Singular behavior of the Emery model with O-O hopping for high-T $\mathsf{_c}$ superconductors

Mean field slave boson (MFSB) solution is found analytically for the Emery model of the high-T c cuprates with infinite interaction U d on the Cu-site and finite O-O hopping t', in addition to the Cu-O hopping t 0 . The solution is found for arbitrary Cu-O charge transfer energy $\Delta_{pd}$ and small doping $\delta$ , assuming only t' > 0 for the insulating phase, appropriate for the superconducting cuprates. It is shown analytically that the Brinkmann-Rice metal-insulator transition is preserved, though shifted to higher values of $\Delta_{pd}$ . To the leading order in t', the transition conserves its t'=0 triple point nature with complete electron-hole symmetry with respect to doping. This symmetry is broken by logarithmically small terms related to the t'-induced shift of the chemical potential of the half-filled band from the van Hove singularity. Qualitative change in the behavior of the effective charge transfer energy is found at finite t' for large $\Delta_{pd}$ . The prerequisite to MFSB solution is the discussion of the singularities in the 3-band dispersion of the Emery model. The range of parameters leading to the touching of two bands is determined analytically, showing that it is wider than known before. The anticrossing (rather than touching) is however consistent with the observed Fermi surfaces, leading to the MFSB theory with t' > 0. The detailed comparison of the theory with the angle-resolved photoemission spectroscopy data in La $_{2-\delta}$ Sr $_\delta$ CuO 4 , Bi 2 Sr 2 CaCuO $_{8+\delta}$ and YBa 2 Cu 3 O $_{7-\delta}$ is finally given, using the properties of the resonant band of the physical fermions, discussed in the companion paper. Fast evolution of the band-structure with doping is explained for LSCO. The three-band fits for Bi2212 and Y123 are equally good, although the Luttinger sum rule is not obeyed there. Copyright Springer-Verlag Berlin/Heidelberg 2003