• Wigner, E. On the interaction of electrons in metals. Phys. Rev. 46, 1002–1011 (1934).

    Article 
    ADS 

    Google Scholar
     

  • Smoleński, T. et al. Signatures of Wigner crystal of electrons in a monolayer semiconductor. Nature 595, 53–57 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

  • Tsui, Y.-C. et al. Direct observation of a magnetic-field-induced Wigner crystal. Nature 628, 287–292 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Xiang, Z. et al. Imaging quantum melting in a disordered 2D Wigner solid. Science 388, 736–740 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Crandall, R. S. & Williams, R. Crystallization of electrons on the surface of liquid helium. Phys. Lett. A 34, 404–405 (1971).

    Article 
    ADS 

    Google Scholar
     

  • Zeng, Y. et al. Exciton density waves in Coulomb-coupled dual moiré lattices. Nat. Mater. 22, 175–179 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Lagoin, C., Suffit, S., Baldwin, K., Pfeiffer, L. & Dubin, F. Dual-density waves with neutral and charged dipolar excitons of GaAs bilayers. Nat. Mater. 22, 170–174 (2023).

    ADS 

    Google Scholar
     

  • Xiong, R. et al. Correlated insulator of excitons in WSe2/WS2 moiré superlattices. Science 380, 860–864 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Gao, B. et al. Excitonic Mott insulator in a Bose-Fermi-Hubbard system of moiré WS2/WSe2 heterobilayer. Nat. Commun. 15, 2305 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Lian, Z. et al. Valley-polarized excitonic Mott insulator in WS2/WSe2 moiré superlattice. Nat. Phys. 20, 34–39 (2024).

    Article 

    Google Scholar
     

  • Lagoin, C., Suffit, S., Baldwin, K., Pfeiffer, L. & Dubin, F. Mott insulator of strongly interacting two-dimensional semiconductor excitons. Nat. Phys. 18, 149–153 (2022).

    Article 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

  • Lagoin, C. et al. Extended Bose–Hubbard model with dipolar excitons. Nature 609, 485–489 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Bai, Y. et al. Evidence for exciton crystals in a 2D semiconductor heterotrilayer. Nano Lett. 23, 11621–11629 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Lagoin, C., Baldwin, K., Pfeiffer, L. & Dubin, F. Superlattice quantum solid of dipolar excitons. Phys. Rev. Lett. 132, 176001 (2024).

    Article 
    ADS 

    Google Scholar
     

  • Lagoin, C., Morin, C., Baldwin, K., Pfeiffer, L. & Dubin, F. Bose-Hubbard simulator with long-range hopping. Preprint at https://arxiv.org/abs/2410.17162 (2025).

  • Zhang, Z. et al. Correlated interlayer exciton insulator in heterostructures of monolayer WSe2 and moiré WS2/WSe2. Nat. Phys. 18, 1214–1220 (2022).

    Article 

    Google Scholar
     

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

    Article 

    Google Scholar
     

  • Ma, L. et al. Strongly correlated excitonic insulator in atomic double layers. Nature 598, 585–589 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Qi, R. et al. Thermodynamic behavior of correlated electron-hole fluids in van der Waals heterostructures. Nat. Commun. 14, 8264 (2023).

    Article 
    ADS 

    Google Scholar
     

  • Qi, R. et al. Perfect Coulomb drag and exciton transport in an excitonic insulator. Science 388, 278–283 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Nguyen, P. X. et al. Perfect Coulomb drag in a dipolar excitonic insulator. Science 388, 274–278 (2025).

    Article 
    ADS 

    Google Scholar
     

  • Joglekar, Y. N., Balatsky, A. V. & Das Sarma, S. Wigner supersolid of excitons in electron-hole bilayers. Phys. Rev. B 74, 233302 (2006).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

  • Scuri, G. et al. Large excitonic reflectivity of monolayer MoSe2 encapsulated in hexagonal boron nitride. Phys. Rev. Lett. 120, 037402 (2018).

    Article 
    ADS 

    Google Scholar
     

  • 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
     

  • Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).

    Article 
    ADS 

    Google Scholar
     

  • Nguyen, P. X. et al. Quantum oscillations in a dipolar excitonic insulator. Nat. Mater. 25, 42–48 (2026).

    Article 
    ADS 

    Google Scholar
     

  • Qi, R. et al. Competition between excitonic insulators and quantum Hall states in correlated electron–hole bilayers. Nat. Mater. 25, 35–41 (2026).

    Article 
    ADS 

    Google Scholar
     

  • Sung, J. et al. An electronic microemulsion phase emerging from a quantum crystal-to-liquid transition. Nat. Phys. 21, 437–443 (2025).

    Article 

    Google Scholar
     

  • Hong, J. et al. Deciphering the intense postgap absorptions of monolayer transition metal dichalcogenides. ACS Nano 15, 7783–7789 (2021).

    Article 

    Google Scholar
     

  • Wessel, S. & Troyer, M. Supersolid hard-core bosons on the triangular lattice. Phys. Rev. Lett. 95, 127205 (2005).

    Article 
    ADS 

    Google Scholar
     

  • Gan, J.-Y., Wen, Y.-C. & Yu, Y. Supersolidity and phase diagram of softcore bosons in a triangular lattice. Phys. Rev. B 75, 094501 (2007).

    Article 
    ADS 

    Google Scholar
     

  • Koziol, J. A., Morigi, G. & Schmidt, K. P. Quantum phases of hardcore bosons with repulsive dipolar density-density interactions on two-dimensional lattices. SciPost Phys. 17, 111 (2024).

    Article 
    ADS 
    MathSciNet 

    Google Scholar
     

  • Du, L. et al. Evidence for a topological excitonic insulator in InAs/GaSb bilayers. Nat. Commun. 8, 1971 (2017).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 

    Google Scholar
     

  • 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).

    Article 

    Google Scholar
     

  • Li, H. et al. Electrode-free anodic oxidation nanolithography of low-dimensional materials. Nano Lett. 18, 8011–8015 (2018).

    Article 
    ADS 

    Google Scholar