Possible role of the alkaline-earth ions in high-temperature superconductivity

In high-temperature superconductors with $T_c$ exceeding the temperature of liquid nitrogen, there is no conventional isotope shift. This suggests an unconventional pairing mechanism, but we notice a systematic upward "polarizability shift" in $T_c$. The shift in $T_c$ of about 20% occurs in the 1:2:3, 2:2:1:2, and 2:2:2:3 high-temperature superconducting compounds when the more polarizable Ba replaces Sr. A semiquantitative calculation enables us to interpret our result in the framework of the two-hole resonance mechanism. The role of the alkaline-earth ion is to partially screen the electron-electron Coulomb repulsion $U$, lowering the energy of the $d^8$ state and hence increasing $T_c$.