Colloquium: Modeling the unconventional superconducting properties of expanded A₃C₆₀ fullerides

The trivalent alkali fulleride solids of generic composition A₃C₆₀, where C₆₀ is the fullerene molecule and A=K, Rb, and Cs, are a well-established family of molecular superconductors. The superconductive electron pairing is of regular s-wave symmetry and is accounted for by conventional coupling of electrons to phonons, in particular by well-understood Jahn-Teller intramolecular C₆₀ vibrations. A source of renewed interest in these systems is the surprising indication of strong electron-electron repulsion phenomena, which has emerged in compounds where the C₆₀-C₆₀ distance is expanded, by either a large cation size or other chemical or physical means. Several examples are now known where this kind of expansion, while leading to a high superconducting temperature at first, gradually or suddenly causes a decline of superconductivity and its eventual disappearance in favor of a Mott insulating state. This type of insulating state is the hallmark of strong electron correlations in cuprate and organic superconductors, and its appearance suggests that fullerides might also be members of that family. Our approach to fullerides is theoretical, and based on the solution of a Hubbard-type model, where electrons hop between molecular sites. In a Hubbard model of fullerides, unlike models for the strongly correlated cuprates, all important electron correlations occur within the molecular site, so it is efficiently soluble in the dynamical mean-field theory (DMFT) approximation. DMFT solutions confirm that superconductivity in this model fulleride, although of s-wave symmetry rather than d-wave, shares many of the properties that are characteristic of high-T_c cuprates. The calculations are heavy, and while the working model used is several years old, the new results presented pertain to the interesting case of three electrons per C₆₀ molecule, appropriate to A₃C₆₀, and have become possible only recently due to a stronger computational effort. The zero-temperature phase diagram is calculated as a function of the ratio of intramolecular repulsion parameter U to the electron bandwidth W, the increase of U∕W representing the main effect of lattice expansion. The phase diagram is close to that of actual materials, with a dome-shaped superconducting order parameter region preceding the Mott transition for increasing cell volume. Unconventional properties of expanded fulleride superconductors predicted by this model include (i) an energy pseudogap in the normal phase; (ii) a gain of electron kinetic energy and of conducting Drude weight at the onset of superconductivity, as in high-T_c cuprates; (iii) a spin susceptibility and a specific-heat behavior that are not drastically different from those of a regular phonon superconductor, despite strong correlations; and (iv) the emergence of more than one energy scale governing the renormalized single-particle dispersion, electronic entropy, and specific-heat jump. These predictions, which if confirmed should establish fullerides as members of the wider family of strongly correlated superconductors, are discussed in light of existing and foreseeable experiments.