Electron correlations in C$_{60}$ and aromatic superconductors

Recent discovery of superconductivity in fcc/A15 Cs$_3$C$_{60}$ under pressure and in aromatic compounds (ex. alkali-doped picene) has stimulated a renewed interest in molecular superconductors such as K$_3$C$_{60}$ and Rb$_3$C$_{60}$. To clarify the mechanism of the superconductivity, it is essential to understand low-energy electronic structure of these systems. In the present study, we perform a systematic study for understanding the relation between electronic correlation and superconductivity in C$_{60}$ and aromatic compounds [1]. We derived, from first principles, extended Hubbard models for twelve compounds: fcc K$_3$C$_{60}$, Rb$_3$C$_{60}$, Cs$_3$C$_{60}$ (with three different lattice constants), A15 Cs$_3$C$_{60}$ (with four different lattice constants), doped solid picene, coronene, and phenanthrene. We show that these compounds are strongly correlated and have similar energy scales of their bandwidths and interaction parameters. However, they have a different trend in the relation between the strength of the electronic correlation and superconducting-transition temperature. While the C$_{60}$ compounds have a positive correlation, the aromatic compounds exhibit a negative correlation. [1] Y. Nomura, K. Nakamura, and R. Arita, Phys. Rev. B ${\bf 85}$, 155452 (2012).