A model is proposed such that quasi-particles (electrons or holes) residing in the CuO2 planes of cuprates may interact leading to metallic or superconducting behaviors. The metallic phase is obtained when the quasi-particles are treated as having classical kinetic energies and the superconducting phase occurs when the quasi-particles are taken as extremely relativistic objects. The interaction between both kinds of particles is provided by a force dependent-on-velocity. In the case of the superconducting behavior, the motion of apical oxygen ions provides the glue to establish the Cooper pair. The model furnishes explicit relations for the Fermi velocity, the perpendicular and the in-plane coherence lengths, the zero-temperature energy gap, the critical current density, the critical parallel and perpendicular magnetic fields. All these mentioned quantities are expressed in terms of fundamental physical constants as: charge and mass of the electron, light velocity in vacuum, Planck constant, electric permittivity of the vacuum. Numerical evaluation of these quantities show that their values are close those found for the superconducting YBaCuO, leading to think the model as being a possible scenario to explain superconductivity in cuprates.
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