Kosterlitz-Thouless transition and charge redistribution in the superconductivity of YBCO/PBCO superlattices

Recent experimental measurements of the resistive transition in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$/${\mathrm{PrBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathit{x}}$ superlattices show a dramatic suppression in the resistive transition temperature ${\mathit{T}}_{\mathit{c}}$ as the thickness of the Pr layer increases while the thickness of the Y layer decreases. We show that the qualitative features of these experiments (and in particular most of the suppression in ${\mathit{T}}_{\mathit{c}}$) can be accounted for within the Kosterlitz-Thouless theory. A small further suppression in ${\mathit{T}}_{\mathit{c}}$ is shown to occur due to charge transfer from Y to the Pr layers.