Exchange and spin-fluctuation mechanisms of superconductivity in cuprates

Abstract

We propose a microscopical theory of superconductivity in CuO2 layer within the effective two-band Hubbard model in the strong correlation limit. By applying a projection technique for the matrix Green function in terms of the Hubbard operators, the Dyson equation is derived. It is proved that in the mean-field approximation d-wave superconducting pairing mediated by the conventional exchange interaction occurs. Allowing for the self-energy corrections due to kinematic interaction, a spin-fluctuation d-wave pairing is also obtained. Tc dependence on the hole concentration and kdependence of the gap function are derived. The results show that the exchange interaction (which stems from the interband hopping) prevails over the kinematic interaction (which stems from the intraband hopping).

Magnon–phonon coupling and implications for charge-density wave states and superconductivity in cuprates

“…The energy scale given by two-magnon excitations in optimally doped Bi2212 cuprates [43] is J ~ ω(2M)/2.7 = = 833 K (573 cm -1 ), which is almost two times less than in the parent compound (J ~ 1150 cm -1 [44] provide an estimate T c ~ 0.3J = 250 K, which is well above the experimental value. For estimates below, we will use empirical relation T c ~ 0.1J, calculated for T c ~90 K, J = = 833 K. One of the missing parameters for discussion is doping dependence of J, which we derive from the paper by Sugai et al [43] to be dJ/dδ = -6.4·10 3 K, δ -doping parameter, δ = 0.16 for optimum doping [43].…”

“…For estimates below, we will use empirical relation T c ~ 0.1J, calculated for T c ~90 K, J = = 833 K. One of the missing parameters for discussion is doping dependence of J, which we derive from the paper by Sugai et al [43] to be dJ/dδ = -6.4·10 3 K, δ -doping parameter, δ = 0.16 for optimum doping [43]. It is interesting to note here that pairing temperature T * = 0.3J, as estimated from the Hubbard model [44], follows closely pseudogap dependence [45] in Bi2212 material.…”

Electronic spectrum and superconductivity in Hubbard model

“…where N d ( ) and N sf ( ) are the density of electronic states for the exchange and spin-fluctuation interactions and the effective spin-fluctuation coupling constant is given by the hopping parameter averaged over the Fermi surface: λ sf = t 2 (k) η 2 (k) FS /ω s (for details see [21]). The integration over energy for the first term in (46) extends over all energies in the subband of the renormalized widthW , while for the second term the integration is restricted as discussed above.…”

“…Expressing the Fermi operators in terms of the Hubbard operators as a iσ = X The anomalous averages X 02 i N j can be calculated directly by using the equation for the pair commutator GF L ij (t−t ) = X 02 i (t) | N j (t ) without any decoupling approximations [21]. Here we present only the result for the correlation function for the two-hole band, in which the pairing occurs under the hole doping, n = 1 + δ > 1:…”

“…A general formulation of a superconductivity theory within the Dyson equation for the normal and anomalous GFs in the Hubbard model was given in [20]. A weak-coupling approximation in the theory was considered in [21] where T c (n) dependence was calculated and the d-wave symmetry of the superconducting gap was confirmed.…”