Skip to main content
Log in

Coulomb repulsion of holes and competition between \({d_{{x^2} - {y^2}}}\) -wave and s-wave parings in cuprate superconductors

  • Order, Disorder, and Phase Transition in Condensed System
  • Published:
Journal of Experimental and Theoretical Physics Aims and scope Submit manuscript

Abstract

The effect of the Coulomb repulsion of holes on the Cooper instability in an ensemble of spin–polaron quasiparticles has been analyzed, taking into account the peculiarities of the crystallographic structure of the CuO2 plane, which are associated with the presence of two oxygen ions and one copper ion in the unit cell, as well as the strong spin–fermion coupling. The investigation of the possibility of implementation of superconducting phases with d-wave and s-wave of the order parameter symmetry has shown that in the entire doping region only the d-wave pairing satisfies the self-consistency equations, while there is no solution for the s-wave pairing. This result completely corresponds to the experimental data on cuprate HTSC. It has been demonstrated analytically that the intersite Coulomb interaction does not affect the superconducting d-wave pairing, because its Fourier transform V q does not appear in the kernel of the corresponding integral equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. P. W. Anderson, Science 235, 1196 (1987).

    Article  ADS  Google Scholar 

  2. N. F. Mott, Metal-Insulator Transitions (Nauka, Moscow, 1979; Taylor, London, 1974).

    Google Scholar 

  3. J. C. Hubbard, Proc. R. Soc. London A 276, 238 (1963).

    Article  ADS  Google Scholar 

  4. R. O. Zaitsev and V. A. Ivanov, Sov. Phys. Solid State 29, 1475 (1987).

    Google Scholar 

  5. J. C. Hubbard, Proc. R. Soc. London A 285, 542 (1965).

    Article  ADS  Google Scholar 

  6. S. Shubin and S. Vonsowsky, Proc. R. Soc. A 145, 159 (1934).

    Article  ADS  Google Scholar 

  7. S. Shubin and S. Vonsowsky, Phys. Zs. UdSSR 7, 292 (1935); Phys. Zs. UdSSR 10, 348 (1936).

    Google Scholar 

  8. R. O. Zaitsev, V. A. Ivanov, and Yu. V. Mikhailova, Fiz. Met. Metalloved. 65, 1032 (1988); Fiz. Met. Metalloved. 68, 1108 (1989).

    ADS  Google Scholar 

  9. R. O. Zaitsev, J. Exp. Theor. Phys. 98, 780 (2004).

    Article  ADS  Google Scholar 

  10. V. V. Val’kov and M. M. Korovushkin, J. Exp. Theor. Phys. 112, 108 (2011).

    Article  ADS  Google Scholar 

  11. V. J. Emery, Phys. Rev. Lett. 58, 2794 (1987).

    Article  ADS  Google Scholar 

  12. J. E. Hirsch, Phys. Rev. Lett. 59, 228 (1987).

    Article  ADS  Google Scholar 

  13. Yu. B. Gaididei and V. M. Loktev, Phys. Status Solidi B 147, 307 (1988).

    Article  ADS  Google Scholar 

  14. C. M. Varma, S. Schmitt-Rink, and E. Abrahams, Solid State Comm. 62, 681 (1987).

    Article  ADS  Google Scholar 

  15. F. C. Zhang and T. M. Rice, Phys. Rev. B 37, 3759 (1988).

    Article  ADS  Google Scholar 

  16. J. H. Jefferson, H. Eskes, and L. F. Feiner, Phys. Rev. B 45, 7959 (1992).

    Article  ADS  Google Scholar 

  17. V. I. Belinicher and A. L. Chernyshev, Phys. Rev. B 47, 390 (1993).

    Article  ADS  Google Scholar 

  18. L. F. Feiner, J. H. Jefferson, and R. Raimondi, Phys. Rev. B 53, 8751 (1996).

    Article  ADS  Google Scholar 

  19. V. Gavrichkov, A. Borisov, and S. G. Ovchinnikov, Phys. Rev. B 64, 235124 (2001).

    Article  ADS  Google Scholar 

  20. M. Yu. Kagan and T. M. Rice, J. Phys.: Condens. Matter 6, 3771 (1994).

    ADS  Google Scholar 

  21. Yu. A. Izyumov, Phys. Usp. 40, 445 (1997); Phys. Usp. 42, 215 (1999).

    Article  Google Scholar 

  22. N. M. Plakida, High-Temperature Cuprate Superconductors (Springer, Berlin, Heidelberg, 2010).

    Book  Google Scholar 

  23. V. Yu. Yushankhai, G. M. Vujicic, and R. B. Zakula, Phys. Lett. A 151, 254 (1990).

    Article  ADS  Google Scholar 

  24. V. V. Val’kov, T. A. Val’kova, D. M. Dzebisashvili, and S. G. Ovchinnikov, JETP Lett. 75, 378 (2002).

    Article  ADS  Google Scholar 

  25. N. M. Plakida and V. S. Oudovenko, Eur. Phys. J. B 86, 115 (2013); J. Exp. Theor. Phys. 59, 554 (2013).

    Google Scholar 

  26. N. M. Plakida, Physica C 531, 39 (2016).

    Article  ADS  Google Scholar 

  27. R. O. Zaitsev, KINE Preprint No. IAE-3927/1 (Kurchatov Inst. Nuclear Energy, Moscow, 1984).

    Google Scholar 

  28. H. Fröhlich, Phys. Rev. 79, 845 (1950).

    Article  ADS  Google Scholar 

  29. V. V. Tolmachev, Sov. Phys. Dokl. 6, 800 (1961).

    ADS  Google Scholar 

  30. V. V. Val’kov, D. M. Dzebisashvili, M. M. Korovushkin, and A. F. Barabanov, JETP Lett. 103, 385 (2016).

    Article  ADS  Google Scholar 

  31. A. F. Barabanov, L. A. Maksimov, and G. V. Uimin, JETP Lett. 47, 622 (1988); Sov. Phys. JETP 69, 371 (1989).

    Google Scholar 

  32. P. Prelovšek, Phys. Lett. A 126, 287 (1988).

    Article  ADS  Google Scholar 

  33. J. Zaanen and A. M. Olés, Phys. Rev. B 37, 9423 (1988).

    Article  ADS  Google Scholar 

  34. E. B. Stechel and D. R. Jennison, Phys. Rev. B 38, 4632 (1988).

    Article  ADS  Google Scholar 

  35. V. J. Emery and G. Reiter, Phys. Rev. B 38, 4547 (1988).

    Article  ADS  Google Scholar 

  36. H. Matsukawa and H. Fukuyama, J. Phys. Soc. Jpn. 58, 2845 (1989).

    Article  ADS  Google Scholar 

  37. M. H. Fischer and E.-A. Kim, Phys. Rev. B 84, 144502 (2011).

    Article  ADS  Google Scholar 

  38. O. A. Starykh, O. F. A. Bonfim, and G. F. Reiter, Phys. Rev. B 52, 12534 (1995).

    Article  ADS  Google Scholar 

  39. M. Ogata and H. Fukuyama, Rep. Progr. Phys. 71, 036501 (2008).

    Article  ADS  Google Scholar 

  40. M. S. Hybertsen, M. Schluter, and N. E. Christensen, Phys. Rev. B 39, 9028 (1989).

    Article  ADS  Google Scholar 

  41. D. M. Dzebisashvili, V. V. Val’kov, and A. F. Barabanov, JETP Lett. 98, 528 (2013).

    Article  ADS  Google Scholar 

  42. R. Zwanzig, Phys. Rev. 124, 983 (1961).

    Article  ADS  Google Scholar 

  43. H. Mori, Progr. Theor. Phys. 33, 423 (1965).

    Article  ADS  Google Scholar 

  44. L. M. Roth, Phys. Rev. Lett. 20, 1431 (1968).

    Article  ADS  Google Scholar 

  45. A. F. Barabanov, A. A. Kovalev, O. V. Urazaev, A. M. Belemuk, and R. Hayn, J. Exp. Theor. Phys. 92, 677 (2001).

    Article  ADS  Google Scholar 

  46. V. V. Val’kov, D. M. Dzebisashvili, and A. F. Barabanov, J. Exp. Theor. Phys. 118, 959 (2014).

    Article  ADS  Google Scholar 

  47. V. V. Val’kov, D. M. Dzebisashvili, and A. F. Barabanov, Phys. Lett. A 379, 421 (2015).

    Article  Google Scholar 

  48. D. N. Zubarev, Sov. Phys. Usp. 3, 320 (1960).

    Article  ADS  Google Scholar 

  49. V. V. Val’kov, D. M. Dzebisashvili, and A. F. Barabanov, J. Low Temp. Phys. 181, 134 (2015).

    Article  ADS  Google Scholar 

  50. V. V. Val’kov, D. M. Dzebisashvili, and A. F. Barabanov, J. Supercond. Nov. Magn. 29, 1049 (2016).

    Article  Google Scholar 

  51. M. Yu. Kagan, V. A. Mitskan, and M. M. Korovushkin, Phys. Usp. 58, 733 (2015).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to V. V. Val’kov.

Additional information

Original Russian Text © V.V. Val’kov, D.M. Dzebisashvili, M.M. Korovushkin, A.F. Barabanov, 2017, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2017, Vol. 152, No. 5, pp. 957–969.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Val’kov, V.V., Dzebisashvili, D.M., Korovushkin, M.M. et al. Coulomb repulsion of holes and competition between \({d_{{x^2} - {y^2}}}\) -wave and s-wave parings in cuprate superconductors. J. Exp. Theor. Phys. 125, 810–821 (2017). https://doi.org/10.1134/S1063776117110085

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063776117110085

Navigation