Pairing and charge distribution in Emery ladders preserving the ratio of Cu to O atoms

We study the Emery model (three-band Hubbard model) for superconducting cuprates on three distinct ladder-like lattices that are supercell of the CuO${}_2$ plane and thus preserve the ratio of copper to oxygen atoms. Using the density-matrix renormalization group method we confirm that these Emery ladders are charge-transfer insulators for the hole concentration corresponding to undoped cuprates but become Luther-Emery liquids with enhanced pairing correlations upon doping. The preservation of the Cu to O ratio allows us to study the distribution of charges between these atoms in the Luther-Emery phase. We show that these Emery ladders can describe the relations between charge distribution, pairing strength, and interactions that have been observed in the Emery model on two-dimensional clusters and in experiments.