The half-filled superconducting system with on-site inter-band interactions

A two-band electronic Hamiltonian is investigated in the zero single-electron hopping limit as well as in the presence of the finite width of one of the bands. The hopping of c-electron pairs competes with the on-site pair-exchange potential, the anisotropic Kondo lattice spin-spin interaction and the local Coulomb potential in the f-band. The hopping of single electrons in c-band is also admitted in the beginning. The only interaction approximated by the mean-field method is the pair-hopping one while the remaining potentials are treated exactly what allows one to go to some extent beyond the mean-field approach. Such a handling this problem reveals significant differences between the exact and the mean-field results concerning the order parameters and the ground state energy. In this paper one addresses the case with the zero hopping of f-electron pairs in more detail, though it is possible to consider the opposite situation. It turns out that, if one admits the extremely anisotropic spin-spin interaction, i.e., the Ising component is present in the system only while the spin-flip one is neglected, the appearance of two critical temperatures and two gaps in the excitation spectrum of c-electrons at sufficiently low temperatures take place. The influence of the finite width of the conduction c-band in which the hopping of pairs takes place is investigated as well. This concerns the scenario without the Kondo lattice terms. In the end the effect of diagonal disorder is considered in a very rudimentary manner.