Pairing in alkaline-earth-metal-doped fullerenes

Among the alkaline-earth-metal-doped fullerenes are several superconductors: ${\mathrm{Ca}}_5$${\mathrm{C}}_{60}$ (${\mathit{T}}_{\mathit{c}}$=8.4 K), ${\mathrm{Ba}}_6$${\mathrm{C}}_{60}$ (${\mathit{T}}_{\mathit{c}}$=7 K), and ${\mathrm{Sr}}_6$${\mathrm{C}}_{60}$ (${\mathit{T}}_{\mathit{c}}$=4 K). While the relevant molecular orbitals of the alkali-metal-doped fullerenes has ${\mathit{t}}_{1\mathit{u}}$ symmetry, superconductivity in the alkaline-earth-metal-doped fullerenes is derived from the ${\mathit{t}}_{1\mathit{g}}$ level that lies immediately above the ${\mathit{t}}_{1\mathit{u}}$ manifold. We calculate and compare the effective on-ball pairing interaction in these states due to phonon exchange and electron-electron repulsion.