Superconducting gap anisotropy within the framework of a simple exchange model for layered cuprates. The theory of HTSC

The oxygen O2p_sigma and copper Cu4s and Cu3d_x^2-y^2 orbitals are involved in a simple LCAO model for determination of the conduction band and the oxygen-oxygen hopping is considered as a small parameter with respect to the transition amplitude between nearest neighbours. The traditional Cooper pairing is obtained by taking into account the double-electron exchange between the nearest neighbours within the two-dimensional CuO_2 plane. The equation for the superconducting gap is obtained as a result of the standard BCS treatment. It is shown that the order parameter could have either s-type or d-type symmetry depending on the ratio between the transition amplitudes. This model allows understanding the experiments reporting a pi-shift of the Josephson phase indicative for a d-type gap symmetry as well as the observed s-type in the case of strongly irradiated samples.