Madelung energy and charge transfer in ${\mathrm{Pb}}_2$${\mathrm{Sr}}_2$${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Ca}}_{\mathit{x}}$${\mathrm{Cu}}_3$${\mathrm{O}}_{8+\mathrm{\delta }}$: Possible extra superconducting regions

Electronic configurations in the ${\mathrm{Pb}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{Y}}_{1\mathrm{-}\mathit{x}}$ ${\mathrm{Ca}}_{\mathit{x}}$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{8+\mathrm{\delta }}$ superconducting layered compounds are examined through the calculation of the Madelung energy in the ionic model. It is shown that the carrier distributions in the compounds exhibit strong contrast with those in the well-understood ${\mathrm{Ba}}_2$ ${\mathrm{YCu}}_3$ ${\mathrm{O}}_{6+\mathrm{\delta }}$ compounds despite their structural similarity. We demonstrate how the charge transfer between structural building blocks, i.e., the copper-oxygen planes and the charge reservoir, controls the region (x,δ) where the superconductivity emerges. The existence of new superconducting regions separable from the known one is predicted.