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

V. V. Valkov   ; D. M. Dzebisashvili   ; A. F. Barabanov

Teoretičeskaâ i matematičeskaâ fizika, Tome 191 (2017) no. 2, pp. 319-333

Résumé

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 $p_x$ and $p_y$ 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.

Détail

Keywords: strong electron correlation, Kondo lattice model, spin polaron.
Mots-clés : spin–fermion model

Bibliographie

[1] B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, J. Zaanen, “From quantum matter to high-temperature superconductivity in copper oxides”, Nature, 518:7538 (2015), 179–186 | DOI

[2] N. Plakida, High-Temperature Cuprate Supercoductors. Experiment, Theory, and Applications, Springer, Berlin, 2010 | DOI

[3] V. J. Emery, “Theory of high-$T_\mathrm{c}$ superconductivity in oxides”, Phys. Rev. Lett., 58:26 (1987), 2794–2797 | DOI

[4] C. M. Varma, S. Schmitt-Rink, E. Abrahams, “Charge transfer excitations and superconductivity in “ionic” metals”, Solid State Commun., 62:10 (1987), 681–685 | DOI | MR

[5] J. E. Hirsch, “Antiferromagnetism, localization, and pairing in a two-dimensional model for CuO$_2$”, Phys. Rev. Lett., 59:2 (1987), 228–231 | DOI

[6] V. J. Emery, G. Reiter, “Mechanism for high-temperature superconductivity”, Phys. Rev. B, 38:7 (1988), 4547–4556 | DOI

[7] V. J. Emery, G. Reiter, “Quasiparticles in the copper-oxygen planes of high-$T_\mathrm{c}$ superconductors: an exact solution for a ferromagnetic background”, Phys. Rev. B, 38:16 (1988), 11938–11941 | DOI

[8] J. Zaanen, A. M. Oles, “Canonical perturbation theory and the two-band model for high-$T_\mathrm{c}$ superconductors”, Phys. Rev. B, 37:16 (1988), 9423–9438 | DOI

[9] A. F. Barabanov, L. A. Maksimov, G. V. Uimin, “Ob elementarnykh vozbuzhdeniyakh v ploskostyakh CuO$_2$”, Pisma v ZhETF, 47:10 (1988), 532

[10] P. Prelovšek, “Two band model for superconducting copper oxides”, Phys. Lett. A, 126:4 (1988), 287–290 | DOI

[11] H. Matsukawa, H. Fukuyama, “Effective Hamiltonian for high-$T_\mathrm{c}$ Cu oxides”, J. Phys. Soc. Japan, 58:8 (1989), 2845–2866 | DOI | MR

[12] M. Inui, S. Doniach, M. Gabay, “Doping dependence of antiferromagnetic correlations in high-temperature superconductors”, Phys. Rev. B, 38:10 (1988), 6631–6635 | DOI

[13] J. F. Annett, R. M. Martin, A. K. McMahan, S. Satpathy, “Electronic Hamiltonian and antiferromagnetic interactions in La$_2$CuO$_4$”, Phys. Rev. B, 40:4 (1989), 2620–2623 | DOI

[14] J. Kondo, K. Yamaji, Progr. Theor. Phys., 47 (1972), 807 | DOI

[15] H. Shimahara, S. Takada, “Green's function theory of the two-dimensional Heisenberg model-spin wave in short range order”, J. Phys. Soc. Japan, 60:7 (1991), 2394–2405 | DOI

[16] A. F. Barabanov, V. M. Berezovskii, “Fazovye perekhody vtorogo roda v sfericheski simmetrichnoi teorii 2D geizenbergovskogo frustrirovannogo antiferromagnetika”, ZhETF, 106:4 (1994), 1156–1168

[17] B. S. Shastry, “$t$–$J$ model and nuclear magnetic relaxation in high-$T_\mathrm{c}$ materials”, Phys. Rev. Lett., 63:12 (1989), 1288–1291 | DOI

[18] J. H. Jefferson, H. Eskes, L. F. Feiner, “Derivation of a single-band model for CuO$_2$ planes by a cell-perturbation method”, Phys. Rev. B, 45:14 (1992), 7959–7972 | DOI

[19] V. A. Gavrichkov, S. G. Ovchinnikov, “Nizkoenergeticheskii spektr elektronov v oksidakh medi v mnogozonnoi $p$–$d$ modeli”, FTT, 40:2 (1998), 184–190 | DOI

[20] D. F. Digor, V. A. Moskalenko, “Predstavlenie Vane dlya trekhzonnoi modeli Khabbarda”, TMF, 130:2 (2002), 320–338 | DOI | DOI | Zbl

[21] M. S. Hybertsen, M. Schlüter, N. E. Christensen, “Calculation of Coulomb-interaction parameters for La$_2$CuO$_4$ using a constrained-density-functional approach”, Phys. Rev. B, 39:13 (1989), 9028–9041 | DOI

[22] M. Ogata, H. Fukuyama, “The $t$–$J$ model for the oxide high-$T_\mathrm{c}$ superconductors”, Rep. Progr. Phys., 71:3 (2008), 036501, 46 pp. | DOI

[23] F. C. Zhang, T. M. Rice, “Effective Hamiltonian for the superconducting Cu oxides”, Phys. Rev. B, 37:7 (1988), 3759–3761 | DOI

[24] A. Ramsak, P. Prelovsek, “Comparison of effective models for CuO$_2$ layers in oxide superconductors”, Phys. Rev. B, 40:4 (1989), 2239–2246 | DOI

[25] A. Ramsak, P. Prelovsek, “Dynamics of a fermion in the Kondo-lattice model for strongly correlated systems”, Phys. Rev. B, 42:16 (1990), 10415–10426 | DOI

[26] R. Zwanzig, “Memory effects in irreversible thermodynamics”, Phys. Rev., 124:4 (1961), 983–992 | DOI | Zbl

[27] H. Mori, “Transport, collective motion, and brownian motion”, Progr. Theoret. Phys., 33:3 (1965), 423–455 | DOI | Zbl

[28] A. F. Barabanov, A. A. Kovalev, O. V. Urazaev, A. M. Belemuk, R. Khain, “Evolyutsiya fermi-poverkhnosti kupratov na osnove spin-polyaronnogo podkhoda”, ZhETF, 119:4 (2001), 777–798 | DOI

[29] V. V. Valkov, D. M. Dzebisashvili, A. F. Barabanov, “Vliyanie kontsentratsionno-zavisimykh spin-zaryadovykh korrelyatsii na evolyutsiyu energeticheskoi struktury dvumernoi modeli Emeri”, ZhETF, 145:6 (2014), 1087–1100 | DOI

[30] D. M. Dzebisashvili, V. V. Valkov, A. F. Barabanov, “Evolyutsiya fermi-poverkhnosti ansamblya spin-polyaronnykh kvazichastits v La$_{2\text{--}x}$Sr$_x$CuO$_4$”, Pisma v ZhETF, 98:9 (2013), 596–601 | DOI

[31] T. Yoshida, X. J. Zhou, D. H. Lu, S. Komiya, Y. Ando, H. Eisaki, T. Kakeshita, S. Uchida, Z. Hussain, Z.-X. Shen, A. Fujimori, “Low-energy electronic structure of the high-$T_\mathrm{c}$ cuprates La$_{2\text{--}x}$Sr$_x$CuO$_4$ studied by angle-resolved photoemission spectroscopy”, J. Phys.: Condens. Matter, 19:12 (2007), 125209, 24 pp. | DOI

[32] R. O. Kuzian, R. Hayn, A. F. Barabanov, L. A. Maksimov, “Spin-polaron damping in the spin-fermion model for cuprate superconductors”, Phys. Rev. B, 58:10 (1998), 6194–6207 | DOI

[33] V. V. Val'kov, D. M. Dzebisashvili, A. F. Barabanov, “$d$-Wave pairing in an ensemble of spin polaron quasiparticles in the spin-fermion model of the electronic structure of the CuO$_2$ plane”, Phys. Lett. A, 379:5 (2015), 421–426 | DOI | Zbl

[34] A. F. Barabanov, A. M. Belemuk, “Psevdoschelevoe sostoyanie dvumernoi kondo-reshetki”, ZhETF, 138:2(8) (2010), 289–294 | DOI

[35] I. A. Larionov, A. F. Barabanov, “Elektrosoprotivlenie, koeffitsient Kholla i termoEDS optimalno dopirovannykh vysokotemperaturnykh sverkhprovodnikov”, Pisma v ZhETF, 100:11 (2014), 811–817 | DOI