The renaissance of fullerene superconductivity

Unconventional high-T_c superconductivity, defined both in terms of the magnitude of the superconducting transition temperature, T_c, and the key role played by electronic correlations, not only is the realm of atom-based low-dimensional layered systems such as the cuprates or the iron pnictides but is also accessible in molecular systems such as the cubic alkali fullerides with stoichiometry A₃C₆₀ (A=alkali metal). In fulleride superconductors, isotropic high-T_c superconductivity occurs in competition with electronic ground states resulting from a fine balance between electron correlations and electron-phonon coupling in an electronic phase diagram strikingly similar to those of unconventional superconductors such as the cuprates and the heavy fermions. Superconductivity at the highest T_c (38 K) known for any molecular material emerges from the antiferromagnetic insulating state solely by changing an electronic parameter - the overlap between the outer wave functions of the constituent molecules - and T_c scales universally in a structure-independent dome-like relationship with proximity to the Mott metal-insulator transition (quantified by V, the volume/C₆₀, or equivalently by (U/W), the ratio of the on-site Coulomb energy, U, to the electronic bandwidth, W), a hallmark of electron correlations characteristic of high-T_c superconductors other than fullerides. The C₆₀ molecular electronic structure plays a key role in the Mott-Jahn-Teller (MJT) insulator formed at large V, with the on-molecule dynamic Jahn-Teller (JT) effect distorting the C₆₀ ^3- units and quenching the t1u orbital degeneracy responsible for metallicity. As V decreases, the MJT insulator transforms first into an unconventional correlated JT metal (where localised electrons coexist with metallicity and the on-molecule distortion persists) and then into a Fermi liquid with a less prominent molecular electronic signature. This normal state crossover is mirrored in the evolution of thesuperconducting state, with the highest T_c found at the boundary between unconventional correlated and conventional weak-coupling BCS superconductivity, where the interplay between extended and molecular aspects of the electronic structure is optimised to create the superconductivity dome.