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Long-range ferroelectric order in two-dimensional excitonic insulators

M. M. Glazov1,* and A. İmamoğlu2,†

  • *Contact author: glazov@coherent.ioffe.ru
  • †Contact author: imamoglu@phys.ethz.ch
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Phys. Rev. Research 8, 033220 – Published 24 August, 2026

DOI: https://doi.org/10.1103/mvym-8n1z

Abstract

It is generally argued that Mermin-Wagner theorem excludes the possibility of long-range order in two-dimensional bosonic systems at nonzero temperatures. In contrast, we show here that generic bilayer semiconductors could demonstrate true Bose-Einstein condensation of interlayer excitons. We find that the key requirements include (1) reduction of the interlayer band gap using an applied electric field so that excitons spontaneously appear in the ground state, (2) band structure that allows for long-range electron-hole exchange interaction, and (3) a finite magnetic field. When these conditions are fulfilled, superfluidity and ferroelectric order can coexist in two-dimensional excitonic insulators. Our results provide an example where coupling to the vacuum electromagnetic near field leads to a finite temperature second-order phase transition.

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References (69)

  1. L. V. Keldysh and Y. V. Kopaev, Possible instability of semimetallic state toward Coulomb interaction, Phys. Solid State 6, 2219 (1965).
  2. D. Jérome, T. M. Rice, and W. Kohn, Excitonic insulator, Phys. Rev. 158, 462 (1967).
  3. H. Cercellier, C. Monney, F. Clerc, C. Battaglia, L. Despont, M. G. Garnier, H. Beck, P. Aebi, L. Patthey, H. Berger, and L. Forró, Evidence for an excitonic insulator phase in 1T–TiSe2, Phys. Rev. Lett. 99, 146403 (2007).
  4. K. Seki, Y. Wakisaka, T. Kaneko, T. Toriyama, T. Konishi, T. Sudayama, N. L. Saini, M. Arita, H. Namatame, M. Taniguchi, N. Katayama, M. Nohara, H. Takagi, T. Mizokawa, and Y. Ohta, Excitonic Bose-Einstein condensation in Ta2NiSe5 above room temperature, Phys. Rev. B 90, 155116 (2014).
  5. L. Du, X. Li, W. Lou, G. Sullivan, K. Chang, J. Kono, and R.-R. Du, Evidence for a topological excitonic insulator in InAs/GaSb bilayers, Nat. Commun. 8, 1971 (2017).
  6. A. Kogar, M. S. Rak, S. Vig, A. A. Husain, F. Flicker, Y. I. Joe, L. Venema, G. J. MacDougall, T. C. Chiang, E. Fradkin, J. van Wezel, and P. Abbamonte, Signatures of exciton condensation in a transition metal dichalcogenide, Science 358, 1314 (2017).
  7. S. S. Ataei, D. Varsano, E. Molinari, and M. Rontani, Evidence of ideal excitonic insulator in bulk MoS2 under pressure, Proc. Natl. Acad. Sci. USA 118, e2010110118 (2021).
  8. Z. Sun, Y. Murakami, F. Xuan, T. Kaneko, D. Golež, and A. J. Millis, Dynamical exciton condensates in biased electron-hole bilayers, Phys. Rev. Lett. 133, 217002 (2024).
  9. L. Ma, P. X. Nguyen, Z. Wang, Y. Zeng, K. Watanabe, T. Taniguchi, A. H. MacDonald, K. F. Mak, and J. Shan, Strongly correlated excitonic insulator in atomic double layers, Nature (London) 598, 585 (2021).
  10. N. D. Mermin and H. Wagner, Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models, Phys. Rev. Lett. 17, 1133 (1966).
  11. P. C. Hohenberg, Existence of long-range order in one and two dimensions, Phys. Rev. 158, 383 (1967).
  12. L. C. Andreani and F. Bassani, Exchange interaction and polariton effects in quantum-well excitons, Phys. Rev. B 41, 7536 (1990).
  13. M. M. Glazov, T. Amand, X. Marie, D. Lagarde, L. Bouet, and B. Urbaszek, Exciton fine structure and spin decoherence in monolayers of transition metal dichalcogenides, Phys. Rev. B 89, 201302(R) (2014).
  14. H. Yu, G.-B. Liu, P. Gong, X. Xu, and W. Yao, Dirac cones and Dirac saddle points of bright excitons in monolayer transition metal dichalcogenides, Nat. Commun. 5, 3876 (2014).
  15. D. Y. Qiu, T. Cao, and S. G. Louie, Nonanalyticity, valley quantum phases, and lightlike exciton dispersion in monolayer transition metal dichalcogenides: Theory and first-principles calculations, Phys. Rev. Lett. 115, 176801 (2015).
  16. V. M. Agranovich and M. D. Galanin, Electronic Excitation Energy Transfer in Condensed Matter (North-Holland Publishing Company, Amsterdam, 1982).
  17. A. M. Shentsev and M. M. Glazov, Electromagnetic field assisted exciton diffusion in moiré superlattices, Phys. Rev. B 111, 045301 (2025).
  18. T. Portengen, Th. Östreich, and L. J. Sham, Theory of electronic ferroelectricity, Phys. Rev. B 54, 17452 (1996).
  19. Z. Sun, T. Kaneko, D. Golež, and A. J. Millis, Second-order Josephson effect in excitonic insulators, Phys. Rev. Lett. 127, 127702 (2021).
  20. P. I. Arseev, Electrostatic mechanism of ferroelectric instability, Fiz. Tverd. Tela 67, 314 (2025).
  21. H. Yu, G.-B. Liu, and W. Yao, Brightened spin-triplet interlayer excitons and optical selection rules in van der Waals heterobilayers, 2D Mater. 5, 035021 (2018).
  22. M. Förg, L. Colombier, R. K. Patel, J. Lindlau, A. D. Mohite, H. Yamaguchi, M. M. Glazov, D. Hunger, and A. Högele, Cavity-control of interlayer excitons in van der Waals heterostructures, Nat. Commun. 10, 3697 (2019).
  23. K. K. Grigoryan and M. M. Glazov, Intersubband electric dipole spin resonance in transition metal dichalcogenide heterobilayers, Phys. Rev. B 113, 179605 (2026).
  24. M. A. Semina, Excitons and trions in bilayer van der Waals heterostructures, Phys. Solid State 61, 2218 (2019).
  25. V. V. Tolmachev and S. V. Tiablikov, A new method in the theory of superconductivity. II, J. Exptl. Theoret. Phys. (U.S.S.R.) 34, 66 (1958) [JETP 34, 46 (1958)].
  26. A. N. Kozlov and L. A. Maksimov, The metal-dielectric divalent crystal phase transition, J. Exptl. Theoret. Phys. (U.S.S.R.) 48, 1184 (1965) [JETP 21, 790 (1965)].
  27. A. N. Kozlov and L. A. Maksimov, Collective excitations in semimetals, J. Exptl. Theoret. Phys. (U.S.S.R.) 49, 1284 (1965) [JETP 22, 889 (1966)].
  28. R. R. Guseinov and L. V. Keldysh, Nature of the phase transition under the conditions of an “excitonic” instability in the electronic spectrum of a crystal, Zh. Eksp. Teor. Fiz. 63, 2255 (1972) [JETP 36, 1193 (1973)].
  29. Yu. E. Lozovik and V. I. Yudson, A new mechanism for superconductivity: Pairing between spatially separated electrons and holes, Zh. Eksp. Teor. Fiz. 71, 738 (1976) [JETP 44, 389 (1976)].
  30. Yu. E. Lozovik and V. I. Yudson, The phase fixation in the systems with e-h pairing; collective modes and current states, Solid State Commun. 22, 117 (1977).
  31. P. B. Littlewood, P. R. Eastham, J. M. J. Keeling, F. M. Marchetti, B. D. Simons, and M. H. Szymanska, Models of coherent exciton condensation, J. Phys.: Condens. Matter 16, S3597 (2004).
  32. E. Manousakis, Transition to an excitonic insulator from a two-dimensional conventional insulator, Phys. Rev. B 107, 075105 (2023).
  33. M. Trushin, Interlayer excitonic insulator in two-dimensional double-layer semiconductor junctions: An explicitly solvable model, Phys. Rev. B 106, 125311 (2022).
  34. V. L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. Classical systems, Zh. Eksp. Teor. Fiz. 59, 907 (1970) [JETP 32, 493 (1971)].
  35. V. L. Berezinskii, Destruction of long-range order in one-dimensional and two-dimensional systems possessing a continuous symmetry group. II. Quantum systems, Zh. Eksp. Teor. Fiz. 61, 1144 (1971) [JETP 34, 610 (1972)].
  36. J. M. Kosterlitz and D. J. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C: Solid State Phys. 6, 1181 (1973).
  37. E. M. Lifshitz and L. P. Pitaevskii, Statistical Physics: Theory of the Condensed State (Butterworth-Heinemann, Oxford, 2002).
  38. E. L. Ivchenko, Optical Spectroscopy of Semiconductor Nanostructures (Alpha Science, Harrow, UK, 2005).
  39. F. Stern, Polarizability of a two-dimensional electron gas, Phys. Rev. Lett. 18, 546 (1967).
  40. A. V. Chaplik, Absorption and emission of electromagnetic waves by two-dimensional plasmons, Surf. Sci. Rep. 5, 289 (1985).
  41. M. Z. Maialle, E. A. de A. e. Silva, and L. J. Sham, Exciton spin dynamics in quantum wells, Phys. Rev. B 47, 15776 (1993).
  42. S. V. Gupalov, E. L. Ivchenko, and A. V. Kavokin, Fine structure of localized exciton levels in quantum wells, J. Exp. Theor. Phys. 86, 388 (1998).
  43. P. W. Anderson, Random-phase approximation in the theory of superconductivity, Phys. Rev. 112, 1900 (1958).
  44. P. B. Littlewood and C. M. Varma, Amplitude collective modes in superconductors and their coupling to charge-density waves, Phys. Rev. B 26, 4883 (1982).
  45. D. Pekker and C. M. Varma, Amplitude/Higgs modes in condensed matter physics, Annu. Rev. Condens. Matter Phys. 6, 269 (2015).
  46. P. W. Anderson, Higgs, Anderson and all that, Nat. Phys. 11, 93 (2015).
  47. A. Altland and B. D. Simons, Condensed Matter Field Theory, 2nd ed. (Cambridge University Press, Cambridge, 2010).
  48. W. Chen, C.-J. Huang, and Q. Zhu, Searching for unconventional superfluid in excitons of monolayer semiconductors, Phys. Rev. Lett. 131, 236004 (2023).
  49. A. Griffin, D. W. Snoke, and S. Stringari, Bose-Einstein Condensation (Cambridge University Press, Cambridge, 1996).
  50. K. Huang, C. N. Yang, and J. M. Luttinger, Imperfect Bose gas with hard-sphere interaction, Phys. Rev. 105, 776 (1957).
  51. P. E. Faria, Jr. and J. Fabian, Signatures of electric field and layer separation effects on the spin-valley physics of MoSe2/WSe2 heterobilayers: From energy bands to dipolar excitons, Nanomaterials 13, 1187 (2023).
  52. R. Gillen, Interlayer excitonic spectra of vertically stacked MoSe2/WSe2 heterobilayers, Phys. Status Solidi (B) 258, 2000614 (2021).
  53. L. P. Pitaevskii and S. Stringari, Bose-Einstein Condensation, International Series of Monographs on Physics (Clarendon Press, Oxford, 2003).
  54. M. M. Glazov and R. A. Suris, Collective states of excitons in semiconductors, Phys. Usp. 63, 1051 (2021).
  55. C. Poellmann, P. Steinleitner, U. Leierseder, P. Nagler, G. Plechinger, M. Porer, R. Bratschitsch, C. Schuller, T. Korn, and R. Huber, Resonant internal quantum transitions and femtosecond radiative decay of excitons in monolayer WSe2, Nat. Mater. 14, 889 (2015).
  56. A. Kormanyos, G. Burkard, M. Gmitra, J. Fabian, V. Zólyomi, N. D Drummond, and V. Fal’ko, k·p theory for two-dimensional transition metal dichalcogenide semiconductors, 2D Mater. 2, 022001 (2015).
  57. M. M. Glazov, L. E. Golub, G. Wang, X. Marie, T. Amand, and B. Urbaszek, Intrinsic exciton-state mixing and nonlinear optical properties in transition metal dichalcogenide monolayers, Phys. Rev. B 95, 035311 (2017).
  58. K.-Q. Lin, C. S. Ong, S. Bange, P. E. Faria, Jr., B. Peng, J. D. Ziegler, J. Zipfel, C. Bäuml, N. Paradiso, K. Watanabe, T. Taniguchi, C. Strunk, B. Monserrat, J. Fabian, A. Chernikov, D. Y. Qiu, S. G. Louie, and J. M. Lupton, Narrow-band high-lying excitons with negative-mass electrons in monolayer WSe2, Nat. Commun. 12, 5500 (2021).
  59. K.-Q. Lin, J. D. Ziegler, M. A. Semina, J. V. Mamedov, K. Watanabe, T. Taniguchi, S. Bange, A. Chernikov, M. M. Glazov, and J. M. Lupton, High-lying valley-polarized trions in 2D semiconductors, Nat. Commun. 13, 6980 (2022).
  60. K.-Q. Lin, P. E. Faria, Jr., R. Hübner, J. D. Ziegler, J. M. Bauer, F. Buchner, M. Florian, F. Hofmann, K. Watanabe, T. Taniguchi, J. Fabian, A. Steinhoff, A. Chernikov, S. Bange, and J. M. Lupton, Ultraviolet interlayer excitons in bilayer WSe2, Nat. Nanotechnol. 19, 196 (2024).
  61. I. Amelio, N. D. Drummond, E. Demler, R. Schmidt, and A. Imamoglu, Polaron spectroscopy of a bilayer excitonic insulator, Phys. Rev. B 107, 155303 (2023).
  62. Y. Xu, S. Liu, D. A. Rhodes, K. Watanabe, T. Taniguchi, J. Hone, V. Elser, K. F. Mak, and J. Shan, Correlated insulating states at fractional fillings of moiré superlattices, Nature (London) 587, 214 (2020).
  63. C. Zerba, C. Kuhlenkamp, A. Imamoglu, and M. Knap, Realizing topological superconductivity in tunable Bose-Fermi mixtures with transition metal dichalcogenide heterostructures, Phys. Rev. Lett. 133, 056902 (2024).
  64. J. von Milczewski, X. Chen, A. Imamoglu, and R. Schmidt, Superconductivity induced by strong electron-exciton coupling in doped atomically thin semiconductor heterostructures, Phys. Rev. Lett. 133, 226903 (2024).
  65. M. Xie, M. Hafezi, and S. Das Sarma, Long-lived topological flatband excitons in semiconductor moiré heterostructures: A bosonic Kane-Mele model platform, Phys. Rev. Lett. 133, 136403 (2024).
  66. R. Perea-Causin, H. Liu, and E. J. Bergholtz, Exciton fractional Chern insulators in moiré heterostructures, Phys. Rev. Res. 7, L042033 (2025).
  67. Y. Ashida, A. Imamoglu, J. Faist, D. Jaksch, A. Cavalleri, and E. Demler, Quantum electrodynamic control of matter: Cavity-enhanced ferroelectric phase transition, Phys. Rev. X 10, 041027 (2020).
  68. H. Gao, F. Schlawin, and D. Jaksch, Higgs mode stabilization by photoinduced long-range interactions in a superconductor, Phys. Rev. B 104, L140503 (2021).
  69. L. V. Keldysh and A. N. Kozlov, Collective properties of excitons in semiconductors, Sov. Phys. JETP 27, 79 (1968).

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Phys. Rev. Research 8, 033220– Published 24 August, 2026
  • Received 14 December 2025
  • Accepted 23 July 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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