Shiro Sakai

<jats:p>Alkali-doped fullerides<jats:italic>A</jats:italic><jats:sub>3</jats:sub>C<jats:sub>60</jats:sub>(<jats:italic>A</jats:italic>= K, Rb, Cs) are surprising materials where conventional phonon-mediated superconductivity and unconventional Mott physics meet, leading to a remarkable phase diagram as a function of volume per C<jats:sub>60</jats:sub>molecule. We address these materials with a state-of-the-art calculation, where we construct a realistic low-energy model from first principles without using a priori information other than the crystal structure and solve it with an accurate many-body theory. Remarkably, our scheme comprehensively reproduces the experimental phase diagram including the low-spin Mott-insulating phase next to the superconducting phase. More remarkably, the critical temperatures<jats:italic>T</jats:italic><jats:sub>c</jats:sub>’s calculated from first principles quantitatively reproduce the experimental values. The driving force behind the surprising phase diagram of<jats:italic>A</jats:italic><jats:sub>3</jats:sub>C<jats:sub>60</jats:sub>is a subtle competition between Hund’s coupling and Jahn-Teller phonons, which leads to an effectively inverted Hund’s coupling. Our results establish that the fullerides are the first members of a novel class of molecular superconductors in which the multiorbital electronic correlations and phonons cooperate to reach high<jats:italic>T</jats:italic><jats:sub>c</jats:sub><jats:italic>s</jats:italic>-wave superconductivity.</jats:p>