Stability of the d-wave pairing with respect to the intersite Coulomb repulsion in cuprate superconductors

It is known that the real structure of CuO2 plane is characterized by the spatial separation of the subsystem of holes located at oxygen ions and the subsystem of spins localized at copper ions (Fig. 1). Besides, a number of features is caused by the presence of two oxygen ions in the unit cell of copper-oxygen plane. The minimal realistic microscopic model for cuprates is the three-band p− d model (the Emery model) [1, 2]. This model takes into account the dx2−y2-orbitals of copper ions and pxand py-orbitals of oxygen ions. However, along with the realism, the multiband character of the Emery model leads to cumbersome analysis of cuprates physics. That is why a number of studies in this direction is carried out in the framework of the Hubbard model and its effective low-energy variants, such as t−J and t−J models on the simple square lattice. In these models, the same fermions form the charge and the spin subsystems. Along with the number of important results, such an approach has a serious disadvantage: the Cooper pairing of fermions caused by the kinematic [3], exchange [4, 5], and spin-fluctuation mechanisms considered in the Hubbard [6,7], t−J [4,5], or t−J [8,9] models is suppressed by the intersite Coulomb repulsion V1 of charge carriers located at the neighboring sites. This effect is most pronounced in the d channel [10] and the Cooper instability disappears completely at V1 ∼ 1 − 2 eV. In our previous paper [11], it has been shown that, because of the two-orbital character of the subsystem of holes located at oxygen sites and the spatial separation of this subsystem from that of spins at copper ions, the superconducting phase in high-Tc cuprates is stable with respect to the strong Coulomb repulsion of holes located at the nearest-neighbor oxygen sites if the order parameter has the dx2−y2-symmetry. This effect is due to the symmetry properties of the Coulomb potential. Fig. 1. Structure of CuO2 plane. Here V1 denotes the Coulomb interaction between holes located at the nearest-neighbor oxygen sites and V2 and V ′ 2 correspond to the Coulomb interactions of holes located at the nextnearest-neighbor oxygen sites.