Spectral Function of a $d-p$ Hubbard Model

Abstract

This work investigates a d-p Hubbard model by the n-pole approximation in the hole-doped regime. In particular, the spectral function $A(\omega,\vec{k})$ is analyzed varying the filling, the local Coulomb interaction and the $d-p$ hybridization. It should be remarked that the original n-pole approximation (Phys. Rev. 184 (1969) 451) has been improved in order to include adequately the $\vec{k}$-dependence of the important correlation function $< \vec{S}_j\cdot\vec{S}_i>$ present in the poles of the Green's functions. It has been verified that the topology of the Fermi surface (defined by $A(\omega=0,\vec{k})$) is deeply affected by the doping, the strength of the Coulomb interaction and also by the hybridization. Particularly, in the underdoped regime, the spectral function $A(\omega=0,\vec{k})$ presents very low intensity close to the anti-nodal points $(0,\pm \pi)$ and $(\pm \pi,0)$. Such a behavior produces an anomalous Fermi surface (pockets) with pseudogaps in the region of the anti-nodal points. On the other hand, if the $d-p$ hybridization is enhanced sufficiently, such pseudogaps vanish. It is precisely the correlation function $< \vec{S}_j\cdot\vec{S}_i>$ present in the poles of the Green's functions which plays the important role in the underdoped situation. In fact, antiferromagnetic correlations coming from $< \vec{S}_j\cdot\vec{S}_i>$ strongly modify the quasi-particle band structure. This is the ultimate source of anomalies in the Fermi surface in the present approach.