Charge fluctuations in the four-band extended Hubbard model

Abstract

We investigate the extended four-band Hubbard model for the ${\mathrm{CuO}}_{2}$ planes of high-temperature superconductors. We consider the limit of U=\ensuremath{\infty} and we include the nearest-neighbor (n-n) Coulombic repulsion between the holes on 2${\mathit{p}}_{\mathit{x}}$,2${\mathit{p}}_{\mathit{y}}$ orbitals on oxygen and the holes on ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ or ${\mathit{d}}_{3\mathit{z}}^{2}$-${\mathit{r}}^{2}$ orbitals on copper (${\mathit{V}}_{\mathit{x}}$ and ${\mathit{V}}_{\mathit{z}}$, respectively, with ${\mathit{V}}_{\mathit{x}}$>${\mathit{V}}_{\mathit{z}}$). As in the three-band version of this model, a phase-separation instability is induced by nearest-neighbor repulsions. The presence of holes of ${\mathit{d}}_{3\mathit{z}}^{2}$-${\mathit{r}}^{2}$ character experiencing a smaller n-n repulsion than the ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ holes leads to a reduction of the overall n-n repulsion. This reduces the intermediate-doping region of instability with respect to the three-band case. Nevertheless, the interplay between the ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ and the ${\mathit{d}}_{3\mathit{z}}^{2}$-${\mathit{r}}^{2}$ occupations introduces a new phase-separation instability in the region of large differences between the copper and oxygen atomic levels. Both instabilities are driven by p-d charge fluctuations which provide an effective attractive interaction leading to superconductivity.