Recently, within a generalized Hubbard model which includes correlated nearest (∆t) and next-nearest hopping interactions (∆t_3 ), a comparative study between d- and s*- wave superconducting ground states on a square lattice was performed. It was found that the critical temperature of transition T_c (n), as a function of the electron concentration n, reaches a maximum (T_(c-max) at a given optimal doping (n_op) for each value of the ratio (t’)⁄t, where t and t’ are the tight-binding nearest and next-nearest hopping parameter of a square lattice, respectively. From all values obtained for T_(c-max) ((t’)⁄(t,n_op) a global minimum one was encountered for both symmetries. Likewise, in the same space, a minimal ground state energy E_g was also obtained. For d-wave channel both minima are localized around the same optimal doping, however, for s* symmetry, the two minima are located at different electron concentrations. In this work, we additionally study how the p-wave ground-state energy and the critical temperature depend on the hoppings parameters and the electron concentration. The results show that for p-wave, minimum global values of and in the space do exist too, they are found around half filling but, as occurs for s*- wave, the minimum of T_(c-max) does not occur at the same point as . Moreover, we present a ground-state phase diagram in the space (t’)⁄(t,n_op) where it is possible to find zones of coexistence and competition between the s*-, p- and d-wave symmetries. Also, an analysis of the shape of the Fermi surface and the single-particle energy, as functions of the wave vector of an electron in the Cooper pair, has been done for different regions of the mentioned space.
Square-lattice model and the Jordan–Wigner fermions: the ground-state and thermodynamic properties