Effective Hamiltonian for the superconducting Cu oxides

Although assuming that doping creates holes primarily on oxygen sites, we derive explicitly a single-band effective Hamiltonian for the high-${T}_{c}$ Cu-oxide superconductors. Cu-O hybridization strongly binds a hole on each square of O atoms to the central ${\mathrm{Cu}}^{2+}$ ion to form a local singlet. This moves through the lattice in a similar way as a hole in the single-band effective Hamiltonian of the strongly interacting Hubbard model.