Superconducting and pseudogap transition temperatures in high-Tc cuprates and the Tc dependence on pressure

We derive universal analytic expressions for the critical temperatures of the superconducting (SC) and pseudogap (PG) transitions of the high-T-c cuprates as a function of doping. These are in excellent agreement with the experimental data both for single-layered materials such as LSCO, Bi2201 and Hg1201 and multi-layered ones, such as Bi2212, Bi2223, Hg1212 and Hg1223. Optimal doping occurs when the chemical potential vanishes. We show that the SC coupling is enhanced with the number of layers, N, which allows for an accurate description of Tc in the Bi, Hg and Tl multi-layered families of cuprates. We also study the pressure dependence of the SC transition temperatures, obtaining excellent agreement with the experimental data for different materials and dopings. These results are obtained from an effective Hamiltonian for the itinerant oxygen holes, which includes both the electric repulsion between them and their magnetic interactions with the localized copper ions. We show that the former interaction is responsible for the PG and the latter, for the SC phases, the phase diagram of cuprates resulting from the competition between both. The Hamiltonian is defined on a bipartite oxygen lattice, which results from the fact that only the p(x) and p(y) oxygen orbitals alternatively hybridize with the 3d copper orbitals. From this, we can provide an unified explanation for the d(x2-y2) symmetry of both the SC and PG order parameters and obtain the Fermi pockets observed in ARPES experiments.