Derivation of a single-band model forCuO2planes by a cell-perturbation method

A cell-perturbation method is developed for ${\mathrm{CuO}}_2$ planes in the cuprate superconductors described by a d-p model. It is shown that a single-band t-t’-J-J’ model accurately describes the low-energy physics and how the parameters of this model vary with those of the underlying d-p model. The method is similar in spirit to Anderson’s original treatment of superexchange [Phys. Rev. 115, 2 (1959)], where the exchange interaction is obtained in second order rather than given by the usual fourth-order result of ordinary perturbation theory (a poor approximation). It is shown that O-O hopping can appreciably affect the absolute and relative magnitudes of the effective single-band parameters and that a regime with J∼t is quite conceivable. Although triplet (intermediate) states can appreciably enhance the magnitude of the ‘‘diagonal’’ effective hopping t’, an effective single-band description should remain valid for all reasonable estimates of the underlying d-p parameters. Correction terms involving hole pairs on neighboring cells are derived and shown to be small. For the ‘‘undoped’’ case, an estimate is made of the critical charge-transfer energy for an insulator-metal transition.