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  • Review Article
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Dipolar many-body complexes and their interactions in stacked 2D heterobilayers

Nature Reviews Physics volume 6, pages 439–454 (2024)Cite this article

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Abstract

In the past decade, dipolar many-body complexes have been observed in 2D van der Waals heterobilayers. These complexes show compelling dipolar characteristics such as long-range and anisotropic interactions among dipoles, and their high tunability and long coherence time make them promising for applications in quantum information processing and optoelectronic devices. The presence of powerful dipole–dipole interactions among long-lived interlayer excitons can cause the system to enter unique classical and quantum phases with multiparticle correlations, which can host rich many-body physics such as dipolar liquids, dipolar crystals and superfluids. The strong binding energy of interlayer excitons in 2D heterobilayers enhances the critical temperature of these exotic phenomena. In this Review, we discuss recent work on dipolar complexes and many-body effects in transition metal dichalcogenide double layers and present potential opportunities in the field.

Key points

  • Stacked 2D heterobilayers host many-body excitonic states with strong dipole–dipole interactions, enabling the investigation of multiparticle correlations and novel quantum physics.

  • The physics of dipole–dipole interactions in 2D heterobilayers is at the origin of several important phenomena, including Bose–Einstein condensation, superfluidity and supersolids.

  • 2D heterobilayers, with their long-range dipolar interactions, offer a promising platform characterized by distinctive tunability across various parameters, including interlayer distance, excitation densities, external fields, environmental stimuli and moiré superlattice structure.

  • The strong binding energy of dipolar complexes in 2D stacked heterobilayers allows for the pursuit of room-temperature condensation and superfluidity.

  • The impact of dipolar many-body complexes extends beyond excitonic physics discoveries and forms the basis of several key concepts, including Wigner crystallization, tunable quantum light emitters and scalable quantum devices.

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Fig. 1: Interlayer excitons and multicomplexes in 2D semiconducting bilayers.
Fig. 2: Dipolar repulsive interaction and modulation in carrier diffusion.
Fig. 3: Dipolar interlayer trions.
Fig. 4: Interlayer biexcitons and interactions.
Fig. 5: Exciton condensation in atomically thin double layers.

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References

  1. Kruckenhauser, A. et al. Quantum many-body physics with ultracold polar molecules: nanostructured potential barriers and interactions. Phys. Rev. A 102, 023320 (2020).

    Article  ADS  Google Scholar 

  2. Baranov, M. A. Theoretical progress in many-body physics with ultracold dipolar gases. Phys. Rep. 464, 71–111 (2008).

    Article  ADS  Google Scholar 

  3. Yao, N. Y. et al. Many-body localization in dipolar systems. Phys. Rev. Lett. 113, 243002 (2014).

    Article  ADS  Google Scholar 

  4. Chuang, C. & Cao, J. Universal scalings in two-dimensional anisotropic dipolar excitonic systems. Phys. Rev. Lett. 127, 047402 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  5. Özçelik, V. O., Azadani, J. G., Yang, C., Koester, S. J. & Low, T. Band alignment of two-dimensional semiconductors for designing heterostructures with momentum space matching. Phys. Rev. B 94, 035125 (2016).

    Article  ADS  Google Scholar 

  6. Chiu, M.-H. et al. Determination of band alignment in the single-layer MoS2/WSe2 heterojunction. Nat. Commun. 6, 7666 (2015).

    Article  ADS  Google Scholar 

  7. Wilson, N. R. et al. Determination of band offsets, hybridization, and exciton binding in 2D semiconductor heterostructures. Sci. Adv. 3, e1601832 (2017).

    Article  ADS  Google Scholar 

  8. Zhang, C. et al. Systematic study of electronic structure and band alignment of monolayer transition metal dichalcogenides in van der Waals heterostructures. 2D Mater. 4, 015026 (2016).

    Article  Google Scholar 

  9. Merkl, P. et al. Ultrafast transition between exciton phases in van der Waals heterostructures. Nat. Mater. 18, 691–696 (2019).

    Article  ADS  Google Scholar 

  10. Schmitt, D. et al. Formation of moiré interlayer excitons in space and time. Nature 608, 499–503 (2022).

    Article  ADS  Google Scholar 

  11. Gu, J. et al. Dipolar excitonic insulator in a moiré lattice. Nat. Phys. 18, 395–400 (2022).

    Article  Google Scholar 

  12. Turunen, M. et al. Quantum photonics with layered 2D materials. Nat. Rev. Phys. 4, 219–236 (2022).

    Article  Google Scholar 

  13. Yi, Y., Chen, Z., Yu, X. F., Zhou, Z. K. & Li, J. Recent advances in quantum effects of 2D materials. Adv. Quantum Technol. 2, 1800111 (2019).

    Article  Google Scholar 

  14. Wilson, N. P., Yao, W., Shan, J. & Xu, X. Excitons and emergent quantum phenomena in stacked 2D semiconductors. Nature 599, 383–392 (2021).

    Article  ADS  Google Scholar 

  15. Davis, E. J. et al. Probing many-body dynamics in a two-dimensional dipolar spin ensemble. Nat. Phys. 19, 836–844 (2023).

    Article  Google Scholar 

  16. Montblanch, A. R.-P., Barbone, M., Aharonovich, I., Atatüre, M. & Ferrari, A. C. Layered materials as a platform for quantum technologies. Nat. Nanotechnol. https://doi.org/10.1038/s41565-023-01354-x (2023).

  17. Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).

    Article  ADS  Google Scholar 

  18. Rivera, P. et al. Valley-polarized exciton dynamics in a 2D semiconductor heterostructure. Science 351, 688–691 (2016).

    Article  ADS  Google Scholar 

  19. Jiang, C. et al. Microsecond dark-exciton valley polarization memory in two-dimensional heterostructures. Nat. Commun. 9, 753 (2018).

    Article  ADS  Google Scholar 

  20. Rivera, P. et al. Observation of long-lived interlayer excitons in monolayer MoSe2–WSe2 heterostructures. Nat. Commun. 6, 6242 (2015).

    Article  ADS  Google Scholar 

  21. Montblanch, A. R.-P. et al. Confinement of long-lived interlayer excitons in WS2/WSe2 heterostructures. Commun. Phys. 4, 119 (2021).

    Article  Google Scholar 

  22. Bondarev, I. V. & Vladimirova, M. R. Complexes of dipolar excitons in layered quasi-two-dimensional nanostructures. Phys. Rev. B 97, 165419 (2018).

    Article  ADS  Google Scholar 

  23. Wang, Z. et al. Evidence of high-temperature exciton condensation in two-dimensional atomic double layers. Nature 574, 76–80 (2019).

    Article  ADS  Google Scholar 

  24. Sigl, L. et al. Signatures of a degenerate many-body state of interlayer excitons in a van der Waals heterostack. Phys. Rev. Res. 2, 042044 (2020).

    Article  Google Scholar 

  25. Keldysh, L. V. & Kozlov, A. N. Collective properties of excitons in semiconductors. Sov. J. Exp. Theor. Phys. 27, 521 (1968).

    ADS  Google Scholar 

  26. Zhu, X., Littlewood, P., Hybertsen, M. S. & Rice, T. Exciton condensate in semiconductor quantum well structures. Phys. Rev. Lett. 74, 1633 (1995).

    Article  ADS  Google Scholar 

  27. Lozovik, Y. E. & Berman, O. Phase transitions in a system of two coupled quantum wells. J. Exp. Theor. Phys. Lett. 64, 573–579 (1996).

    Article  Google Scholar 

  28. Laikhtman, B. & Rapaport, R. Exciton correlations in coupled quantum wells and their luminescence blue shift. Phys. Rev. B 80, 195313 (2009).

    Article  ADS  Google Scholar 

  29. Comte, C. & Nozières, P. Exciton Bose condensation: the ground state of an electron–hole gas - I. Mean field description of a simplified model. J. Phys. Fr. 43, 1069–1081 (1982).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. Combescot, M., Combescot, R. & Dubin, F. Bose–Einstein condensation and indirect excitons: a review. Rep. Prog. Phys. 80, 066501 (2017).

    Article  ADS  Google Scholar 

  32. Tran, K. et al. Evidence for moiré excitons in van der Waals heterostructures. Nature 567, 71–75 (2019).

    Article  ADS  Google Scholar 

  33. Seyler, K. L. et al. Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers. Nature 567, 66–70 (2019).

    Article  ADS  Google Scholar 

  34. Yuan, L. et al. Twist-angle-dependent interlayer exciton diffusion in WS2–WSe2 heterobilayers. Nat. Mater. 19, 617–623 (2020).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  36. Conti, S., Neilson, D., Peeters, F. M. & Perali, A. Transition metal dichalcogenides as strategy for high temperature electron–hole superfluidity. Condens. Matter 5, 22 (2020).

    Article  Google Scholar 

  37. Zhu, Q., Tu, M. W.-Y., Tong, Q. & Yao, W. Gate tuning from exciton superfluid to quantum anomalous Hall in van der Waals heterobilayer. Sci. Adv. 5, eaau6120 (2019).

    Article  ADS  Google Scholar 

  38. Guo, H., Zhang, X. & Lu, G. Tuning moiré excitons in Janus heterobilayers for high-temperature Bose–Einstein condensation. Sci. Adv. 8, eabp9757 (2022).

    Article  ADS  Google Scholar 

  39. Xie, Y.-M., Zhang, C.-P., Hu, J.-X., Mak, K. F. & Law, K. T. Valley-polarized quantum anomalous hall state in moiré MoTe2/WSe2 heterobilayers. Phys. Rev. Lett. 128, 026402 (2022).

    Article  ADS  Google Scholar 

  40. Bondarev, I. V., Berman, O. L., Kezerashvili, R. Y. & Lozovik, Y. E. Crystal phases of charged interlayer excitons in van der Waals heterostructures. Commun. Phys. 4, 134 (2021).

    Article  Google Scholar 

  41. Slagle, K. & Fu, L. Charge transfer excitations, pair density waves, and superconductivity in moiré materials. Phys. Rev. B 102, 235423 (2020).

    Article  ADS  Google Scholar 

  42. Hubert, C. et al. Attractive dipolar coupling between stacked exciton fluids. Phys. Rev. X 9, 021026 (2019).

    Google Scholar 

  43. Wang, X. et al. Moiré trions in MoSe2/WSe2 heterobilayers. Nat. Nanotechnol. 16, 1208–1213 (2021).

    Article  ADS  Google Scholar 

  44. Calman, E. et al. Indirect excitons and trions in MoSe2/WSe2 van der Waals heterostructures. Nano Lett. 20, 1869–1875 (2020).

    Article  ADS  Google Scholar 

  45. Kremser, M. et al. Discrete interactions between a few interlayer excitons trapped at a MoSe2–WSe2 heterointerface. npj 2D Mater. Appl. 4, 8 (2020).

    Article  Google Scholar 

  46. Sun, X. et al. Enhanced interactions of interlayer excitons in free-standing heterobilayers. Nature 610, 478–484 (2022).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  48. Jiang, Y., Chen, S., Zheng, W., Zheng, B. & Pan, A. Interlayer exciton formation, relaxation, and transport in TMD van der Waals heterostructures. Light Sci. Appl. 10, 72 (2021).

    Article  ADS  Google Scholar 

  49. Regan, E. C. et al. Emerging exciton physics in transition metal dichalcogenide heterobilayers. Nat. Rev. Mater. 7, 778–795 (2022).

    Article  ADS  Google Scholar 

  50. Lin, Z. et al. Defect engineering of two-dimensional transition metal dichalcogenides. 2D Mater. 3, 022002 (2016).

    Article  ADS  Google Scholar 

  51. Li, J. et al. General synthesis of two-dimensional van der Waals heterostructure arrays. Nature 579, 368–374 (2020).

    Article  ADS  Google Scholar 

  52. Duong, D. L., Yun, S. J. & Lee, Y. H. van der Waals layered materials: opportunities and challenges. ACS Nano 11, 11803–11830 (2017).

    Article  Google Scholar 

  53. Novoselov, K. S., Mishchenko, A., Carvalho, O. A. & Castro Neto, A. 2D materials and van der Waals heterostructures. Science 353, aac9439 (2016).

    Article  Google Scholar 

  54. Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).

    Article  ADS  Google Scholar 

  55. Geim, A. K. & Grigorieva, I. V. van der Waals heterostructures. Nature 499, 419–425 (2013).

    Article  Google Scholar 

  56. Koma, A. & Yoshimura, K. Ultrasharp interfaces grown with van der Waals epitaxy. Surf. Sci. 174, 556–560 (1986).

    Article  ADS  Google Scholar 

  57. Wang, G. et al. Colloquium: excitons in atomically thin transition metal dichalcogenides. Rev. Mod. Phys. 90, 021001 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  58. He, K. et al. Tightly bound excitons in monolayer WSe2. Phys. Rev. Lett. 113, 026803 (2014).

    Article  ADS  Google Scholar 

  59. Berkelbach, T. C., Hybertsen, M. S. & Reichman, D. R. Theory of neutral and charged excitons in monolayer transition metal dichalcogenides. Phys. Rev. B 88, 045318 (2013).

    Article  ADS  Google Scholar 

  60. 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).

    Article  ADS  Google Scholar 

  61. Paik, E. Y. et al. Interlayer exciton laser of extended spatial coherence in atomically thin heterostructures. Nature 576, 80–84 (2019).

    Article  ADS  Google Scholar 

  62. Jin, C. et al. Ultrafast dynamics in van der Waals heterostructures. Nat. Nanotechnol. 13, 994–1003 (2018).

    Article  ADS  Google Scholar 

  63. Liu, J., Li, Z., Zhang, X. & Lu, G. Unraveling energy and charge transfer in type-II van der Waals heterostructures. npj Comput. Mater. 7, 191 (2021).

    Article  ADS  Google Scholar 

  64. Yu, H. & Yao, W. Luminescence anomaly of dipolar valley excitons in homobilayer semiconductor moiré superlattices. Phys. Rev. X 11, 021042 (2021).

    MathSciNet  Google Scholar 

  65. Tagarelli, F. et al. Electrical control of hybrid exciton transport in a van der Waals heterostructure. Nat. Photon. 17, 615–621 (2023).

    Article  ADS  Google Scholar 

  66. Alexeev, E. M. et al. Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures. Nature 567, 81–86 (2019).

    Article  ADS  Google Scholar 

  67. Ruiz-Tijerina, D. A. & Fal’ko, V. I. Interlayer hybridization and moiré superlattice minibands for electrons and excitons in heterobilayers of transition-metal dichalcogenides. Phys. Rev. B 99, 125424 (2019).

    Article  ADS  Google Scholar 

  68. Deilmann, T. & Thygesen, K. S. Interlayer trions in the MoS2/WS2 van der Waals heterostructure. Nano Lett. 18, 1460–1465 (2018).

    Article  ADS  Google Scholar 

  69. Jones, A. M. et al. Spin-layer locking effects in optical orientation of exciton spin in bilayer WSe2. Nat. Phys. 10, 130–134 (2014).

    Article  Google Scholar 

  70. Zhang, L. et al. Discovery of type II interlayer trions. Adv. Mater. 35, 2206212 (2023).

    Article  Google Scholar 

  71. Zhang, C. et al. Interlayer couplings, moiré patterns, and 2D electronic superlattices in MoS2/WSe2 hetero-bilayers. Sci. Adv. 3, e1601459 (2017).

    Article  ADS  Google Scholar 

  72. Jin, C. et al. Observation of moiré excitons in WSe2/WS2 heterostructure superlattices. Nature 567, 76–80 (2019).

    Article  ADS  Google Scholar 

  73. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    Article  ADS  Google Scholar 

  74. Tang, K. & Qi, W. Moiré‐pattern‐tuned electronic structures of van der Waals heterostructures. Adv. Funct. Mater. 30, 2002672 (2020).

    Article  Google Scholar 

  75. Zhang, W. et al. One‐interlayer‐twisted multilayer MoS2 moiré superlattices. Adv. Funct. Mater. 32, 2111529 (2022).

    Article  Google Scholar 

  76. Brem, S., Linderälv, C., Erhart, P. & Malic, E. Tunable phases of moiré excitons in van der Waals heterostructures. Nano Lett. 20, 8534–8540 (2020).

    Article  ADS  Google Scholar 

  77. Bloch, I. Ultracold quantum gases in optical lattices. Nat. Phys. 1, 23–30 (2005).

    Article  Google Scholar 

  78. Förg, M. et al. Moiré excitons in MoSe2–WSe2 heterobilayers and heterotrilayers. Nat. Commun. 12, 1656 (2021).

    Article  ADS  Google Scholar 

  79. Choi, J. et al. Moiré potential impedes interlayer exciton diffusion in van der Waals heterostructures. Sci. Adv. 6, eaba8866 (2020).

    Article  ADS  Google Scholar 

  80. Zhao, S. et al. Excitons in mesoscopically reconstructed moiré heterostructures. Nat. Nanotechnol. 18, 572–579 (2023).

    Article  ADS  Google Scholar 

  81. Li, W., Lu, X., Dubey, S., Devenica, L. & Srivastava, A. Dipolar interactions between localized interlayer excitons in van der Waals heterostructures. Nat. Mater. 19, 624–629 (2020).

    Article  ADS  Google Scholar 

  82. Nagler, P. et al. Interlayer exciton dynamics in a dichalcogenide monolayer heterostructure. 2D Mater. 4, 025112 (2017).

    Article  ADS  Google Scholar 

  83. Lin, K.-Q. A roadmap for interlayer excitons. Light Sci. Appl. 10, 99 (2021).

    Article  ADS  Google Scholar 

  84. Sun, Z. et al. Excitonic transport driven by repulsive dipolar interaction in a van der Waals heterostructure. Nat. Photon. 16, 79–85 (2022).

    Article  ADS  Google Scholar 

  85. Erkensten, D., Brem, S. & Malic, E. Exciton–exciton interaction in transition metal dichalcogenide monolayers and van der Waals heterostructures. Phys. Rev. B 103, 045426 (2021).

    Article  ADS  Google Scholar 

  86. Chen, Y. et al. Robust interlayer coupling in two-dimensional perovskite/monolayer transition metal dichalcogenide heterostructures. ACS Nano 14, 10258–10264 (2020).

    Article  Google Scholar 

  87. Yao, W. et al. Layer-number engineered momentum-indirect interlayer excitons with large spectral tunability. Nano Lett. 22, 7230–7237 (2022).

    Article  ADS  Google Scholar 

  88. Lee, R., Drummond, N. & Needs, R. Exciton–exciton interaction and biexciton formation in bilayer systems. Phys. Rev. B 79, 125308 (2009).

    Article  ADS  Google Scholar 

  89. Erkensten, D., Brem, S., Perea-Causín, R. & Malic, E. Microscopic origin of anomalous interlayer exciton transport in van der Waals heterostructures. Phys. Rev. Mater. 6, 094006 (2022).

    Article  Google Scholar 

  90. Zimmerman, M., Rapaport, R. & Gazit, S. Collective interlayer pairing and pair superfluidity in vertically stacked layers of dipolar excitons. Proc. Natl Acad. Sci. USA 119, e2205845119 (2022).

    Article  Google Scholar 

  91. Butov, L. Exciton condensation in coupled quantum wells. Solid State Commun. 127, 89–98 (2003).

    Article  ADS  Google Scholar 

  92. Butov, L., Gossard, A. & Chemla, D. Macroscopically ordered state in an exciton system. Nature 418, 751–754 (2002).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  94. Shilo, Y. et al. Particle correlations and evidence for dark state condensation in a cold dipolar exciton fluid. Nat. Commun. 4, 2335 (2013).

    Article  ADS  Google Scholar 

  95. Stern, M., Umansky, V. & Bar-Joseph, I. Exciton liquid in coupled quantum wells. Science 343, 55–57 (2014).

    Article  ADS  Google Scholar 

  96. Schindler, C. & Zimmermann, R. Analysis of the exciton–exciton interaction in semiconductor quantum wells. Phys. Rev. B 78, 045313 (2008).

    Article  ADS  Google Scholar 

  97. Meyertholen, A. & Fogler, M. Biexcitons in two-dimensional systems with spatially separated electrons and holes. Phys. Rev. B 78, 235307 (2008).

    Article  ADS  Google Scholar 

  98. Choksy, D. et al. Attractive and repulsive dipolar interaction in bilayers of indirect excitons. Phys. Rev. B 103, 045126 (2021).

    Article  ADS  Google Scholar 

  99. Olivares-Robles, M. & Ulloa, S. Interaction potential between dynamic dipoles: polarized excitons in strong magnetic fields. Phys. Rev. B 64, 115302 (2001).

    Article  ADS  Google Scholar 

  100. Chen, M., Chen, F., Cheng, B., Liang, S. J. & Miao, F. Moiré heterostructures: highly tunable platforms for quantum simulation and future computing. J. Semicond. 44, 010301 (2023).

    Article  ADS  Google Scholar 

  101. Kennes, D. M. et al. Moiré heterostructures as a condensed-matter quantum simulator. Nat. Phys. 17, 155–163 (2021).

    Article  Google Scholar 

  102. Du, L. et al. Moiré photonics and optoelectronics. Science 379, eadg0014 (2023).

    Article  Google Scholar 

  103. Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020).

    Article  ADS  Google Scholar 

  104. Zhang, L., Ni, R. & Zhou, Y. Controlling quantum phases of electrons and excitons in moiré superlattices. J. Appl. Phys. 133, 080901 (2023).

    Article  ADS  Google Scholar 

  105. Andrei, E. Y. et al. The marvels of moiré materials. Nat. Rev. Mater. 6, 201–206 (2021).

    Article  ADS  Google Scholar 

  106. Calman, E. V. et al. Indirect excitons in van der Waals heterostructures at room temperature. Nat. Commun. 9, 1895 (2018).

    Article  ADS  Google Scholar 

  107. Shanks, D. N. et al. Interlayer exciton diode and transistor. Nano Lett. 22, 6599–6605 (2022).

    Article  ADS  Google Scholar 

  108. Jauregui, L. A. et al. Electrical control of interlayer exciton dynamics in atomically thin heterostructures. Science 366, 870–875 (2019).

    Article  ADS  Google Scholar 

  109. Vörös, Z., Balili, R., Snoke, D., Pfeiffer, L. & West, K. Long-distance diffusion of excitons in double quantum well structures. Phys. Rev. Lett. 94, 226401 (2005).

    Article  ADS  Google Scholar 

  110. Rapaport, R., Chen, G. & Simon, S. H. Nonlinear dynamics of a dense two-dimensional dipolar exciton gas. Phys. Rev. B 73, 033319 (2006).

    Article  ADS  Google Scholar 

  111. Unuchek, D. et al. Room-temperature electrical control of exciton flux in a van der Waals heterostructure. Nature 560, 340–344 (2018).

    Article  ADS  Google Scholar 

  112. Tang, Y. et al. Tuning layer-hybridized moiré excitons by the quantum-confined Stark effect. Nat. Nanotechnol. 16, 52–57 (2021).

    Article  ADS  Google Scholar 

  113. Erkensten, D. et al. Electrically tunable dipolar interactions between layer-hybridized excitons. Nanoscale, 15, 11064–11071 (2023).

    Article  Google Scholar 

  114. Mahdikhanysarvejahany, F. et al. Localized interlayer excitons in MoSe2–WSe2 heterostructures without a moiré potential. Nat. Commun. 13, 5354 (2022).

    Article  ADS  Google Scholar 

  115. Wang, W. & Ma, X. Strain-induced trapping of indirect excitons in MoSe2/WSe2 heterostructures. ACS Photon. 7, 2460–2467 (2020).

    Article  Google Scholar 

  116. Jin, C. et al. Identification of spin, valley and moiré quasi-angular momentum of interlayer excitons. Nat. Phys. 15, 1140–1144 (2019).

    Article  Google Scholar 

  117. Yu, H., Liu, G.-B. & Yao, W. Brightened spin-triplet interlayer excitons and optical selection rules in van der Waals heterobilayers. 2D Mater. 5, 035021 (2018).

    Article  Google Scholar 

  118. He, F. et al. Moiré patterns in 2D materials: a review. ACS Nano 15, 5944–5958 (2021).

    Article  Google Scholar 

  119. Uddin, S. Z. et al. Neutral exciton diffusion in monolayer MoS2. ACS Nano 14, 13433–13440 (2020).

    Article  Google Scholar 

  120. Li, Z. et al. Interlayer exciton transport in MoSe2/WSe2 heterostructures. ACS Nano 15, 1539–1547 (2021).

    Article  Google Scholar 

  121. Brem, S. & Malic, E. Bosonic delocalization of dipolar Moiré excitons. Nano Lett. 23, 4627–4633 (2023).

    Article  ADS  Google Scholar 

  122. Witham, O., Hunt, R. J. & Drummond, N. D. Stability of trions in coupled quantum wells modeled by two-dimensional bilayers. Phys. Rev. B 97, 075424 (2018).

    Article  ADS  Google Scholar 

  123. Liu, E. et al. Signatures of moiré trions in WSe2/MoSe2 heterobilayers. Nature 594, 46–50 (2021).

    Article  ADS  Google Scholar 

  124. Mak, K. F. et al. Tightly bound trions in monolayer MoS2. Nat. Mater. 12, 207–211 (2013).

    Article  ADS  Google Scholar 

  125. Ross, J. S. et al. Electrical control of neutral and charged excitons in a monolayer semiconductor. Nat. Commun. 4, 1474 (2013).

    Article  ADS  Google Scholar 

  126. Sidler, M. et al. Fermi polaron-polaritons in charge-tunable atomically thin semiconductors. Nat. Phys. 13, 255–261 (2017).

    Article  Google Scholar 

  127. Schmidt, R., Enss, T., Pietilä, V. & Demler, E. Fermi polarons in two dimensions. Phys. Rev. A 85, 021602 (2012).

    Article  ADS  Google Scholar 

  128. Siviniant, J., Scalbert, D., Kavokin, A., Coquillat, D. & Lascaray, J. Chemical equilibrium between excitons, electrons, and negatively charged excitons in semiconductor quantum wells. Phys. Rev. B 59, 1602 (1999).

    Article  ADS  Google Scholar 

  129. Ciarrocchi, A. et al. Polarization switching and electrical control of interlayer excitons in two-dimensional van der Waals heterostructures. Nat. Photon. 13, 131–136 (2019).

    Article  ADS  Google Scholar 

  130. Perea-Causin, R. et al. Exciton optics, dynamics, and transport in atomically thin semiconductors. APL Mater. 10, 100701 (2022).

    Article  ADS  Google Scholar 

  131. Baek, H. et al. Highly energy-tunable quantum light from moiré-trapped excitons. Sci. Adv. 6, eaba8526 (2020).

    Article  ADS  Google Scholar 

  132. Baek, H. et al. Optical read-out of Coulomb staircases in a moiré superlattice via trapped interlayer trions. Nat. Nanotechnol. 16, 1237–1243 (2021).

    Article  ADS  Google Scholar 

  133. Pei, J., Yang, J., Yildirim, T., Zhang, H. & Lu, Y. Many‐body complexes in 2D semiconductors. Adv. Mater. 31, 1706945 (2019).

    Article  Google Scholar 

  134. Hao, K. et al. Neutral and charged inter-valley biexcitons in monolayer MoSe2. Nat. Commun. 8, 15552 (2017).

    Article  ADS  Google Scholar 

  135. Tan, M., Drummond, N. & Needs, R. Exciton and biexciton energies in bilayer systems. Phys. Rev. B 71, 033303 (2005).

    Article  ADS  Google Scholar 

  136. Zhang, L. et al. Modulated interlayer charge transfer dynamics in a monolayer TMD/metal junction. Nanoscale 11, 418–425 (2019).

    Article  Google Scholar 

  137. Tongay, S. et al. Tuning interlayer coupling in large-area heterostructures with CVD-grown MoS2 and WS2 monolayers. Nano Lett. 14, 3185–3190 (2014).

    Article  ADS  Google Scholar 

  138. Yuan, L. et al. Photocarrier generation from interlayer charge-transfer transitions in WS2-graphene heterostructures. Sci. Adv. 4, e1700324 (2018).

    Article  ADS  Google Scholar 

  139. He, Y.-M. et al. Cascaded emission of single photons from the biexciton in monolayered WSe2. Nat. Commun. 7, 13409 (2016).

    Article  ADS  Google Scholar 

  140. Li, Z. et al. Revealing the biexciton and trion–exciton complexes in BN encapsulated WSe2. Nat. Commun. 9, 3719 (2018).

    Article  ADS  Google Scholar 

  141. Atatüre, M., Englund, D., Vamivakas, N., Lee, S.-Y. & Wrachtrup, J. Material platforms for spin-based photonic quantum technologies. Nat. Rev. Mater. 3, 38–51 (2018).

    Article  ADS  Google Scholar 

  142. Dalfovo, F., Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of Bose–Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463 (1999).

    Article  ADS  Google Scholar 

  143. Penrose, O. & Onsager, L. Bose–Einstein condensation and liquid helium. Phys. Rev. 104, 576 (1956).

    Article  ADS  Google Scholar 

  144. 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).

    Article  ADS  Google Scholar 

  145. Yanagisawa, T. Mechanism of high-temperature superconductivity in correlated-electron systems. Condens. Matter 4, 57 (2019).

    Article  Google Scholar 

  146. Zhang, C. et al. Bipolaronic high-temperature superconductivity. Phys. Rev. X 13, 011010 (2023).

    Google Scholar 

  147. Butov, L., Lai, C., Ivanov, A., Gossard, A. & Chemla, D. Towards Bose–Einstein condensation of excitons in potential traps. Nature 417, 47–52 (2002).

    Article  ADS  Google Scholar 

  148. Nozieres, P. & Saint James, D. Particle vs. pair condensation in attractive Bose liquids. J. Phys. 43, 1133–1148 (1982).

    Article  Google Scholar 

  149. Büchler, H. P. et al. Strongly correlated 2D quantum phases with cold polar molecules: controlling the shape of the interaction potential. Phys. Rev. Lett. 98, 060404 (2007).

    Article  ADS  Google Scholar 

  150. Astrakharchik, G., Boronat, J., Kurbakov, I. & Lozovik, Y. E. Quantum phase transition in a two-dimensional system of dipoles. Phys. Rev. Lett. 98, 060405 (2007).

    Article  ADS  Google Scholar 

  151. Sellin, K. & Babaev, E. Superfluid drag in the two-component Bose–Hubbard model. Phys. Rev. B 97, 094517 (2018).

    Article  ADS  Google Scholar 

  152. Trefzger, C., Menotti, C. & Lewenstein, M. Pair-supersolid phase in a bilayer system of dipolar lattice bosons. Phys. Rev. Lett. 103, 035304 (2009).

    Article  ADS  Google Scholar 

  153. Gupta, S., Kutana, A. & Yakobson, B. I. Heterobilayers of 2D materials as a platform for excitonic superfluidity. Nat. Commun. 11, 2989 (2020).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  155. Bianco, R., Calandra, M. & Mauri, F. Electronic and vibrational properties of TiSe2 in the charge-density-wave phase from first principles. Phys. Rev. B 92, 094107 (2015).

    Article  ADS  Google Scholar 

  156. Pasquier, D. & Yazyev, O. V. Excitonic effects in two-dimensional TiSe2 from hybrid density functional theory. Phys. Rev. B 98, 235106 (2018).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  158. 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).

    Article  ADS  Google Scholar 

  159. Sun, Z. et al. Charged bosons made of fermions in bilayer structures with strong metallic screening. Nano Lett. 21, 7669–7675 (2021).

    Article  ADS  Google Scholar 

  160. Sun, Z. et al. Charged bosons made of fermions in a solid state system without Cooper pairing. Preprint at https://arxiv.org/abs/2003.05850 (2021).

  161. Kornilovitch, P. Stable pair liquid phase in fermionic systems. Phys. Rev. B 107, 115135 (2023).

    Article  ADS  Google Scholar 

  162. Altland, A. & Simons, B. D. Condensed Matter Field Theory (Cambridge Univ. Press, 2010).

  163. Götting, N., Lohof, F. & Gies, C. Moiré-Bose–Hubbard model for interlayer excitons in twisted transition metal dichalcogenide heterostructures. Phys. Rev. B 105, 165419 (2022).

    Article  ADS  Google Scholar 

  164. Rosati, R. et al. Interface engineering of charge-transfer excitons in 2D lateral heterostructures. Nat. Commun. 14, 2438 (2023).

    Article  ADS  Google Scholar 

  165. Yuan, L. et al. Strong dipolar repulsion of one-dimensional interfacial excitons in monolayer lateral heterojunctions. ACS Nano 17, 15379–15387 (2023).

    Article  Google Scholar 

  166. Najafidehaghani, E. et al. 1D p–n junction electronic and optoelectronic devices from transition metal dichalcogenide lateral heterostructures grown by one-pot chemical vapor deposition synthesis. Adv. Funct. Mater. 31, 2101086 (2021).

    Article  Google Scholar 

  167. Boening, J., Filinov, A. & Bonitz, M. Crystallization of an exciton superfluid. Phys. Rev. B 84, 075130 (2011).

    Article  ADS  Google Scholar 

  168. Bondarev, I. V. & Lozovik, Y. E. Magnetic-field-induced Wigner crystallization of charged interlayer excitons in van der Waals heterostructures. Commun. Phys. 5, 315 (2022).

    Article  Google Scholar 

  169. Lozovik, Y. E. & Yudson, V. Crystallization of a two-dimensional electron gas in a magnetic field. ZhETF Pisma Redaktsiiu 22, 26 (1975).

    ADS  Google Scholar 

  170. Ma, M. K. et al. Thermal and quantum melting phase diagrams for a magnetic-field-induced Wigner solid. Phys. Rev. Lett. 125, 036601 (2020).

    Article  ADS  Google Scholar 

  171. Pan, J.-W., Simon, C., Brukner, Č. & Zeilinger, A. Entanglement purification for quantum communication. Nature 410, 1067–1070 (2001).

    Article  ADS  Google Scholar 

  172. Vajner, D. A., Rickert, L., Gao, T., Kaymazlar, K. & Heindel, T. Quantum communication using semiconductor quantum dots. Adv. Quantum Technol. 5, 2100116 (2022).

    Article  Google Scholar 

  173. Peng, C.-Z. et al. Experimental free-space distribution of entangled photon pairs over 13 km: towards satellite-based global quantum communication. Phys. Rev. Lett. 94, 150501 (2005).

    Article  ADS  Google Scholar 

  174. Gisin, N. & Thew, R. Quantum communication. Nat. Photon. 1, 165–171 (2007).

    Article  ADS  Google Scholar 

  175. Ihara, T. Biexciton cascade emission reveals absolute absorption cross section of single semiconductor nanocrystals. Phys. Rev. B 93, 235442 (2016).

    Article  ADS  Google Scholar 

  176. Huber, D. et al. Strain-tunable GaAs quantum dot: a nearly dephasing-free source of entangled photon pairs on demand. Phys. Rev. Lett. 121, 033902 (2018).

    Article  ADS  Google Scholar 

  177. Mannix, A. J. et al. Robotic four-dimensional pixel assembly of van der Waals solids. Nat. Nanotechnol. 17, 361–366 (2022).

    Article  ADS  Google Scholar 

  178. Hu, Z. et al. Research progress of low dielectric constant polymer materials. J. Polym. Eng. 42, 677–687 (2022).

    Article  Google Scholar 

  179. Volksen, W., Miller, R. D. & Dubois, G. Low dielectric constant materials. Chem. Rev. 110, 56–110 (2010).

    Article  Google Scholar 

  180. Luo, Y. et al. Deterministic coupling of site-controlled quantum emitters in monolayer WSe2 to plasmonic nanocavities. Nat. Nanotechnol. 13, 1137–1142 (2018).

    Article  ADS  Google Scholar 

  181. Cai, T. et al. Radiative enhancement of single quantum emitters in WSe2 monolayers using site-controlled metallic nanopillars. ACS Photon. 5, 3466–3471 (2018).

    Article  Google Scholar 

  182. Peyskens, F., Chakraborty, C., Muneeb, M., Van Thourhout, D. & Englund, D. Integration of single photon emitters in 2D layered materials with a silicon nitride photonic chip. Nat. Commun. 10, 4435 (2019).

    Article  ADS  Google Scholar 

  183. Bao, X. et al. Giant out-of-plane exciton emission enhancement in two-dimensional indium selenide via a plasmonic nanocavity. Nano Lett. 23, 3716–3723 (2023).

    Article  ADS  Google Scholar 

  184. Park, K.-D., Jiang, T., Clark, G., Xu, X. & Raschke, M. B. Radiative control of dark excitons at room temperature by nano-optical antenna-tip Purcell effect. Nat. Nanotechnol. 13, 59–64 (2018).

    Article  ADS  Google Scholar 

  185. Li, G.-C., Zhang, Q., Maier, S. A. & Lei, D. Plasmonic particle-on-film nanocavities: a versatile platform for plasmon-enhanced spectroscopy and photochemistry. Nanophotonics 7, 1865–1889 (2018).

    Article  Google Scholar 

  186. Zhou, Y. et al. Probing dark excitons in atomically thin semiconductors via near-field coupling to surface plasmon polaritons. Nat. Nanotechnol. 12, 856–860 (2017).

    Article  ADS  Google Scholar 

  187. Datta, B. et al. Highly nonlinear dipolar exciton–polaritons in bilayer MoS2. Nat. Commun. 13, 6341 (2022).

    Article  ADS  Google Scholar 

  188. Louca, C. et al. Nonlinear interactions of dipolar excitons and polaritons in MoS2 bilayers. Nat. Commun. 4, 3818 (2023).

    Article  ADS  Google Scholar 

  189. König, J. K., Fitzgerald, J. M., Hagel, J., Erkensten, D. & Malic, E. Interlayer exciton polaritons in homobilayers of transition metal dichalcogenides. 2D Mater. 10, 025019 (2023).

    Article  Google Scholar 

  190. Zhang, S. et al. Extraordinary photoluminescence and strong temperature/angle-dependent Raman responses in few-layer phosphorene. ACS Nano 8, 9590–9596 (2014).

    Article  Google Scholar 

  191. Pei, J. et al. Producing air-stable monolayers of phosphorene and their defect engineering. Nat. Commun. 7, 10450 (2016).

    Article  ADS  Google Scholar 

  192. Liu, J. et al. Two-dimensional CH3NH3PbI3 perovskite: synthesis and optoelectronic application. ACS Nano 10, 3536–3542 (2016).

    Article  Google Scholar 

  193. Yang, J. et al. Optical tuning of exciton and trion emissions in monolayer phosphorene. Light Sci. Appl. 4, e312 (2015).

    Article  Google Scholar 

  194. Zhang, L. et al. Efficient and layer‐dependent exciton pumping across atomically thin organic–inorganic type‐I heterostructures. Adv. Mater. 30, 1803986 (2018).

    Article  Google Scholar 

  195. Zhang, Y. et al. Wavelength‐tunable mid‐infrared lasing from black phosphorus nanosheets. Adv. Mater. 32, 1808319 (2020).

    Article  Google Scholar 

  196. Heo, H. et al. Interlayer orientation-dependent light absorption and emission in monolayer semiconductor stacks. Nat. Commun. 6, 7372 (2015).

    Article  ADS  Google Scholar 

  197. Nayak, P. K. et al. Probing evolution of twist-angle-dependent interlayer excitons in MoSe2/WSe2 van der Waals heterostructures. ACS Nano 11, 4041–4050 (2017).

    Article  ADS  Google Scholar 

  198. Alexeev, E. M. et al. Imaging of interlayer coupling in van der Waals heterostructures using a bright-field optical microscope. Nano Lett. 17, 5342–5349 (2017).

    Article  ADS  Google Scholar 

  199. Ji, Z. et al. Robust stacking-independent ultrafast charge transfer in MoS2/WS2 bilayers. ACS Nano 11, 12020–12026 (2017).

    Article  Google Scholar 

  200. Miller, B. et al. Long-lived direct and indirect interlayer excitons in van der Waals heterostructures. Nano Lett. 17, 5229–5237 (2017).

    Article  ADS  Google Scholar 

  201. Ye, T., Li, J. & Li, D. Charge‐accumulation effect in transition metal dichalcogenide heterobilayers. Small 15, 1902424 (2019).

    Article  Google Scholar 

  202. Ovesen, S. et al. Interlayer exciton dynamics in van der Waals heterostructures. Commun. Phys. 2, 23 (2019).

    Article  Google Scholar 

  203. Rasmussen, F. A. & Thygesen, K. S. Computational 2D materials database: electronic structure of transition-metal dichalcogenides and oxides. J. Phys. Chem. C 119, 13169–13183 (2015).

    Article  Google Scholar 

  204. Qiu, D. Y., da Jornada, F. H. & Louie, S. G. Optical spectrum of MoS2: many-body effects and diversity of exciton states. Phys. Rev. Lett. 111, 216805 (2013).

    Article  ADS  Google Scholar 

  205. Shi, H., Pan, H., Zhang, Y.-W. & Yakobson, B. I. Quasiparticle band structures and optical properties of strained monolayer MoS2and WS2. Phys. Rev. B 87, 155304 (2013).

    Article  ADS  Google Scholar 

  206. Plechinger, G. et al. Identification of excitons, trions and biexcitons in single-layer WS2. Phys. Status Solidi Rapid Res. Lett. 9, 457–461 (2015).

    Article  ADS  Google Scholar 

  207. Jones, A. M. et al. Optical generation of excitonic valley coherence in monolayer WSe2. Nat. Nanotechnol. 8, 634–638 (2013).

    Article  ADS  Google Scholar 

  208. You, Y. et al. Observation of biexcitons in monolayer WSe2. Nat. Phys. 11, 477–481 (2015).

    Article  Google Scholar 

  209. Pei, J. et al. Excited state biexcitons in atomically thin MoSe2. ACS Nano 11, 7468–7475 (2017).

    Article  Google Scholar 

  210. Kamban, H. C. & Pedersen, T. G. Interlayer excitons in van der Waals heterostructures: binding energy, stark shift, and field-induced dissociation. Sci. Rep. 10, 5537 (2020).

    Article  ADS  Google Scholar 

  211. Guo, H., Zhang, X. & Lu, G. Shedding light on moiré excitons: a first-principles perspective. Sci. Adv. 6, eabc5638 (2020).

    Article  ADS  Google Scholar 

  212. Mahdikhanysarvejahany, F. et al. Temperature dependent moiré trapping of interlayer excitons in MoSe2-WSe2 heterostructures. npj 2D Mater. Appl. 5, 67 (2021).

    Article  Google Scholar 

  213. Lahaye, T., Menotti, C., Santos, L., Lewenstein, M. & Pfau, T. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009).

    Article  ADS  Google Scholar 

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Acknowledgements

The authors acknowledge funding support from the ANU PhD student scholarship, Australian Research Council (grant nos: DP240101011, DP220102219, DP180103238), ARC Centre of Excellence in Quantum Computation and Communication Technology (project number CE170100012) and the National Health and Medical Research Council (NHMRC; ID: GA275784).

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  1. School of Engineering, College of Engineering, Computing and Cybernetics, The Australian National University, Canberra, Australian Capital Territory, Australia

    Xueqian Sun & Yuerui Lu

  2. Department of Physics, Philipps-Universität Marburg, Marburg, Germany

    Ermin Malic

  3. Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology, The Australian National University, Canberra, Australian Capital Territory, Australia

    Yuerui Lu

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Y.L. and X.S. conceived the study. All authors contributed to the writing and all aspects of the manuscript and were supervised by Y.L.

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Sun, X., Malic, E. & Lu, Y. Dipolar many-body complexes and their interactions in stacked 2D heterobilayers. Nat Rev Phys 6, 439–454 (2024). https://doi.org/10.1038/s42254-024-00721-4

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