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Current issue   Ukr. J. Phys. 2014, Vol. 59, N 5, p.487-494
https://doi.org/10.15407/ujpe59.05.0487    Paper

Bariakhtar I.1,2, Nazarenko A.1,3

1 Institute of Magnetism, Nat. Acad. of Sci. of Ukraine
(36-b, Vernadsky Blvd., Kyiv 03142, Ukraine)
2 Boston College, Department of Physics
(140, Commonwealth Avenue, Chestnut Hill, MA 02467, USA)
3 Harvard University, IAM-HUIT
(1033, Massachusetts Avenue, Cambridge, MA 02138, USA)

A Model for dx2 – y2 Superconductivity in the Strongly Correlated Fermionic System

Section: Solid matter
Original Author's Text: English

Abstract: Based on the known phenomenology of high-Tc cuprates and the available numerical calculations of the t−J model, a two-dimensional effective fermionic model with the nearest neighbor attraction is proposed. Numerical calculations suggest that the model has the dx2 – y2 superconductivity (SC) in the ground state at a low fermionic density. We argue that this model captures the important physics of the dx2 – y2 superconducting correlations found earlier in the t−J model by the exact diagonalization approach. Within a self-consistent RPA diagrammatic study, the density and the coupling strength dependence of the critical temperature is calculated. We also investigate the influence of the impurities on our results and show that the suppression of the superconductivity is insignificant, when the retardation effects are accounted for as opposed to the Hartree–Fock approximation.

Key words: superconductivity, strongly correlated fermionic system, t−J model, mean-field approximation.

References:

  1. A.J. Leggett, in Modern Trends in the Theory of Condensed Matter, edited by A. Pekalski and R. Przystawa, (Springer, Berlin, 1980).
  2. R.T. Scalettar et al., Phys. Rev. Lett. 62, 1407 (1989);
    https://doi.org/10.1103/PhysRevLett.62.1407
    A. Moreo and D. Scalapino, Phys. Rev. Lett. 66, 946 (1991); M. Randeria, N. Trivedi, A. Moreo, and R.T. Scalettar, Phys. Rev. Lett. 69, 2001 (1992).
  3. D.J. Scalapino, Phys. Rep. 250, 331 (1995).
    https://doi.org/10.1016/0370-1573(94)00086-I
  4. N.M. Plakida, High-Temperature Superconductivity: Experiment and Theory (Springer, Berlin, 1995).
    https://doi.org/10.1007/978-3-642-78406-4
  5. C.A.R. S’a de Melo, M. Randeria, and J.R. Engelbrecht, Phys. Rev. Lett. 71, 3202 (1993).
  6. W. Li et al., arXiv:1203.2581 (2012); A. Kordyuk, Visnyk NAN Ukrainy, No. 9, 46 (2012).
    A. Kordyuk, Visnyk NAN Ukrainy, No. 9, 46 (2012).
  7. R. Micnas et al., Rev. Mod. Phys. 62, 113 (1990);
    https://doi.org/10.1103/RevModPhys.62.113
    E. Dagotto et al., Phys. Rev. B 49, 3548 (1994).
    https://doi.org/10.1103/PhysRevB.49.3548
  8. S. Haas et al., Phys. Rev. B 51, 5989 (1995).
    https://doi.org/10.1103/PhysRevB.51.5989
  9. A. Sboychakov et al., Phys. Rev. B 77, 224504 (2008).
    https://doi.org/10.1103/PhysRevB.77.224504
  10. E. Dagotto, Rev. Mod. Phys. 66, 763 (1994).
    https://doi.org/10.1103/RevModPhys.66.763
  11. R. Gonczarek, M. Krzyzosiak, and A. Gonczarek, Eur. Phys. J. B 61, 299 (2008).
    https://doi.org/10.1140/epjb/e2008-00072-6
  12. E.A. Pashitskii and V.I. Pentegov, Low Temp. Phys. 34, 113, (2008).
    https://doi.org/10.1063/1.2834256
  13. M.M. Korshunov et al., JETP 99, 559 (2004).
    https://doi.org/10.1134/1.1809685
  14. Strong numerical indications of -wave SC have been found before in the related models, in particular, in the − model (see, e.g., E. Dagotto and J. Riera, Phys. Rev. Lett. 70, 682 (1993);
    Y. Ohta et al., Phys. Rev. Lett. 73, 324 (1994);
    https://doi.org/10.1103/PhysRevLett.73.324
    A. Nazarenko et al., Phys. Rev. B 54, R768 (1996)).
    https://doi.org/10.1103/PhysRevB.54.R768
  15. E. Dagotto, A. Nazarenko, and A. Moreo, Phys. Rev. Lett. 74, 728 (1994).
    https://doi.org/10.1103/PhysRevLett.73.728
  16. E. Dagotto, A. Nazarenko, and M. Boninsegni, Phys. Rev. Lett. 73, 310 (1995);
    https://doi.org/10.1103/PhysRevLett.74.310
    A. Nazarenko and E. Dagotto, Phys. Rev. B 54, 13158 (1996).
    https://doi.org/10.1103/PhysRevB.54.13158
  17. C. D¨urr et al., Phys. Rev. B 63, 014505 (2001).
    https://doi.org/10.1103/PhysRevB.63.014505
  18. D. Duffy et al., Phys. Rev. B 56, 5597 (1997).
    https://doi.org/10.1103/PhysRevB.56.5597
  19. P. Monthoux and D. Pines, Phys. Rev. Lett 69, 961 (1992).
    https://doi.org/10.1103/PhysRevLett.69.961
  20. D.Z. Liu, K. Levin, and J. Maly, Phys. Rev. B 51, 8680 (1995).
    https://doi.org/10.1103/PhysRevB.51.8680
  21. S. Ovchinnikov et al., Phys. Sol. State 53, 242 (2011).
    https://doi.org/10.1134/S1063783411020235
  22. P. Monthoux and D. Scalapino, Phys. Rev. Lett. 72, 1874 (1994).
    https://doi.org/10.1103/PhysRevLett.72.1874
  23. Our numerical calculations reveal that keeping only the one-loop diagram in the effective potential produces a spurious -wave condensate.
  24. Yu.G. Pogorelov, M.C. Santos, V.M. Loktev, Low Temp. Phys., 37, 633 (2011);
    https://doi.org/10.1063/1.3651472
    Yu.G. Pogorelov, V.M. Loktev, Phys. Rev. B 69, 214508 (2004).
    https://doi.org/10.1103/PhysRevB.69.214508
  25. A.A. Abrikosov, L.P. Gorkov, and I.E. Dzyaloshinsky, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1975).
  26. For a uniform system, the tadpole diagram including the fermionic Green's function.