# Dynamical Mean-Field Theory and Strongly Correlated Superconductors: Can repulsion favour superconductivity?

The most striking realizations of superconductivity have been uncovered in materials where electron-electron correlations are strong, leading to Mott insulating states. This is an intuitively surprising situation, because superconductivity requires attractive interactions and Mott physics arises from strong repulsion. While this link between superconductivity and correlations is almost universally recognized for copper-oxides, it has been revealed recently also for organic superconductors like the alkali-metal doped fullerides such as Cs$_3$C$_{60}$, despite the pairing in these materials is likely driven by phonons.

We discuss how superconductivity can be favoured by electron-electron repulsion by solving models for these two families of superconductors using Dynamical Mean-Field Theory (DMFT), a powerful nonperturbative approach for correlated materials. For the case of fullerene superconductors, our calculations predicted a transition between superconductor and a Mott insulator [1] and several properties that have been confirmed experimentally in later experiments [2]

The first part of the talk will be devoted to a brief introduction to DMFT and to its use for superconductors. In the second part we will present results for fullerenes and discuss the relevance of our theory for different compounds including potassium-doped picene, another surprising organic superconductor [3].

[1] M. Capone, M. Fabrizio, C. Castellani and E. Tosatti, Rev. Mod. Phys. {\bf 81}, Rev. Mod. Phys. 81, 943 (2009); Science {\bf 296}, 2364 (2002)

[2] Y. Takabayashi et al., Science 323, 1585 (2009); A.Y. Ganin et al. Nature Materials 7 367 (2008)

[3] R. Mitsuhashi et al. Nature 464. 76 (2010); G. Giovannetti and M. Capone, Phys. Rev. B {\bf 83}, 134508 (2011)