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Collective excitations of the U(1)-symmetric exciton insulator in a cavity

Katharina Lenk and Martin Eckstein

  • Department of Physics, University of Erlangen-Nürnberg, 91058 Erlangen, Germany

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Phys. Rev. B 102, 205129 – Published 24 November, 2020

DOI: https://doi.org/10.1103/PhysRevB.102.205129

Abstract

We investigate the equilibrium state and the collective modes of an excitonic insulator (EI) in a Fabry-Pérot cavity. In an EI, two bands of a semiconductor or semimetal spontaneously hybridize due to the Coulomb interaction between electrons and holes, leading to the opening of a gap. The coupling to the electromagnetic field reduces the symmetry of the system with respect to phase rotations of the excitonic order parameter from U(1) to Z2. While the reduction to a discrete symmetry would, in general, lead to a gapped phase mode and enhance the stability of the ordered phase, the coupling to the cavity leaves the mean-field ground state unaffected. Its energy remains invariant under U(1) phase rotations, in spite of the lower Z2 symmetry imposed by the cavity. In a dipolar gauge, this can be traced back to the balancing of the linear light-matter coupling and the dipolar self-interaction at zero frequency. At nonzero frequency, however, the collective excitations do reflect the lower Z2 symmetry. While our model is studied using a mean-field decoupling of the light-matter approximation (which is exact in the single-mode limit), the results show that fluctuations beyond mean field could play a crucial role in finding the true phase at finite temperature.

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References (38)

  1. D. N. Basov, R. D. Averitt, and D. Hsieh, Nat. Mater. 16, 1077 (2017).
  2. A. Frisk Kockum, A. Miranowicz, S. De Liberato, S. Savasta, and F. Nori, Nat. Rev. Phys. 1, 19 (2019).
  3. J. Schachenmayer, C. Genes, E. Tignone, and G. Pupillo, Phys. Rev. Lett. 114, 196403 (2015).
  4. M. Kiffner, J. R. Coulthard, F. Schlawin, A. Ardavan, and D. Jaksch, Phys. Rev. B 99, 085116 (2019).
  5. F. Schlawin, A. Cavalleri, and D. Jaksch, Phys. Rev. Lett. 122, 133602 (2019).
  6. M. A. Sentef, M. Ruggenthaler, and A. Rubio, Sci. Adv. 4, eaau6969 (2018).
  7. G. Mazza and A. Georges, Phys. Rev. Lett. 122, 017401 (2019).
  8. X. Wang, E. Ronca, and M. A. Sentef, Phys. Rev. B 99, 235156 (2019).
  9. J. B. Curtis, Z. M. Raines, A. A. Allocca, M. Hafezi, and V. M. Galitski, Phys. Rev. Lett. 122, 167002 (2019).
  10. M. Kiffner, J. Coulthard, F. Schlawin, A. Ardavan, and D. Jaksch, New J. Phys. 21, 073066 (2019).
  11. E. Orgiu, J. George, J. A. Hutchison, E. Devaux, J. F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachenmayer, C. Genes, G. Pupillo, P. Samorì, and T. W. Ebbesen, Nat. Mater. 14, 1123 (2015).
  12. N. F. Mott, Philos. Mag.: J. Theor. Expt. Appl. Phys. 6, 287 (1961).
  13. B. I. Halperin and T. M. Rice, Rev. Mod. Phys. 40, 755 (1968).
  14. D. Jérome, T. M. Rice, and W. Kohn, Phys. Rev. 158, 462 (1967).
  15. T. Kaneko, T. Toriyama, T. Konishi, and Y. Ohta, Phys. Rev. B 87, 035121 (2013).
  16. G. Mazza, M. Rösner, L. Windgätter, S. Latini, H. Hübener, A. J. Millis, A. Rubio, and A. Georges, Phys. Rev. Lett. 124, 197601 (2020).
  17. 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, Science 358, 1314 (2017).
  18. T. Rohwer, S. Hellmann, M. Wiesenmayer, C. Sohrt, A. Stange, B. Slomski, A. Carr, Y. Liu, L. M. Avila, M. Kalläne, S. Mathias, L. Kipp, K. Rossnagel, and M. Bauer, Nature (London) 471, 490 (2011).
  19. S. Mathias, S. Eich, J. Urbancic, S. Michael, A. V. Carr, S. Emmerich, A. Stange, T. Popmintchev, T. Rohwer, M. Wiesenmayer, A. Ruffing, S. Jakobs, S. Hellmann, P. Matyba, C. Chen, L. Kipp, M. Bauer, H. C. Kapteyn, H. C. Schneider, K. Rossnagel, M. M. Murnane, and M. Aeschlimann, Nat. Commun. 7, 12902 (2016).
  20. D. Golež, P. Werner, and M. Eckstein, Phys. Rev. B 94, 035121 (2016).
  21. M. Porer, U. Leierseder, J. M. Ménard, H. Dachraoui, L. Mouchliadis, I. E. Perakis, U. Heinzmann, J. Demsar, K. Rossnagel, and R. Huber, Nat. Mater. 13, 857 (2014).
  22. D. Werdehausen, T. Takayama, M. Höppner, G. Albrecht, A. W. Rost, Y. Lu, D. Manske, H. Takagi, and S. Kaiser, Sci. Adv. 4, eaap8652 (2018).
  23. S. Mor, M. Herzog, D. Golež, P. Werner, M. Eckstein, N. Katayama, M. Nohara, H. Takagi, T. Mizokawa, C. Monney, and J. Stähler, Phys. Rev. Lett. 119, 086401 (2017).
  24. B. Zenker, H. Fehske, and H. Beck, Phys. Rev. B 90, 195118 (2014).
  25. B. Zenker, H. Fehske, H. Beck, C. Monney, and A. R. Bishop, Phys. Rev. B 88, 075138 (2013).
  26. Y. Murakami, N. Tsuji, M. Eckstein, and P. Werner, Phys. Rev. B 96, 045125 (2017).
  27. T. Portengen, T. Östreich, and L. J. Sham, Phys. Rev. B 54, 17452 (1996).
  28. C. D. Batista, Phys. Rev. Lett. 89, 166403 (2002).
  29. B. Zenker, H. Fehske, and C. D. Batista, Phys. Rev. B 82, 165110 (2010).
  30. G. M. Andolina, F. M. D. Pellegrino, V. Giovannetti, A. H. MacDonald, and M. Polini, Phys. Rev. B 100, 121109(R) (2019).
  31. O. Di Stefano, A. Settineri, V. Macrì, L. Garziano, R. Stassi, S. Savasta, and F. Nori, Nat. Phys. 15, 803 (2019).
  32. D. De Bernardis, P. Pilar, T. Jaako, S. De Liberato, and P. Rabl, Phys. Rev. A 98, 053819 (2018).
  33. J. Li, D. Golež, G. Mazza, A. Millis, G. Antoine, and M. Eckstein, Phys. Rev. B 101, 205140 (2020).
  34. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
  35. B. Zenker, D. Ihle, F. X. Bronold, and H. Fehske, Phys. Rev. B 85, 121102(R) (2012).
  36. In contrast, in a geometry different from the Fabry-Pérot cavity, a polarization generates stray fields. The existence of metallic mirrors will partially quench these external fields, and therefore change the energetics of the transition and shift the phase transition.
  37. C. Schäfer, M. Ruggenthaler, V. Rokaj, and A. Rubio, arXiv:1911.08427.
  38. Z. Nussinov and J. van den Brink, Rev. Mod. Phys. 87, 1 (2015).

Outline

Information

Phys. Rev. B 102, 205129– Published 24 November, 2020
  • Received 27 February 2020
  • Revised 30 October 2020
  • Accepted 30 October 2020
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