Appearance of antiferromagnetism and superconductivity in superconducting cuprates

• The mean-field and CP approximations were used to resolve Hubbard Hamiltonian.
• The influence of inter-site hopping interaction on AF and SC was investigated.
• Influence of Coulomb repulsion on the range of existence of AF and SC was examined.
• The AF and SC phase diagrams were presented.

We represent the superconducting ceramic compounds by the single band extended Hubbard model. We use this model for solving the simultaneous presence of antiferromagnetism and the d-wave superconductivity in the Hartree–Fock (H–F) and in the coherent potential (CP) approximation, which is applied to the on-site Coulomb repulsion U.The hopping interaction used in addition to the Coulomb repulsion causes rapid expansion of the band at carrier concentrations departing from unity. This expansion shifts the d-wave superconductivity away from the half filled point reducing its occupation range approximately to the experimental range in the YBaCuO compound.The CP approximation used for the Coulomb repulsion is justified by the large ratio of Coulomb repulsion to the effective width of perturbed density of states being reduced by the hopping interaction.The experimentally observed fast disappearance of antiferromagnetism is supported in calculations by the relatively large value of the total width of unperturbed density of states and the high values of the hopping interaction.It is shown that our model is capable of describing the electron doped compounds as well.