. Ab initio studies of exciton g factors: monolayer transition metal dichalcogenides in magnetic fields. Phys. Rev. Lett. 124, 226402 (2020). Larentis, S. et al. Large effective mass and interaction-enhanced Zeeman splitting of K-valley electrons in MoSe2. Phys. Rev. B 97, 201407 (2018). Gustafsson, M. V. et al. Ambipolar Landau levels and strong band-selective carrier interactions in monolayer WSe2. Nat. Mater. 17, 411–415 (2018). Zhou, J., Shan, W.-Y., Yao, W. & Xiao, D. Berry phase modification to the energy spectrum of excitons. Phys. Rev. Lett. 115, 166803 (2015). Acknowledgements We thank M. Zaletel, T. Wang and Z. Dong for insightful discussions. Funding This study was primarily funded by the US Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division under contract number DE-AC02-05-CH11231 within the van der Waals heterostructure program KCFW16 (device fabrication and dilution refrigerator MCD measurements). Reflection spectroscopy of the excitonic insulator was supported by the AFOSR award FA9550−23-1-0246. K.W. and T.T. acknowledge support from the JSPS KAKENHI (grant numbers 21H05233 and 23H02052), CREST (JPMJCR24A5), JST and the World Premier International Research Center Initiative, MEXT. R.Q. and H.K. acknowledge support from Kavli ENSI Graduate Student Fellowship. Author information Authors and Affiliations Contributions F.W. and R.Q. conceived the project. K.W. and T.T. synthesized the hBN crystals. Q.L., R.Q., R.X. and J.N. fabricated the devices. H.L. and J.X. assisted with twist-angle determination. R.Q., H.K. and Q.L. set up and carried out the optical measurements. R.Q. performed the theoretical calculations. R.Q., Q.L., J.N. and F.W. analysed the data, with input from M.F.C. and A.H.M. All authors discussed the results and contributed to writing the paper. Corresponding authors Ethics declarations Competing interests The authors declare no competing interests. Peer review Peer review information Nature thanks the anonymous reviewers for their contribution to the peer review of this work. Peer reviewer reports are available. Additional information Extended data figures and tables Extended Data Fig. 1 Summary of MCD results for multiple devices. Evolution of condensate phases with interlayer distance \(d\) and MoSe2-WSe2 relative rotation angle \(\theta \). Each subpanel plots the eMCD (vertical axis) versus \(B\) (horizontal axis, all in range \(-0.1\) to \(0.1\,{\rm{T}}\)) for one device, measured at exciton density \(0.4\times {10}^{12}\,{\rm{c}}{{\rm{m}}}^{-2}\). For ~60° devices, the two-component condensates exhibit the first order phase transition between IIA and IIB states. The transition critical field decreases with increasing interlayer spacing. For ~0° devices, no such transition is observed, and the condensate stays in IIB even at zero field. For devices near 30°, SHG cannot easily distinguish between 30°\(+\delta \) and 30°\(-\delta \); we therefore report the nominal angle 30° and plot \(\delta \) as the uncertainty (error bar). Extended Data Fig. 2 Main results for device D2. a, An optical image of device D2. In this device, the same TMD flakes are made into different regions with relative angle 0°, 30° and 60°. b, Interlayer tunneling current, which is still on the nanoampere scale but larger than device D1. The increased tunneling generates more heating, which likely causes a higher electron temperature for this device. c, eMCD (left axis) and hMCD (right axis) at exciton density \({n}_{{\rm{x}}}=0.2\times {10}^{12}\,{\rm{c}}{{\rm{m}}}^{-2}\), measured in the 60° region. They closely mirror each other up to the optical scale factor. d, eMCD and hMCD at pair densities 0.1, 0.5 and 0.85 × \({10}^{12}\,{\rm{c}}{{\rm{m}}}^{-2}\) for the 60° region. e, d(eMCD)/dB along the charge neutral line for the 60° region. f,g, Same data but measured in the 0° region. Phase IIA is almost unrecognizable. h,i, Same data but measured in the 30° region. Phase IIA is weak. Extended Data Fig. 3 Main results for device D3. a, An optical image of device D3. In this device, the same TMD flakes are made into two different regions with relative angle 30° and 60°. b,c, eMCD and hMCD at pair densities 0.3 and \(0.9\times {10}^{12}\,{\rm{c}}{{\rm{m}}}^{-2}\), measured in the 60° region (b) and the 30° region (c) respectively. The 60° region exhibits the IIA phase at low fields and switches to IIB at moderate fields, while the 30° region does not show such switching. Extended Data Fig. 4 Exciton condensates in an away-from-60° device (D10, 10° angle, 6-layer hBN spacer). a, Field dependence of eMCD and hMCD at exciton density \({n}_{{\rm{x}}}=0.3\times {10}^{12}{\rm{c}}{{\rm{m}}}^{-2}\). This device does not exhibit obvious features related to IIA. b, Field dependence of eMCD (left axis) and hMCD (right axis) in an extended field range. They mirror each other up to the optical scale factor. For a better comparison, the green dashed line shows –hMCD, which overlaps with the eMCD trace. c, Same as b but acquired at \(T=4\,{\rm{K}}\), which is above the condensate transition temperature. The eMCD and hMCD become independent, with holes polarizing substantially faster (saturating earlier) because of their larger g-factor. d, Temperature and density dependence of d(eMCD)/dB averaged in \(|B| < 100\,{\rm{mT}}\). A dome with enhanced susceptibility suggests the IIB condensate. Its boundary is very similar to the main device (Extended Data Fig. 9c). e, A vertical linecut through panel d at \({n}_{{\rm{x}}}=0.3\times {10}^{12}{\rm{c}}{{\rm{m}}}^{-2}\). The susceptibility shows a kink at \(T\approx 1.2\,{\rm{K}}\). The overall curve shape is similar to the window B susceptibility shown in Fig. 4b. f, Corresponding data for the hole side, with a similar enhancement dome at low temperatures. Extended Data Fig. 5 Density-dependent charge gap and exciton Mott transition. The charge gap as a function of pair density. In the dilute limit, the gap (exciton binding energy) is about 30 meV. It continuously decreases to zero at the Mott density \({n}_{{\rm{Mott}}}\approx 0.75\times {10}^{12}{\rm{c}}{{\rm{m}}}^{-2}\), beyond which the system becomes gapless. After this point, \({n}_{{\rm{x}}}\) should be interpreted as the e-h pair density rather than the exciton density. Extended Data Fig. 6 Additional data for the hole side. a,b, Comparison of density- and field-dependent hMCD signal in the 2DHG phase (a) and along the charge neutral line (b). The 2DHG exhibits linear-in-B polarization; the excitonic insulator phase has a reduced signal in IIA. c, d(hMCD)/dB as a function of \(B\) and \(T\) at \({n}_{{\rm{x}}}=0.4\times {10}^{12}{\rm{c}}{{\rm{m}}}^{-2}\). The hole susceptibility is highly correlated with the electron behavior in Fig. 4a. d, Temperature dependence of d(hMCD)/dB in the two field windows, \(|B| < 25\,{\rm{mT}}\) (corresponding to phase IIA, blue) and \(30\,{\rm{mT}} < B < 70\,{\rm{mT}}\) (phase IIB, yellow). Lower panel shows their difference. They follow the same temperature dependence as the electron susceptibility data in Fig. 4b. Extended Data Fig. 7 Interlayer tunneling. a, Interlayer tunneling current as a function of \({V}_{{\rm{G}}}\) and \({V}_{{\rm{B}}}\) (device D1). b, Tunneling current versus \({V}_{{\rm{B}}}\) along the charge neutrality line (blue dotted line in a). The tunneling current \(I\) is about 0.3 nA for a pair density of ~1012 cm−2 and heterostructure area \(A\, > \,\)100 μm2. Assuming all the current is from e-h recombination in the region of interest, the tunneling lifetime can be estimated as \(\tau \approx \frac{e{n}_{{\rm{x}}}A}{I}\approx 0.5\,{\rm{ms}}\). Extended Data Fig. 8 Additional calculation results. a, Calculated electron (red) and hole (green) spin-valley polarizations with a positive \({g}_{{\rm{X}}}=1.5\) (atomic units) and a positive splitting \(\Delta =0.3\,{\rm{\mu }}{\rm{eV}}\) favoring intravalley flavors (parameters used in the main text). Total exciton density \({n}_{{\rm{x}}}=0.4\times {10}^{12}{\rm{c}}{{\rm{m}}}^{-2}\). Inset, a magnified plot near zero field. b, Calculated condensate total energy per area for three competing condensate states: intravalley two-component condensate (IIA, blue), intervalley two-component condensate (IIB, yellow), and single-component condensate (I, pink). Inset, a magnified plot near zero field clearly showing the energy crossing between IIA and IIB. c, Condensate density in four exciton flavors. The order parameters suddenly switch from two intravalley flavors to two intervalley flavors at the energy crossing at ~30 mT. d-f, Same as a-c but with a negative \(\Delta =-0.3\,{\rm{\mu }}{\rm{eV}}\). Now phase IIB always has lower energy than IIA even at zero field. This can explain the absence of MCD suppression in near 0° devices. g-i, Same as a-c but with a smaller positive \({g}_{{\rm{X}}}=0.5\). The smaller exchange energy makes polarization faster, but qualitative features remain the same. j-l, Same as a-c but with a negative \({g}_{{\rm{X}}}=-1.5\). Two-component condensates are no longer local energy minima, so their energy cannot be calculated in k. In such single-component condensates, any infinitesimal field will lead to full valley polarization. Extended Data Fig. 9 Temperature dependence of susceptibility in 2DEG, 2DHG and excitonic insulator. a, Temperature dependence of d(eMCD)/dB at small B (\(|B| < 100\,{\rm{mT}}\)) in the 2DEG phase. b,c, Temperature dependence of d(eMCD)/dB in window A (small-B, b) and window B (moderate-B, c) along net charge neutrality. See Fig. 4 for more details. d, Comparison of d(eMCD)/dB in the 2DEG (red) and two different field windows in the excitonic insulator (blue/yellow), at a common density \(0.4\times {10}^{12}\,{\rm{c}}{{\rm{m}}}^{-2}\). The susceptibility in the 2DEG varies smoothly and saturates at low \(T\). It is slightly smaller than the susceptibility in the normal exciton fluid. It does not quantitatively follow the non-interacting Fermi liquid theory owing to strong interaction enhancement39. e, Comparison of d(hMCD)/dB in the 2DHG (green) and two different field windows in the excitonic insulator (blue/yellow). The hole susceptibility in 2DHG is smaller than that in the excitonic insulator. f-i, 2D color plots of eMCD in the \(({V}_{{\rm{G}}},\,{V}_{{\rm{B}}})\) plane at various temperatures (\(B=0.1\,{\rm{T}}\)). j-m, The corresponding hMCD data. The MCD enhancements in the excitonic insulator phase are most prominent at low temperatures when the excitons condense to phase IIB. Above \({T}_{{\rm{c}}}\) a small enhancement remains due to different statistics between fermions and bosons. The difference becomes progressively weaker at higher temperature. Extended Data Fig. 10 Two-component condensate in other TMD combinations (electron-doped WSe2, hole-doped MoSe2; device D3, 60° angle alignment). a,b, 2D color plots of eMCD and hMCD as functions of \({V}_{{\rm{G}}}\) and \({V}_{{\rm{B}}}\) at \(B=0.2\) T. Here eMCD and hMCD are the MCD signal from WSe2 X− and MoSe2 X+ resonances respectively. A large negative electric field (−0.45 V/nm) and a negative bias voltage (positive voltage on MoSe2) reverse the initial type-II band alignment, pushing electrons into WSe2 and holes into MoSe2. A substantially larger \({V}_{{\rm{B}}}\) is required to overcome the bandgap, and contact performance is worse, both leading to a slightly distorted doping phase diagram. Nonetheless, the MCD enhancement in the excitonic insulator phase is still clearly observed. c, \(B\)-derivative of eMCD signal along the charge neutrality line. A similar IIA region appears as a region with a slightly reversed eMCD slope. d, Representative eMCD and hMCD at pair densities 0.1, 0.6 and \(0.9\times {10}^{12}\,{\rm{c}}{{\rm{m}}}^{-2}\). e, Comparison of eMCD (left axis) and hMCD (right axis) at exciton density \(0.3\times {10}^{12}\,{\rm{c}}{{\rm{m}}}^{-2}\). At the phase IIB/I boundary, eMCD and hMCD saturate at the same field. f, Condensate phase diagram in the density-temperature space. The condensate dome has very similar shape to Fig. 4, with similar transition temperature and Mott density. Supplementary information Rights and permissions About this article Cite this article Qi, R., Li, Q., Nie, J. et al. Two-component exciton condensates in an electron–hole bilayer. Nature (2026). https://doi.org/10.1038/s41586-026-10636-y Received: Accepted: Published: Version of record: DOI: https://doi.org/10.1038/s41586-026-10636-y