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Generalized Kondo lattice model and its spin-polaron realization by the projection method for cuprates


The spin–fermion model, which is an effective low-energy realization of the three-band Emery model after passing to the Wannier representation for the px and py orbitals of the subsystem of oxygen ions, reduces to the generalized Kondo lattice model. A specific feature of this model is the existence of spin-correlated hoppings of the current carriers between distant cells. Numerical calculations of the spectrum of spin-electron excitations highlight the important role of the long-range spin-correlated hoppings.

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  1. 1.

    B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, and J. Zaanen, “From quantum matter to hightemperature superconductivity in copper oxides,” Nature, 518, 179–186 (2015).

    ADS  Article  Google Scholar 

  2. 2.

    N. Plakida, High-Temperature Cuprate Supercoductors: Experiment, Theory, and Applications, Springer, Berlin (2010).

    Book  Google Scholar 

  3. 3.

    V. J. Emery, “Theory of high-T c superconductivity in oxides,” Phys. Rev. Lett., 58, 2794–2797 (1987).

    ADS  Article  Google Scholar 

  4. 4.

    C. M. Varma, S. Schmitt-Rink, and E. Abrahams, “Charge transfer excitations and superconductivity in ‘ionic’ metals,” Solid State Commun., 62, 681–685 (1987).

    ADS  Article  Google Scholar 

  5. 5.

    J. E. Hirsch, “Antiferromagnetism, localization, and pairing in a two-dimensional model for CuO2,” Phys. Rev. Lett., 59, 228–231 (1987).

    ADS  Article  Google Scholar 

  6. 6.

    V. J. Emery and G. Reiter, “Mechanism for high-temperature superconductivity,” Phys. Rev. B, 38, 4547–4556 (1988).

    ADS  Article  Google Scholar 

  7. 7.

    V. J. Emery and G. Reiter, “Quasiparticles in the copper–oxygen planes of high T c superconductors: An exact solution for a ferromagnetic background,” Phys. Rev. B, 38, 11938–11941 (1988).

    ADS  Article  Google Scholar 

  8. 8.

    J. Zaanen and A. M. Oles, “Canonical perturbation theory and the two-band model for high T c superconductors,” Phys. Rev. B, 37, 9423–9438 (1988).

    ADS  Article  Google Scholar 

  9. 9.

    A. F. Barabanov, L. A. Maksimov, and G. V. Uimin, “Elementary excitations in CuO2 planes,” JETP Lett., 47, 622–625 (1988).

    ADS  Google Scholar 

  10. 10.

    P. Prelovˇsek, “Two band model for superconducting copper oxides,” Phys. Lett. A, 126, 287–290 (1988).

    ADS  Article  Google Scholar 

  11. 11.

    H. Matsukawa and H. Fukuyama, “Effective Hamiltonian for high T c Cu oxides,” J. Phys. Soc. Japan, 58, 2845–2866 (1989).

    ADS  Article  Google Scholar 

  12. 12.

    M. Inui, S. Doniach, and M. Gabay, “Doping dependence of antiferromagnetic correlations in high-temperature superconductors,” Phys. Rev. B, 38, 6631–6635 (1988).

    ADS  Article  Google Scholar 

  13. 13.

    J. F. Annett, R. M. Martin, A. K. McMahan, and S. Satpathy, “Electronic Hamiltonian and antiferromagnetic interactions in La2CuO4,” Phys. Rev. B, 40, 2620–2623 (1989).

    ADS  Article  Google Scholar 

  14. 14.

    J. Kondo and K. Yamaji, “Green’s-function formalism of the one-dimensional Heisenberg spin system,” Progr. Theoret. Phys., 47, 807–818 (1972).

    ADS  Article  Google Scholar 

  15. 15.

    H. Shimahara and S. Takada, “Green’s function theory of the two-dimensional Heisenberg model-spin wave in short range order,” J. Phys. Soc. Japan, 60, 2394–2405 (1991).

    ADS  Article  Google Scholar 

  16. 16.

    A. F. Barabanov and V. M. Berezovskii, “Second-order phase transitions in a frustrated two-dimensional Heisenberg antiferromagnet,” JETP, 79, 627–633 (1994).

    ADS  Google Scholar 

  17. 17.

    B. S. Shastry, “tJ model and nuclear magnetic relaxation in high-T c materials,” Phys. Rev. Lett., 63, 1288–1291 (1989).

    ADS  Article  Google Scholar 

  18. 18.

    J. H. Jefferson, H. Eskes, and L. F. Feiner, “Derivation of a single-band model for CuO2 planes by a cellperturbation method,” Phys. Rev. B, 45, 7959–7972 (1992).

    ADS  Article  Google Scholar 

  19. 19.

    V. A. Gavrichkov and S. G. Ovchinnikov, “Low-energy electron spectrum in copper oxides in the multiband pd model,” Soviet Phys. Solid State, 40, 163–168 (1998).

    ADS  Article  Google Scholar 

  20. 20.

    D. F. Digor and V. A. Moskalenko, “Wannier representation for the three-band hubbard model,” Theor. Math. Phys., 130, 271–286 (2002).

    Article  MATH  Google Scholar 

  21. 21.

    M. S. Hybertsen, M. Schlüter, and N. E. Christensen, “Calculation of Coulomb-interaction parameters for La2CuO4 using a constrained-density-functional approach,” Phys. Rev. B, 39, 9028–9041 (1989).

    ADS  Article  Google Scholar 

  22. 22.

    M. Ogata and H. Fukuyama, “The tJ model for the oxide high-T c superconductors,” Rep. Progr. Phys., 71, 036501 (2008).

    ADS  Article  Google Scholar 

  23. 23.

    F. C. Zhang and T. M. Rice, “Effective Hamiltonian for the superconducting Cu oxides,” Phys. Rev. B, 37, 3759–3761 (1988).

    ADS  Article  Google Scholar 

  24. 24.

    A. Ramsak and P. Prelovsek, “Comparison of effective models for CuO2 layers in oxide superconductors,” Phys. Rev. B, 40, 2239–2246 (1989).

    ADS  Article  Google Scholar 

  25. 25.

    A. Ramsak and P. Prelovsek, “Dynamics of a fermion in the Kondo-lattice model for strongly correlated systems,” Phys. Rev. B, 42, 10415–10426 (1990).

    ADS  Article  Google Scholar 

  26. 26.

    R. Zwanzig, “Memory effects in irreversible thermodynamics,” Phys. Rev., 124, 983–992 (1961).

    ADS  Article  MATH  Google Scholar 

  27. 27.

    H. Mori, “Transport, collective motion, and brownian motion,” Progr. Theoret. Phys., 33, 423–455 (1965).

    ADS  Article  MATH  Google Scholar 

  28. 28.

    A. F. Barabanov, A. A. Kovalev, O. V. Urazaev, A. M. Belemuk, and R. Hayn, “Evolution of the Fermi surface of cuprates on the basis of the spin-polaron approach,” JETP, 92, 677–695 (2001).

    ADS  Article  Google Scholar 

  29. 29.

    V. V. Val’kov, D. M. Dzebisashvili, and A. F. Barabanov, “Effect of the concentration-dependent spin-charge correlations on the evolution of the energy structure of the 2D Emery model,” JETP, 118, 959–970 (2014).

    ADS  Article  Google Scholar 

  30. 30.

    D. M. Dzebisashvili, V. V. Val’kov, and A. F. Barabanov, “Fermi surface evolution in the ensemble of spinpolarized quasiparticles in La2–x SrxCuO4,” JETP Lett., 98, 528–533 (2013).

    ADS  Article  Google Scholar 

  31. 31.

    T. Yoshida, X. J. Zhou, D. H. Lu, S. Komiya, Y. Ando, H. Eisaki, T. Kakeshita, S. Uchida, Z. Hussain, Z.-X. Shen, and A. Fujimori, “Low-energy electronic structure of the high-T c cuprates La2–x SrxCuO4 studied by angle-resolved photoemission spectroscopy,” J. Phys.: Condens. Matter, 19, 125209 (2007).

    ADS  Google Scholar 

  32. 32.

    R. O. Kuzian, R. Hayn, A. F. Barabanov, and L. A. Maksimov, “Spin-polaron damping in the spin–fermion model for cuprate superconductors,” Phys. Rev. B, 58, 6194–6207 (1998).

    ADS  Article  Google Scholar 

  33. 33.

    V. V. Val’kov, D. M. Dzebisashvili, and A. F. Barabanov, “d-Wave pairing in an ensemble of spin polaron quasiparticles in the spin–fermion model of the electronic structure of the CuO2 plane,” Phys. Lett. A, 379, 421–426 (2015).

    Article  MATH  Google Scholar 

  34. 34.

    A. F. Barabanov and A. M. Belemuk, “Pseudogap state of two-dimensional Kondo lattice,” JETP, 111, 258–262 (2010).

    ADS  Article  Google Scholar 

  35. 35.

    I. A. Larionov and A. F. Barabanov, “Electrical resistivity, hall coefficient, and thermopower of optimally doped high-T c superconductors,” JETP Lett., 100, 712–718 (2014).

    ADS  Article  Google Scholar 

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Corresponding author

Correspondence to V. V. Valkov.

Additional information

This research was supported by the Russian Foundation for Basic Research (Grant No. 16-02-00073, 16-02-00304, and 16-42-240435) and the Siberian Branch of the Russian Academy of Sciences (Complex Program No. II.2P, Grant No. 0358-2015-0005).


Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 191, No. 2, pp. 319–333, May, 2017.

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Valkov, V.V., Dzebisashvili, D.M. & Barabanov, A.F. Generalized Kondo lattice model and its spin-polaron realization by the projection method for cuprates. Theor Math Phys 191, 752–763 (2017).

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  • strong electron correlation
  • spin–fermion model
  • Kondo lattice model
  • spin polaron