About the role of 2D screening in High Temperature Superconductivity
  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. 
Yosdanis Vazquez-Ponce, David Oliva Aguero and Alejandro Cabo Montes   de Oca