Exploring Hund’s correlated metals: charge instabilities and effect of selective interactions

Undoped iron-based superconductors accommodate six electrons in the five d-orbitals belonging to Fe-atom. It is nowadays well established that a correlated model at this filling is characterized by a bad metallic state induced by a sizable value of the Hund’s coupling J even when the Hubbard U becomes substantially larger than the bandwidth. Such systems are usually identified as Hund’s metal. This concept has been introduced to rationalize the observation that, in theoretical models of iron-based superconductors, ruthenates, and other materials, many relevant observables turn out to be remarkably dependent on Hund’s coupling J rather than on the Hubbard interaction U. In this thesis we gave some contributions to the understanding of this –still elusive– regime exploring different regimes of the incredibly rich physics of multi-orbital strongly correlated model.