Quasiparticle bands and superconductivity in bilayer cuprates

We analyze the generic features of the energy spectrum for two coupled CuO$_2$ layers with a realistic extended Hubbard model. The quasiparticle bands exhibit flat regions near X(Y) points in the Brillouin zone with a large reduction of the bonding-antibonding splitting, and pinning of extended van-Hove singularity to the Fermi level, which is more efficient for a bi-layers than for a single layer. In contrast to the results with simpler models, the superconducting temperature for d$_{x^2-y^2}$ pairing is not lowered by the bi-layer hopping.