Quantitative Model for the Superconductivity Suppression inR1−xPrxBa2Cu3O7with Different Rare Earths

We report local density approximation plus Hubbard parameter $U$ calculations of the electronic structure of $A{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{7}$ ($A=\mathrm{Y},\phantom{\rule{0ex}{0ex}}\mathrm{P}\mathrm{r},\phantom{\rule{0ex}{0ex}}\mathrm{N}\mathrm{d}$) including Coulomb correlations in the $f$ shell. For $A=\mathrm{Pr}$ (but not for $A=\mathrm{Nd}$) an additional band crosses the Fermi level, grabbing holes from the (super)conducting $\mathrm{pd}\ensuremath{\sigma}$ band. On doping Y or Nd with Pr the position of the hole-depleting band depends on the atomic number of the host rare earth, through the position of its $f$ level. This makes ${T}_{c}$ suppression in doped compounds different for different hosts the stronger the smaller the atomic number of the host is, and also explains why an external pressure reduces ${T}_{c}$ in doped compounds, opposite to the effect of the "chemical pressure" (substituting one rare earth by another with a smaller size).