Extended Hubbard model applied to study the pressure effects in high-temperature superconductors

We make use of a BCS-type approach based on the extended Hubbard Hamiltonian to study the superconductor transition and to give a microscopic interpretation of the pressure effects on $T_c$ in high-temperature superconductors. This method suggests that the applied pressure causes an increase of the superconducting gap and this effect is explored in order to explain the variations of $T_c.$ Our approach is therefore beyond the scope of previous phenomenological models which basically postulate a pressure-induced charge transfer and an intrinsic term linear in pressure. We obtain a microscopic interpretation of this intrinsic term and a general expansion of $T_c$ in terms of the pressure. To demonstrate the efficiency of the method we apply it to the experimental data of the Hg-based superconductors.