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

Abstract

On the basis of Fermi liquid theory, we study the effect of intralayer and interlayer Coulomb interactions on the energy gap of layered superconductors assuming the BCS d-wave pairing model. The gap equation is derived for the two-square-well model, assuming a boson-mediated attraction and a long-range Coulomb repulsion that leads to intralayer and interlayer Coulomb scattering of Cooper pairs. The d-wave gap amplitude Δ1 at T=0K is evaluated as a function of the attractive pairing strength and of the screened Coulomb interactions. For optimally doped YBa2Cu3O7−δ we find that intralyer Coulomb scattering reduces Δ1 by a factor between 1.5 and 2. The additional 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 three-dimensional phase coherence, that is, the phase difference between adjacent layers Δφ=0, interlayer Coulomb scattering leads to a further reduction of the gap that can be comparable with or larger than the effect of intralyer scattering. If, however, the phase of the gap function alternates, that is Δφ=π, because the interlayer Coulomb scattering dominates the ILT effect, the interlayer Coulomb scattering of Cooper pairs enhances Δ1. This effect is studied as a function of the strength of the Coulomb interaction and it is shown that, with increasing strength, the pseudo-Coulomb parameter μ* decreases and may change sign when the Coulomb interaction is sufficiently strong. The possible role of the interlayer Coulomb effect is discussed in relation to scanning tunneling microscopy experiments.

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