Bad metals, Mott insulators, and superconductivity in fullerenes

Last week in Ljubljana, I had a nice discussion with Denis Arčon about this paper concerning fullerenes, A3C60 where A = alkali metal.

Optimized unconventional superconductivity in a molecular Jahn-Teller metal
Ruth H. Zadik, Yasuhiro Takabayashi, Gyöngyi Klupp, Ross H. Colman, Alexey Y. Ganin, Anton Potočnik, Peter Jeglič, Denis Arčon, Péter Matus, Katalin Kamarás, Yuichi Kasahara, Yoshihiro Iwasa, Andrew N. Fitch, Yasuo Ohishi, Gaston Garbarino, Kenichi Kato, Matthew J. Rosseinsky and Kosmas Prassides

This is a rich system and is summarised in the (temperature vs. volume) phase diagram below. Superconductivity appears in proximity to a Mott (Jahn-Teller) insulator.

The JT metal is a bad metal. The novel signature here is that because the electrons are almost localised on individual molecules there is Jahn-Teller effect. This is seen in the Fano line shape of the associated vibrational spectra.

Aside: I have often wondered about a good theoretical description of the Fano line shape for vibrational spectra in metals because it is quite common in organic charge transfer salts. There is an old theory by Michael Rice.  However, it does not even mention Fano. 

Yesterday, Darko Tanaskovic brought to my attention a nice paper which explicitly relates the Rice theory, the relevant Feynman diagrams, to the Fano form for the spectral density. (See especially, Section III).

Charged-phonon theory and Fano effect in the optical spectroscopy of bilayer graphene 
 E. Cappelluti, L. Benfatto, M. Manzardo, and A. B. Kuzmenko

For these fullerenes the minimal effective Hamiltonian is a three band Hubbard model with Hund's rule coupling and electron-phonon interaction (which leads to the Jahn-Teller effect on isolated C60 molecules. Extensive calculations based on Dynamical Mean-Field Theory (DMFT) describe this phase diagram and have been reviewed by Massimo Capone, Michele Fabrizio, Claudio Castellani, and Erio Tosatti