A model for high-temperature superconductors using the extended Hubbard Hamiltonian

We derive a method to study the phase diagram for high-temperature superconductors (HTCS's). Our starting point is the Hubbard hamiltonian with a weak attractive interaction to obtain the formation of bound pairs. We consider this attractive potential at different positions for different compounds. We then construct a wave function of the BCS type by a variational method using the Fourier transform of this extended Hubbard potential and then derive an energy gap equation which can be applied to the s wave and d wave channel. This simple approach allows us to obtain the critical temperature as a function of the doping concentration which gives very good agreement with the experimental phase diagrams of YBaCuO and La(Sr,Ba)CuO compounds.