Relation between electronic and atomic structure of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{6+\mathit{x}}$

Using a model with strong interatomic correlations previously proposed to explain the electronic structure and pairing in ${\mathrm{CuO}}_2$ superconductors, we obtain a staircase behavior of the Fermi level, and a tendency of O(1) ions to order in Cu-O chains. We study the competition between this tendency and long-range Coulomb repulsion, using an Ising model and group-theoretical techniques. Using the cluster variation method, we also study the orthorhombic-tetragonal transition and correlations of the tetragonal phase. All results agree qualitatively with experiments.