Compressibility of a two-dimensional extended Hubbard model

Abstract

The compressibility of an extended d − p Hubbard model is investigated by the Roth's two-pole approximation. Using the factorization procedure proposed by Beenen and Edwards, superconductivity with singlet d x 2 −y 2 -wave pairing is also considered. Within this framework, the effects of d − p hybridization and Coulomb interaction U on the compressibility are studied carefully. It has been found that the compressibility diverges and then it becomes negative near the half-filling. Within Roth's method, it has been verified that an important contribution for the negative compressibility comes from the spin-correlation term S + j S − i present in Roth's band shift. This correlation function plays an important role due to its high doping dependence. Also, its effects in the band shift and consequently in the compressibility are pronounced near the half-filling. The numerical results show that the hybridization acts in the sense of suppressing the negative compressibility near half-filling. Finally, the possibility of a connection between the negative compressibility and the phase separation is also discussed.The non-Fermi liquid behavior observed in the normal state of the underdoped regime in cuprate systems has been subject of plenty study in recent years [1]. The existence of pseudogap, stripes and phase separation [1,2] in the normal state, becomes appreciably hard the experimental and theoretical understanding of these systems. As the cuprates are strongly correlated electron systems, it is believed that the one-band Hubbard model can capture their main physical properties [2]. However, although this model gives interesting results, probably, a model which takes into account the hybridization between the d− and p−orbitals can be more adequate to treat these systems [3]. Recently, the present authors have applied the Roth's two-pole approximation [4] to study the effects of d − p hybridization on the superconducting properties of an extended d − p Hubbard model [3,5,6]. The authors followed the factorization procedure proposed by Beneen and Edwards [7] to consider d−wave superconductivity. However, near the half-filling, the obtained results show that the compressibility (κ = dnT dµ ) diverges in a critical value of total occupation number n T (where n T = n d σ + n d −σ ), and then, it becomes negative. Nevertheless, the divergence may be associated with phase separation which occurs in the underdoped regime of the cuprate systems [2]. In this work, the nature of the divergence and the negative compressibility has been carefully investigated in the framework of the Roth's approximation [4]. * ggarcia@ccne.ufsm.br 1

Spectral Function of a $d-p$ Hubbard Model

“…It is well known from earlier results [15] that in the normal state the function S j • S i is strongly dependent on the doping and the Coulomb interaction, particularly, on the underdoped regime. Moreover, it has also been verified that the correlation function S + j S − i , which behaves like S j • S i , is also strongly dependent on the d − p hybridization t dp [28]. However, for a given doping δ, U and t pd produce effects in opposite direction, i.e., while U increases the intensity of S j • S i , t dp decreases it.…”

“…In Refs. [13,26,27,28], the band shift has been evaluated following the original Roth's procedure [12], where t d 0j = t d for the z nearest-neighbors has been considered. Consequently, this procedure removes the k-dependence of the correlation functions (mainly S j • S i ) present in the band shift.…”

SPECTRAL FUNCTION OF A d-p HUBBARD MODEL

“…Moreover, it has also been verified that the correlation function S + j S − i , which behaves like S j · S i , is also strongly dependent on the d − p hybridization t dp [28]. However, for a given doping δ, U and t pd produce effects in opposite direction, i.e., while U increases the intensity of S j · S i , t dp decreases it.…”

“…[13,26,27,28], the band shift has been evaluated following the original Roth's procedure [12], where t d 0j = t d for the z nearest-neighbors has been considered. Consequently, this procedure removes the k-dependence of the correlation functions (mainly S j · S i ) present in the band shift.…”