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 nextnearest neighbor hoppings (t’ /t); an optimal electron density (n_(op)) can be found for each t’ /t value, where the temperature is maximum (T_(c-max)). After calculating the superconducting gap at T=0 K and the corresponding ground state energy (E_(g)) for all the carrier concentrations, a ground state energy minimum (E_(g-min)) is found close to half filling. Since T_(c-max) is the highest critical temperature for a given ratio t’ /t, the minimum of all the T_(c-max) values defines a supreme for this set of temperatures, named as T_(c-max-sup). The corresponding optimal doping for T_(c-max-sup) will be called n_(op-sup), and the results show that E_(g-min) is located at n_(op-sup). The Fermi surface (FS) is analyzed for carrier concentrations close to n_(op-sup) and it is suggested that the location for over (OD) and under (UD) doping regimes (n_(OD) > n_(op-sup) > n_(UD)) could define a pseudogap zone for high critical temperature superconductors.