Is there a common theme behind the correlated-electron superconductivity in organic charge-transfer solids, cobaltates, spinels and fullerides?

We posit that there exist deep and fundamental relationships between the above seemingly very different materials. The carrier concentration-dependences of the electronic behavior in the conducting organic charge-transfer solids and layered cobaltates are very similar. These dependences can be explained within a single theoretical model, - the extended Hubbard Hamiltonian with significant nearest neighbor Coulomb repulsion. Interestingly, superconductivity in the cobaltates seems to be restricted to bandfilling exactly or close to one-quarter, as in the organics. We show that dynamic Jahn-Teller effects and the resultant orbital ordering can lead to 1/4-filled band descriptions for both superconducting spinels and fullerides, which show evidence for both strong electron-electron and electron-phonon interactions. The orbital orderings in antiferromagnetic lattice-expanded bcc M$_3$C$_{60}$ and the superconductor are different in our model. Strong correlations, quarter-filled band and lattice frustration are the common characteristics shared by these unusual superconductors.