Understanding the nature and strength of correlations in iron based superconductors (IBS) is key to unveil the nature of the various phases that appear in the phase diagram of these systems. The analysis of correlation effects in IBS however is not an easy task since it is challenged by the multi-orbital character of the electronic band structure close to the Fermi level .
The metallic nature of the spin-density-wave characterized the parent compound has been interpreted as an indication of a weak (or intermediate) regime of correlations. However there is an increasing experimental evidence of the orbital-dependent character of electronic correlations in IBS, with the simultaneous presence of strong- and weak-correlated electrons. In particular, the degree of correlation of each orbital appears to be proportional to its individual deviation from half-filling. In this talk I will discuss how this effect can be explain via strong-correlated model e.g. multiorbital Hubbard model as a consequence of the effective “orbital decoupling” induced by the Hund’s coupling, which makes the occupation of each orbital crucial [2, 3]. I will discuss the nature of the Hund’s metal phase and clarify the connection between Hund’s metal physics and half-filled Mott physics [2, 3]. I will also show that contrary to what happens in Mott systems, the atomic spin polarization promoted by Hund's coupling induces strong correlations, without necessary leading to an increase in the localization of total charge. Indeed, in some cases the polarization may even promote itineracy .
Although a number of experiments calls for a prominent role of correlations coming from local interactions the effect of the correlations on the nematic, superconducting and magnetic states of IBS has been theoretically poorly investigated. I will discuss the nematicity at the Hund's metal crossover . I will show how correlations severely constrain the precise nature of the feasible orbital-ordered state and induces a differentiation in the effective masses of the zx/yz orbitals in the nematic phase. The latter effect leads to distinctive signatures in different probes, so far overlooked in the interpretation of experiments. I will then discuss the consequences of the orbital selectivity on the superconducting phase, in particular concerning the symmetry of the pairing .
 L. De Medici, Springer Series in Materials Science, Vol. 211, 409 (2015)
 L. De Medici, G. Giovannetti and M. Capone, Phys. Rev. Lett. 112, 177001 (2014)
 L. Fanfarillo and E. Bascones, Phys. Rev. B 92, 075136 (2015)
 L. Fanfarillo, G. Giovannetti, M. Capone and E. Bascones, Phys. Rev. B 95, 144511 (2017).
 L. Fanfarillo, A. Valli, M. Capone, in preparation