Two-square-well model for layered superconductors: Effect of intralayer and interlayer Coulomb interactions on the d-wave gap

On the basis of Fermi liquid theory, we study the effect of intralayer and interlayer Coulomb interactions on the energy gap of layered superconductor s assuming the BCS d-wave pairing model. The gap equation is derived for th e two-square-well model, assuming a boson-mediated attraction and a long-ra nge Coulomb repulsion that leads to intralayer and interlayer Coulomb scatt ering of Cooper pairs. The d-wave gap amplitude Delta(1) at T=0 K is evalua ted as a function of the attractive pairing strength and of the screened Co ulomb interactions. For optimally doped YBa2Cu3O7-delta We find that intral yer Coulomb scattering reduces hi by a factor between 1.5 and 2. The additi onal effect of interlayer Coulomb scattering depends in a crucial manner on the relative phases of the gap functions in adjacent layers. If Josephson and boson-assisted interlayer pair tunneling (ILT) are responsible, the thr ee-dimensional phase coherence, that is, the phase difference between adjac ent layers Delta phi=0, interlayer Coulomb scattering leads to a further re duction of the gap that can be comparable with or larger than the effect of intralyer scattering. If, however, the phase of the gap function alternate s, that is Delta phi=pi, because the interlayer Coulomb scattering dominate s the ILT effect, the interlayer Coulomb scattering of Cooper pairs enhance s Delta(1). This effect is studied as a function of the strength of the Cou lomb interaction and it is shown that; with increasing strength, the pseudo -Coulomb parameter mu* decreases and may change sign when the Coulomb inter action is sufficiently strong. The possible role of the interlayer Coulomb effect is discussed in relation to scanning tunneling microscopy experiment s.