BCS-Hubbard model applied to anisotropic superconductors

The BCS formalism applied to a Hubbard model, including correlated hoppings, is used to study d-wave superconductors. The theoretical Tc vs. n relationship is compared with experimental data from BiSr2-xLaxCuO6+δ and La2-xSrxCuO4. The results suggest a nontrivial correlation between the hole and the doping concentrations. Based on the BCS formalism, we study the critical temperature (Tc) as a function of electron density (n) in a square lattice by means of a generalized Hubbard model, in which first (Δt) and second neighbors (Δt3) correlated-hopping interactions are included in addition to the repulsive Coulomb ones. We compare the theoretical Tc vs. n relationship with experimental data of cuprate superconductors BiSr2-xLaxCuO6+δ (BSCO) and La2-xSrxCuO4, (LSCO). The theory agrees very well with BSCO data even though the complicated association between Sr concentration (x) and hole doping (p). For the LSCO system, it is observed that in the underdoped regime, the Tc vs. n behavior can be associated to different systems with small variations of t'. For the overdoped regime, a more complicated dependence n = 1 - p/2 fits better than n = 1 - p. On the other hand, it is proposed that the second neighbor hopping ratio (t'/t) should be replaced by the effective mean field hopping ratio tMF'/tMF, which can be very sensitive to small changes of t' due to the doping.