Optimal doping for d-wave superconducting ground states within the generalized Hubbard model

A single-band generalized Hubbard model that describes two-dimensional superconductivity with d-wave symmetry on a square lattice within the BCS formalism is considered. For a set of Hamiltonian parameters and varying the ratio between nearest-neighbor and next-nearest neighbor hoppings (t'/t), an optimal doping (nop) can be found for each t'/t value, where the critical temperature is maximum (Tc-max). After calculating the superconducting gap at T=0K and the corresponding ground state (Eg ) for all the carrier concentrations, a ground state energy minimum (Eg-min) is found close to half filling. Since Tc-max is the highest critical temperature for a given ratio t'/t, the minimum of all the Tc-max values defines a supreme of this set of temperatures, named as Tc-max-sup. The corresponding optimal doping for Tc-max-sup will be called nop-sup, and the the results show that Eg-min is located at nop-sup. The Fermi surface (FS) is analyzed for carrier concentrations close to nop-sup and it is suggested that the location for over (OD) and under (UD) doping regimes (nOD>nop-sup>nUD) could define a pseudogap zone for high critical temperature superconductors.