Effective Hamiltonian for High-T_c Cu Oxides

Abstract

The effective Hamiltonian for high-T_c Cu-based oxide superconductors is derived based on Cu:d_x²−y² and O:p_σ orbitals in the Cu–O plane by taking into account the intra- and nearest-neighbor interatomic Coulomb interactions for both cases of hole and electron doping. For hole doping, where the stability of Cu⁺⁺ is assumed, the effective Hamiltonian proves to have various interaction processes, some features of which are studied by considering a case with a single Cu spin and one hole in the oxygen band. The spatial extent of the singlet-bound state in this case has been examined to the linear order of the oxygen band width. For electron doping the effective Hamiltonian is much simpler and essentially the same as the t-J model. Based on these results we discuss the relevance of the t-J model to the high-T_c Cu oxides. The effects of Cu:d_3z²−r² orbitals and O:p_z orbitals at the apex of the pyramid or octahedron are also examined.