  The 2D screening is investigated in a simple single band square tight-binding
model which qualitatively resembles the known electronic structure in high
temperature superconductors. The Coulomb kernel for the two particle
Bethe-Salpeter equation in the single loop (RPA) approximation for the
polarization can be evaluated in a strong tight binding limit. The results
indicate an intense screening of the Coulomb repulsion between the particles,
which becomes stronger and anisotropic when the Fermi level approach half
filling (or equivalently, when the Fermi surface approach the Van Hove
singularities) and rapidly decreases away it. The effect is also more
pronounced for quasi-momenta regions near the corners of the Brillouin cell,
which correspond to dual spatial distances of the order few unit cells.
Therefore, a possible mechanism is identified which could explain the existence
of extremely small Cooper pairs in these materials, as bounded anisotropic
composites joined by residual super-exchange or phonon interactions.

Superconductivity;Strongly Correlated Electrons