Abstract
A detailed numerical study of the three-band Hubbard (3BH) model in the underdoped region is carried out, both in the hole- as well as in the electron-doped case, by means of the variational cluster approach. The phase diagram and the low-energy single-particle spectrum are found to be very similar to recent results for the single-band Hubbard model with next-nearest-neighbor hoppings t′. In particular, we obtain a mixed antiferromagnetic+superconducting phase at low doping with a first-order transition to a pure superconducting phase accompanied by phase separation. Despite the fact that the physically relevant and generally accepted parameters (tpp/tpd,tpd/pd) of our 3BH-model are not in the small regime, required for a ‘downward’ projection onto a single-band model, in the single-particle spectrum a clear Zhang–Rice (ZR) singlet band (with a projection on d- and p-orbitals consistent with the phase factor of the ZR singlet wave function) can be seen. It displays an incoherent and a coherent part, in which holes enter upon doping around (π/2, π/2). The latter is very similar to the coherent quasi-particle band crossing the Fermi surface in the t–t′–U single-band model, with generally accepted values of the parameters. Doped electrons go instead into the upper Hubbard band, first filling the regions of the Brillouin zone around (π, 0). This fact can be related to the enhanced robustness of the antiferromagnetic phase as a function of electron doping compared to hole doping.