- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Editors' Suggestion
  • Open Access

Quadrupolar and Dipolar Excitons in Bilayer 2H−MoSe2

Shun Feng1, Aidan J. Campbell1, Bibi Mary Francis1, Hyeonjun Baek2, Takashi Taniguchi3, Kenji Watanabe4, Iann C. Gerber5, Brian D. Gerardot1,*, and Mauro Brotons-Gisbert1,†

  • *Contact author: B.D.Gerardot@hw.ac.uk
  • †Contact author: m.brotons_i_gisbert@hw.ac.uk
PDF

Phys. Rev. Lett. 134, 166901 – Published 25 April, 2025

DOI: https://doi.org/10.1103/PhysRevLett.134.166901

Abstract

We report the experimental observation of quadrupolar exciton states in the reflectance contrast spectrum of 2H-stacked bilayer MoSe2. The application of a vertical electric field results in a quadratic energy redshift of these quadrupolar excitons, in contrast to the linear energy splitting observed in the coexisting dipolar excitons within the bilayer MoSe2. We perform helicity-resolved reflectance contrast measurements to investigate the spin and valley configurations of the quadrupolar exciton states as a function of applied vertical electric and magnetic fields. Comparing our results with a phenomenological coupled-oscillator model indicates that the electric- and magnetic-field dependence of the quadrupolar exciton states can be attributed to the intra- and intervalley hybridization of spin-triplet interlayer excitons with opposite permanent dipole moments, mediated by interlayer hole tunneling. These results position naturally stacked MoSe2 bilayers as a promising platform to explore electric-field-tunable many-body exciton phenomena.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (70)

  1. D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Phys. Rev. Lett. 108, 196802 (2012).
  2. K. F. Mak, K. He, J. Shan, and T. F. Heinz, Nat. Nanotechnol. 7, 494 (2012).
  3. A. Chernikov, T. C. Berkelbach, H. M. Hill, A. Rigosi, Y. Li, B. Aslan, D. R. Reichman, M. S. Hybertsen, and T. F. Heinz, Phys. Rev. Lett. 113, 076802 (2014).
  4. A. V. Stier, N. P. Wilson, K. A. Velizhanin, J. Kono, X. Xu, and S. A. Crooker, Phys. Rev. Lett. 120, 057405 (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., Nat. Commun. 6, 6242 (2015).
  6. P. K. Nayak, Y. Horbatenko, S. Ahn, G. Kim, J.-U. Lee, K. Y. Ma, A.-R. Jang, H. Lim, D. Kim, S. Ryu et al., ACS Nano 11, 4041 (2017).
  7. L. A. Jauregui, A. Y. Joe, K. Pistunova, D. S. Wild, A. A. High, Y. Zhou, G. Scuri, K. De Greve, A. Sushko, C.-H. Yu et al., Science 366, 870 (2019).
  8. A. Ciarrocchi, D. Unuchek, A. Avsar, K. Watanabe, T. Taniguchi, and A. Kis, Nat. Photonics 13, 131 (2019).
  9. H. Baek, M. Brotons-Gisbert, Z. Koong, A. Campbell, M. Rambach, K. Watanabe, T. Taniguchi, and B. Gerardot, Sci. Adv. 6, eaba8526 (2020).
  10. Y. Tang, J. Gu, S. Liu, K. Watanabe, T. Taniguchi, J. Hone, K. F. Mak, and J. Shan, Nat. Nanotechnol. 16, 52 (2021).
  11. Y. Shimazaki, I. Schwartz, K. Watanabe, T. Taniguchi, M. Kroner, and A. Imamoğlu, Nature (London) 580, 472 (2020).
  12. J. Sung, Y. Zhou, G. Scuri, V. Zólyomi, T. I. Andersen, H. Yoo, D. S. Wild, A. Y. Joe, R. J. Gelly, H. Heo et al., Nat. Nanotechnol. 15, 750 (2020).
  13. J. Liang, D. Yang, J. Wu, J. I. Dadap, K. Watanabe, T. Taniguchi, and Z. Ye, Phys. Rev. X 12, 041005 (2022).
  14. K. L. Seyler, P. Rivera, H. Yu, N. P. Wilson, E. L. Ray, D. G. Mandrus, J. Yan, W. Yao, and X. Xu, Nature (London) 567, 66 (2019).
  15. M. Brotons-Gisbert, H. Baek, A. Molina-Sánchez, A. Campbell, E. Scerri, D. White, K. Watanabe, T. Taniguchi, C. Bonato, and B. D. Gerardot, Nat. Mater. 19, 630 (2020).
  16. A. Arora, M. Drüppel, R. Schmidt, T. Deilmann, R. Schneider, M. R. Molas, P. Marauhn, S. Michaelis de Vasconcellos, M. Potemski, M. Rohlfing et al., Nat. Commun. 8, 639 (2017).
  17. Y. Zhang, C. Xiao, D. Ovchinnikov, J. Zhu, X. Wang, T. Taniguchi, K. Watanabe, J. Yan, W. Yao, and X. Xu, Nat. Nanotechnol. 18, 501 (2023).
  18. Z. Lian, D. Chen, Y. Meng, X. Chen, Y. Su, R. Banerjee, T. Taniguchi, K. Watanabe, S. Tongay, C. Zhang et al., Nat. Commun. 14, 5042 (2023).
  19. S. Feng, A. J. Campbell, M. Brotons-Gisbert, D. Andres-Penares, H. Baek, T. Taniguchi, K. Watanabe, B. Urbaszek, I. C. Gerber, and B. D. Gerardot, Nat. Commun. 15, 4377 (2024).
  20. Z. Lian, D. Chen, L. Ma, Y. Meng, Y. Su, L. Yan, X. Huang, Q. Wu, X. Chen, M. Blei et al., Nat. Commun. 14, 4604 (2023).
  21. L. Yu, K. Pistunova, J. Hu, K. Watanabe, T. Taniguchi, and T. F. Heinz, Nat. Mater. 22, 1485 (2023).
  22. W. Li, Z. Hadjri, L. M. Devenica, J. Zhang, S. Liu, J. Hone, K. Watanabe, T. Taniguchi, A. Rubio, and A. Srivastava, Nat. Mater. 22, 1478 (2023).
  23. L. Du, Nat. Rev. Phys. 6, 157 (2024).
  24. T. Deilmann and K. S. Thygesen, 2D Mater. 11, 035032 (2024).
  25. I. C. Gerber, E. Courtade, S. Shree, C. Robert, T. Taniguchi, K. Watanabe, A. Balocchi, P. Renucci, D. Lagarde, X. Marie et al., Phys. Rev. B 99, 035443 (2019).
  26. N. Leisgang, S. Shree, I. Paradisanos, L. Sponfeldner, C. Robert, D. Lagarde, A. Balocchi, K. Watanabe, T. Taniguchi, X. Marie et al., Nat. Nanotechnol. 15, 901 (2020).
  27. N. Peimyoo, T. Deilmann, F. Withers, J. Escolar, D. Nutting, T. Taniguchi, K. Watanabe, A. Taghizadeh, M. F. Craciun, K. S. Thygesen et al., Nat. Nanotechnol. 16, 888 (2021).
  28. L. Sponfeldner, N. Leisgang, S. Shree, I. Paradisanos, K. Watanabe, T. Taniguchi, C. Robert, D. Lagarde, A. Balocchi, X. Marie et al., Phys. Rev. Lett. 129, 107401 (2022).
  29. Ł. Kipczak, A. O. Slobodeniuk, T. Woźniak, M. Bhatnagar, N. Zawadzka, K. Olkowska-Pucko, M. Grzeszczyk, K. Watanabe, T. Taniguchi, A. Babiński et al., 2D Mater. 10, 025014 (2023).
  30. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevLett.134.166901 for additional information about the experimental methods and a detailed discussion of the numerical simulations, which includes Refs. [31–59].
  31. A. J. Campbell, M. Brotons-Gisbert, H. Baek, V. Vitale, T. Taniguchi, K. Watanabe, J. Lischner, and B. D. Gerardot, npj 2D Mater. Appl. 6, 79 (2022).
  32. A. J. Campbell, V. Vitale, M. Brotons-Gisbert, H. Baek, A. Borel, T. V. Ivanova, T. Taniguchi, K. Watanabe, J. Lischner, and B. D. Gerardot, Nat. Phys. 20, 589 (2024).
  33. J. van de Groep, Q. Li, J.-H. Song, P. G. Kik, and M. L. Brongersma, Nanophotonics 12, 3291 (2023).
  34. G. Scuri, Y. Zhou, A. A. High, D. S. Wild, C. Shu, K. De Greve, L. A. Jauregui, T. Taniguchi, K. Watanabe, P. Kim, M. D. Lukin, and H. Park, Phys. Rev. Lett. 120, 037402 (2018).
  35. Y. Zhou, G. Scuri, J. Sung, R. J. Gelly, D. S. Wild, K. De Greve, A. Y. Joe, T. Taniguchi, K. Watanabe, P. Kim et al., Phys. Rev. Lett. 124, 027401 (2020).
  36. I. Epstein, B. Terrés, A. J. Chaves, V.-V. Pusapati, D. A. Rhodes, B. Frank, V. Zimmermann, Y. Qin, K. Watanabe, T. Taniguchi et al., Nano Lett. 20, 3545 (2020).
  37. B. Efron, in Breakthroughs in Statistics: Methodology and Distribution (Springer, New York, 1992), pp. 569–593.
  38. M. Campoy-Quiles, M. I. Alonso, D. D. Bradley, and L. J. Richter, Adv. Funct. Mater. 24, 2116 (2014).
  39. G.-B. Liu, D. Xiao, Y. Yao, X. Xu, and W. Yao, Chem. Soc. Rev. 44, 2643 (2015).
  40. J. Hagel, S. Brem, and E. Malic, 2D Mater. 10, 014013 (2022).
  41. T. Woźniak, P. E. Faria Junior, G. Seifert, A. Chaves, and J. Kunstmann, Phys. Rev. B 101, 235408 (2020).
  42. S. Larentis, H. C. P. Movva, B. Fallahazad, K. Kim, A. Behroozi, T. Taniguchi, K. Watanabe, S. K. Banerjee, and E. Tutuc, Phys. Rev. B 97, 201407(R) (2018).
  43. Y. Zhang, T.-R. Chang, B. Zhou, Y.-T. Cui, H. Yan, Z. Liu, F. Schmitt, J. Lee, R. Moore, Y. Chen et al., Nat. Nanotechnol. 9, 111 (2014).
  44. T. Deilmann, P. Krüger, and M. Rohlfing, Phys. Rev. Lett. 124, 226402 (2020).
  45. Z. Wang, K. F. Mak, and J. Shan, Phys. Rev. Lett. 120, 066402 (2018).
  46. Y. Li, A. Chernikov, X. Zhang, A. Rigosi, H. M. Hill, A. M. Vander Zande, D. A. Chenet, E.-M. Shih, J. Hone, and T. F. Heinz, Phys. Rev. B 90, 205422 (2014).
  47. G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993).
  48. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
  49. P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).
  50. G. Kresse and D. Joubert, Phys. Rev. B 59, 1758 (1999).
  51. S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, J. Chem. Phys. 132, 154104 (2010).
  52. J. Heyd and G. E. Scuseria, J. Chem. Phys. 120, 7274 (2004).
  53. J. Heyd, J. E. Peralta, G. E. Scuseria, and R. L. Martin, J. Chem. Phys. 123, 174101 (2005).
  54. J. Paier, M. Marsman, K. Hummer, G. Kresse, I. C. Gerber, and J. G. Ángyán, J. Chem. Phys. 124, 154709 (2006).
  55. M. Shishkin and G. Kresse, Phys. Rev. B 74, 035101 (2006).
  56. A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Comput. Phys. Commun. 178, 685 (2008).
  57. W. Hanke and L. J. Sham, Phys. Rev. Lett. 43, 387 (1979).
  58. M. Rohlfing and S. G. Louie, Phys. Rev. Lett. 81, 2312 (1998).
  59. D. Das, D. Jana, T. Deilmann, and S. Ghosh, Phys. Rev. B 110, 115201 (2024).
  60. Z. Gong, G.-B. Liu, H. Yu, D. Xiao, X. Cui, X. Xu, and W. Yao, Nat. Commun. 4, 2053 (2013).
  61. R. Pisoni, T. Davatz, K. Watanabe, T. Taniguchi, T. Ihn, and K. Ensslin, Phys. Rev. Lett. 123, 117702 (2019).
  62. I. Paradisanos, S. Shree, A. George, N. Leisgang, C. Robert, K. Watanabe, T. Taniguchi, R. J. Warburton, A. Turchanin, X. Marie et al., Nat. Commun. 11, 2391 (2020).
  63. E. Lorchat, M. Selig, F. Katsch, K. Yumigeta, S. Tongay, A. Knorr, C. Schneider, and S. Höfling, Phys. Rev. Lett. 126, 037401 (2021).
  64. L. Guo, M. Wu, T. Cao, D. M. Monahan, Y.-H. Lee, S. G. Louie, and G. R. Fleming, Nat. Phys. 15, 228 (2019).
  65. G. Wang, A. Chernikov, M. M. Glazov, T. F. Heinz, X. Marie, T. Amand, and B. Urbaszek, Rev. Mod. Phys. 90, 021001 (2018).
  66. H. Yu, G.-B. Liu, and W. Yao, 2D Mater. 5, 035021 (2018).
  67. C. M. Gilardoni, F. Hendriks, C. H. van der Wal, and M. H. D. Guimarães, Phys. Rev. B 103, 115410 (2021).
  68. A. O. Slobodeniuk, Ł. Bala, M. Koperski, M. R. Molas, P. Kossacki, K. Nogajewski, M. Bartos, K. Watanabe, T. Taniguchi, C. Faugeras, M. Potemski et al., 2D Mater. 6, 025026 (2019).
  69. G. Aivazian, Z. Gong, A. M. Jones, R.-L. Chu, J. Yan, D. G. Mandrus, C. Zhang, D. Cobden, W. Yao, and X. Xu, Nat. Phys. 11, 148 (2015).
  70. J. Jasiński, J. Hagel, S. Brem, E. Wietek, T. Taniguchi, K. Watanabe, A. Chernikov, N. Bruyant, M. Dyksik, A. Surrente et al., Nat. Commun. 16, 1382 (2025).

Outline

Information

Phys. Rev. Lett. 134, 166901– Published 25 April, 2025
  • Received 28 November 2024
  • Revised 27 February 2025
  • Accepted 25 March 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation