The reduction of the three-band p-d model for the ${\mathrm{CuO}}_2$ plane in cuprates with the standard set of parameters as derived by Hybertsen et al. [Phys. Rev. B 41, 11 068 (1990)] to an effective t-${\mathrm{t}}^{|\mathrm{I}\mathrm{H}}$-${\mathrm{t}}^{|\mathrm{I}\mathrm{J}}$-J model with a three-site hopping term is discussed in detail in the framework of the cell-perturbation method. The reduction procedure is formulated to avoid any ambiguity in obtaining the correct signs of the hopping parameters in the effective model, and the contributions of first and second order resulting from the intercell hopping are distinguished. Based on the so-defined extended t-J model, the dispersion of a single hole in an antiferromagnetic background is calculated both by a variational ansatz and within the self-consistent Born approximation (SCBA). An extension of the variational method allows us to investigate the influence of a three-site hopping term both on the mean-field level and beyond this approximation. The latter corrections are shown to be small. Both methods give the coinciding result that the additional hopping terms lead to a more isotropic minimum of the dispersion at the point (π/2,π/2) in k space and to a slightly increased bandwidth in comparison to the pure t-J model. These results are compared with recent photoemission measurements for ${\mathrm{Sr}}_2$${\mathrm{CuO}}_2$${\mathrm{Cl}}_2$ [Wells et al., Phys. Rev. Lett. 74, 964 (1995)], showing an improvement against the pure t-J model, but no complete agreement. In particular, a small anisotropy in the calculated effective masses remains. The lifetime of the hole quasiparticles is investigated within the SCBA, and it is shown that the upper part of the hole spectrum loses its quasiparticle character due to a strong increase of damping if the bare hole bandwidth exceeds a certain threshold value of roughly 2J.

DOI:https://doi.org/10.1103/PhysRevB.55.15562