Quantitative Model for the Superconductivity Suppression in $R_{1-x}{\mathrm{Pr}}_x{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ with Different Rare Earths

We report local density approximation plus Hubbard parameter $U$ calculations of the electronic structure of $A{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ ($A=\mathrm{Y},\mathrm{P}\mathrm{r},\mathrm{N}\mathrm{d}$) 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 $\mathrm{pd}\sigma$ 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).