Theoretical Investigation of Fermion Pairing in Three-band Extended Hubbard Model

We analyze for fermion pairing the two-dimensional extended Hubbard model (or d-p model) on a square lattice by a slave-boson method reported in a previous work$^{1}$ . The onsite coulomb repulsion between Cu d holes is assumed to be strong. The nearest-neighbor interaction in momentum space U$_{kq}$ , introduced additionally, for transition from a momentum q to k is assumed to be separable and is expanded in terms of basis functions corresponding to d$_{xy}$ and d$_{x2-y2}$ .The possibility of a mixed (s-d)-wave symmetry also exists for the spin degeneracy N$>>$1 if bose field fluctuations are taken into consideration. For the hole doping ($\delta >$0) case, the additional holes are expected to occpy oxygen sites. This implies that the renormalized charge transfer gap $\Delta _{reg}$ tends towards zero for $\delta >$ 0. We find the approximate Fermi liquid behavior for $\Delta \quad _{reg} \to $ 0 once the pure d$_{x2-y2}$ wave singlet superconducting instability sets in; otherwise non-Fermi liquid behavior is the prevalent one. The charge and the spin ordering gaps appear in the single-particle excitation spectrum when d$_{xy}$ component is taken into account. The latter is expected to shed light on the pseudo-gap phenomenon in cuprates. 1.Partha Goswami, Presented in \textbf{SCES'07} proceedings and accepted for publication in Physica B (see http://dx.doi.org/10.1016/j.physb2007.10.076).