Incommensurate charge-density-wave instability in the extended three-band Hubbard model

The infinite-$U$ three-band Hubbard model is considered in order to describe the ${\mathrm{CuO}}_2$ planes of the high-temperature superconducting cuprates. The charge instabilities are investigated when the model is extended with a nearest-neighbor repulsion between holes on copper $d$ and oxygen $p$ orbitals and in the presence of a long-range Coulombic repulsion. It is found that a first-order valence instability line ending with a critical point is present as in the previously investigated model without long-range forces. However, the dominant critical instability is the formation of incommensurate charge-density waves, which always occur before the valence-instability critical point is reached. An effective singular attraction arises in the proximity of the charge-density wave instability, accounting for both a strong pairing mechanism and for the anomalous normal-state properties.