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Tunneling signatures of interband coherence in dilute exciton condensates
Phys. Rev. B 114, 125128 – Published 24 August, 2026
DOI: https://doi.org/10.1103/mb3n-l45p
Abstract
We theoretically investigate signatures of exciton condensation and the underlying interband coherence in scanning tunneling microscopy. We consider both monolayer and bilayer condensates in the regime of a dilute condensate of tightly bound excitons. For monolayer condensates, interband coherence is directly encoded in spatially oscillating contributions to the tunneling conductance, which break the underlying lattice symmetry. We show how scanning tunneling microscopy allows one to extract the exciton wave function. For bilayer condensates, we show that the formation of the exciton insulator is signaled by the emergence of a characteristic peak in the tunneling conductance, which can be used to extract the (local) exciton density. Our results are based on analytical considerations using a systematic solution of the mean-field equations in powers of the exciton density as well as numerical calculations.
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References (65)
- D. Jérome, T. M. Rice, and W. Kohn, Excitonic insulator, Phys. Rev. 158, 462 (1967).
- B. I. Halperin and T. M. Rice, The excitonic state at the semiconductor-semimetal transition, J. Phys. C: Solid State Phys. 21, 115 (1968).
- L. V. Keldysh and A. N. Kozlov, Collective properties of excitons in semiconductors, Zh. Eksp. Teor. Fiz. 54, 978 (1968) [Sov. J. Exp. Theor. Phys. 27, 521 (1968)].
- A. N. Kozlov and L. A. Maksimov, The metal-dielectric divalent crystal phase transition, J. Exptl. Theoret. Phys. 48, 1184 (1965) [Sov. Phys JETP 21, 790 (1965)].
- Q. Gao, Y.-h. Chan, Y. Wang, H. Zhang, P. Jinxu, S. Cui, Y. Yang, Z. Liu, D. Shen, Z. Sun, J. Jiang, T. C. Chiang, and P. Chen, Evidence of high-temperature exciton condensation in a two-dimensional semimetal, Nat. Commun. 14, 994 (2023).
- Y. Jia, P. Wang, C.-L. Chiu, Z. Song, G. Yu, B. Jäck, S. Lei, S. Klemenz, F. A. Cevallos, M. Onyszczak, N. Fishchenko, X. Liu, G. Farahi, F. Xie, Y. Xu, K. Watanabe, T. Taniguchi, B. A. Bernevig, R. J. Cava, L. M. Schoop, et al., Evidence for a monolayer excitonic insulator, Nat. Phys. 18, 87 (2022).
- B. Sun, W. Zhao, T. Palomaki, Z. Fei, E. Runburg, P. Malinowski, X. Huang, J. Cenker, Y.-T. Cui, J.-H. Chu, X. Xu, S. S. Ataei, D. Varsano, M. Palummo, E. Molinari, M. Rontani, and D. H. Cobden, Evidence for equilibrium exciton condensation in monolayer , Nat. Phys. 18, 94 (2022).
- 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).
- Z. Wang, D. A. Rhodes, K. Watanabe, T. Taniguchi, J. C. Hone, J. Shan, and K. F. Mak, Evidence of high-temperature exciton condensation in two-dimensional atomic double layers, Nature (London) 574, 76 (2019).
- R. Qi, A. Y. Joe, Z. Zhang, Y. Zeng, T. Zheng, Q. Feng, J. Xie, E. Regan, Z. Lu, T. Taniguchi, K. Watanabe, S. Tongay, M. F. Crommie, A. H. MacDonald, and F. Wang, Thermodynamic behavior of correlated electron-hole fluids in van der Waals heterostructures, Nat. Commun. 14, 8264 (2023).
- M. S. Hossain, Z.-J. Cheng, Y.-X. Jiang, T. A. Cochran, S.-B. Zhang, H. Wu, X. Liu, X. Zheng, G. Cheng, B. Kim, Q. Zhang, M. Litskevich, J. Zhang, J. Liu, J.-X. Yin, X. P. Yang, J. D. Denlinger, M. Tallarida, J. Dai, E. Vescovo, et al., Topological excitonic insulator with tunable momentum order, Nat. Phys. 21, 1250 (2025).
- J. Huang, B. Jiang, J. Yao, D. Yan, X. Lei, J. Gao, Z. Guo, F. Jin, Y. Li, Z. Yuan, C. Chai, H. Sheng, M. Pan, F. Chen, J. Liu, S. Gao, G. Qu, B. Liu, Z. Jiang, Z. Liu, et al., Evidence for an excitonic insulator state in , Phys. Rev. X 14, 011046 (2024).
- 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 above room temperature, Phys. Rev. B 90, 155116 (2014).
- Q. He, X. Que, L. Zhou, M. Isobe, D. Huang, and H. Takagi, Tunneling-tip-induced collapse of the charge gap in the excitonic insulator , Phys. Rev. Res. 3, L032074 (2021).
- Y. F. Lu, H. Kono, T. I. Larkin, A. W. Rost, T. Takayama, A. V. Boris, B. Keimer, and H. Takagi, Zero-gap semiconductor to excitonic insulator transition in , Nat. Commun. 8, 14408 (2017).
- K. Kim, H. Kim, J. Kim, C. Kwon, J. S. Kim, and B. J. Kim, Direct observation of excitonic instability in , Nat. Commun. 12, 1969 (2021).
- 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 , Phys. Rev. Lett. 99, 146403 (2007).
- 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).
- K. Rossnagel, On the origin of charge-density waves in select layered transition-metal dichalcogenides, J. Phys.: Condens. Matter 23, 213001 (2011).
- C. Comte and P. Nozières, Exciton Bose condensation : The ground state of an electron-hole gas - I. Mean field description of a simplified model, J. Phys. France 43, 1069 (1982).
- L. Windgätter, M. Rösner, G. Mazza, H. Hübener, A. Georges, A. J. Millis, S. Latini, and A. Rubio, Common microscopic origin of the phase transitions in and the excitonic insulator candidate , npj Comput. Mater. 7, 210 (2021).
- E. Baldini, A. Zong, D. Choi, C. Lee, M. H. Michael, L. Windgaetter, I. I. Mazin, S. Latini, D. Azoury, B. Lv, A. Kogar, Y. Su, Y. Wang, Y. Lu, T. Takayama, H. Takagi, A. J. Millis, A. Rubio, E. Demler, and N. Gedik, The spontaneous symmetry breaking in is structural in nature, Proc. Natl. Acad. Sci. USA 120, e2221688120 (2023).
- P. B. Littlewood and X. Zhu, Possibilities for exciton condensation in semiconductor quantum-well structures, Phys. Scr. T68, 56 (1996).
- S. Gupta, A. Kutana, and B. I. Yakobson, Heterobilayers of 2D materials as a platform for excitonic superfluidity, Nat. Commun. 11, 2989 (2020).
- Y. H. Kwan, T. Devakul, S. L. Sondhi, and S. A. Parameswaran, Theory of competing excitonic orders in insulating monolayers, Phys. Rev. B 104, 125133 (2021).
- J. Lee, C.-J. Kang, M. J. Eom, J. S. Kim, B. I. Min, and H. W. Yeom, Strong interband interaction in the excitonic insulator phase of , Phys. Rev. B 99, 075408 (2019).
- M. Xie and A. MacDonald, Electrical reservoirs for bilayer excitons, Phys. Rev. Lett. 121, 067702 (2018).
- Y. Zeng and A. H. MacDonald, Electrically controlled two-dimensional electron-hole fluids, Phys. Rev. B 102, 085154 (2020).
- R. Qi, A. Y. Joe, Z. Zhang, J. Xie, Q. Feng, Z. Lu, Z. Wang, T. Taniguchi, K. Watanabe, S. Tongay, and F. Wang, Perfect Coulomb drag and exciton transport in an excitonic insulator, Science 388, 278 (2025).
- P. X. Nguyen, L. Ma, R. Chaturvedi, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Perfect Coulomb drag in a dipolar excitonic insulator, Science 388, 274 (2025).
- J. Eisenstein, Exciton condensation in bilayer quantum Hall systems, Annu. Rev. Condens. Matter Phys. 5, 159 (2014).
- D. Nandi, A. D. K. Finck, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Exciton condensation and perfect Coulomb drag, Nature (London) 488, 481 (2012).
- M. Kellogg, J. P. Eisenstein, L. N. Pfeiffer, and K. W. West, Vanishing Hall resistance at high magnetic field in a double-layer two-dimensional electron system, Phys. Rev. Lett. 93, 036801 (2004).
- E. Tutuc, M. Shayegan, and D. A. Huse, Counterflow measurements in strongly correlated GaAs hole bilayers: Evidence for electron-hole pairing, Phys. Rev. Lett. 93, 036802 (2004).
- 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).
- X. Liu, G. Farahi, C.-L. Chiu, Z. Papic, K. Watanabe, T. Taniguchi, M. P. Zaletel, and A. Yazdani, Visualizing broken symmetry and topological defects in a quantum Hall ferromagnet, Science 375, 321 (2022).
- H. Kim, Y. Choi, E. Lantagne-Hurtubise, C. Lewandowski, A. Thomson, L. Kong, H. Zhou, E. Baum, Y. Zhang, L. Holleis, K. Watanabe, T. Taniguchi, A. F. Young, J. Alicea, and S. Nadj-Perge, Imaging inter-valley coherent order in magic-angle twisted trilayer graphene, Nature (London) 623, 942 (2023).
- K. P. Nuckolls, R. L. Lee, M. Oh, D. Wong, T. Soejima, J. P. Hong, D. Călugăru, J. Herzog-Arbeitman, B. A. Bernevig, K. Watanabe, T. Taniguchi, N. Regnault, M. P. Zaletel, and A. Yazdani, Quantum textures of the many-body wavefunctions in magic-angle graphene, Nature (London) 620, 525 (2023).
- D. Călugăru, N. Regnault, M. Oh, K. P. Nuckolls, D. Wong, R. L. Lee, A. Yazdani, O. Vafek, and B. A. Bernevig, Spectroscopy of twisted bilayer graphene correlated insulators, Phys. Rev. Lett. 129, 117602 (2022).
- J. P. Hong, T. Soejima, and M. P. Zaletel, Detecting symmetry breaking in magic angle graphene using scanning tunneling microscopy, Phys. Rev. Lett. 129, 147001 (2022).
- Y. H. Kwan, G. Wagner, T. Soejima, M. P. Zaletel, S. H. Simon, S. A. Parameswaran, and N. Bultinck, Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene, Phys. Rev. X 11, 041063 (2021).
- N. Bultinck, E. Khalaf, S. Liu, S. Chatterjee, A. Vishwanath, and M. P. Zaletel, Ground state and hidden symmetry of magic angle graphene at even integer filling, Phys. Rev. X 10, 031034 (2020).
- M. Papaj, Spectroscopic signatures of excitonic order on quantum spin Hall edge states, Phys. Rev. B 110, 165422 (2024).
- L. Watson, J. Ripoll, Z. Tong, A. Kumar, Y. Que, Y.-H. Chan, H. Lin, S. Mukherjee, M. Garnica, M. T. Edmonds, M. Papaj, A. L. Vazquez de Parga, B. Weber, I. Di Bernardo, and M. S. Fuhrer, Observation of the charge density wave excitonic order parameter in topological insulator monolayer , ACS Nano 19, 32374 (2025).
- R. Maezono, P. López Ríos, T. Ogawa, and R. J. Needs, Excitons and biexcitons in symmetric electron-hole bilayers, Phys. Rev. Lett. 110, 216407 (2013).
- S. De Palo, F. Rapisarda, and G. Senatore, Excitonic condensation in a symmetric electron-hole bilayer, Phys. Rev. Lett. 88, 206401 (2002).
- Y. E. Lozovik and V. I. Yudson, Feasibility of superfluidity of paired spatially separated electrons and holes; a new superconductivity mechanism, Zh. Eksp. Teor. Fiz. 22, 556 (1975) [JETP Lett. 22, 274 (1975)].
- Y. E. Lozovik, I. Kurbakov, G. Astrakharchik, J. Boronat, and M. Willander, Strong correlation effects in 2D Bose–Einstein condensed dipolar excitons, Solid State Commun. 144, 399 (2007).
- For a more quantitative theory, one should also include dielectric effects due to the polarizability of the intrinsic semiconductor. This can be done using the Rytova-Keldysh potential [64, 65] corresponding to the dielectric function , where the characteristic length parametrized the polarizability of the intrinsic semiconductor.
- X. Zhu, P. B. Littlewood, M. S. Hybertsen, and T. M. Rice, Exciton condensate in semiconductor quantum well structures, Phys. Rev. Lett. 74, 1633 (1995).
- M. M. Fogler, L. V. Butov, and K. S. Novoselov, High-temperature superfluidity with indirect excitons in van der Waals heterostructures, Nat. Commun. 5, 4555 (2014).
- Strictly speaking, there is no Bose condensation in the absence of interactions in a homogeneous two-dimensional system. Here, the wave function in Eq. (9) merely motivates the more general variational Hartree-Fock ansatz in Eq. (10) for the interacting system. For a more complete discussion of the nature of exciton condensation in two dimensions, see Refs. [24, 51].
- V. Fock, Näherungsmethode zur Lösung des quantenmechanischen Mehrkörperproblems, Z. Phys. 61, 126 (1930).
- T. Koopmans, Über die Zuordnung von Wellenfunktionen und Eigenwerten zu den einzelnen Elektronen eines Atoms, Physica 1, 104 (1934).
- In monolayer samples, electron and hole numbers are not conserved when going beyond the dominant-term approximation. In this case, the formation of the exciton condensate only involves breaking of the discrete lattice translation symmetry by the formation of a density wave of charge, spin, or magnetization current. This does not occur via a BKT transition and is easily pinned in real samples by residual disorder.
- F.-C. Wu, F. Xue, and A. H. MacDonald, Theory of two-dimensional spatially indirect equilibrium exciton condensates, Phys. Rev. B 92, 165121 (2015).
- Y.-Q. Wang, M. Papaj, and J. E. Moore, Breakdown of helical edge state topologically protected conductance in time-reversal-breaking excitonic insulators, Phys. Rev. B 108, 205420 (2023).
- S. Kwon, K.-H. Jin, J. E. Han, S. Lee, C. Won, S.-W. Cheong, and H. W. Yeom, Yu-Shiba-Rusinov bound states of exciton condensate, arXiv:2512.23724.
- Z. Zhang, J. Xie, W. Zhao, R. Qi, C. Sanborn, S. Wang, S. Kahn, K. Watanabe, T. Taniguchi, A. Zettl, M. Crommie, and F. Wang, Engineering correlated insulators in bilayer graphene with a remote Coulomb superlattice, Nat. Mater. 23, 189 (2024).
- L. Gu, J. Zhu, L. Zhang, S. Felsenfeld, B. Gao, R. Ma, K. Watanabe, T. Taniguchi, J. Hone, C. R. Dean, D. Xiao, and X. Xu, Remote imprinting of moiré lattices, Nat. Mater. 23, 219 (2024).
- X. Zhu, M. S. Hybertsen, and P. B. Littlewood, Electron-hole system revisited: A variational quantum Monte Carlo study, Phys. Rev. B 54, 13575 (1996).
- K. Asano and T. Yoshioka, Exciton–Mott physics in two-dimensional electron–hole systems: Phase diagram and single-particle spectra, J. Phys. Soc. Jpn. 83, 084702 (2014).
- K. Kolář and F. von Oppen, Dataset for tunneling signatures of interband coherence in dilute exciton condensates, [Dataset], Zenodo, 2026, https://doi.org/10.5281/zenodo.18322790.
- N. S. Rytova, Screened potential of a point charge in a thin film, Moscow Univ. Phys. Bull. 3, 30 (1967).
- L. V. Keldysh, Coulomb interaction in thin semiconduc- tor and semimetal films, Zh. Eksp. Teor. Fiz. 29, 716 (1979) [JETP Lett. 29, 658 (1979)].