Electronic correlations in multi-orbital systems

Paper presented at the Condensed Matters in Paris conference that was held in paris on 24-29th August, 2014.The Mott transition, at which a material predicted to be metallic by conventional band theory becomes insulator, is one of the most dramatic effects of interactions. In the case of single orbital systems with local interactions (Hubbard model) the Mott transition takes place when the interaction U is larger than a critical value and the orbital is half-filled. The Mott transition can be tuned with pressure (changing U) or doping. Away from half-filling a clean system is metallic but correlated, being the band mass larger as closer the system is to half-filling. On the other hand several orbitals have to be considered in most correlated materials. In multi-orbital systems the Mott transition happens not only at half-filling but at any commensurate filling. New interactions, like Hund¿s coupling, play a role in determining the strength of correlations in iron pnictides, ruthenates and many oxides. It is already known that depending on orbital filling Hund¿s coupling can promote or suppress metallicity. Closer inspection shows that even for a given filling Hund¿s coupling can enhance or decrease correlations. After an introduction, in this presentation I will focus on our recent results on the different effect which Hund¿s coupling has on the induced correlations for a given orbital filling. I will discuss the energy scales which control this behavior and the resulting mass enhancement. I will then show the dependence of these interaction scales on doping. Conmensurate and non-conmensurate fillings will be discussed. Examples will include cases in which the t2g, the eg, or all the five-d orbitals are relevant. If time allows I will talk about some specific consequences of this physics on the properties of iron pnictides and/or the interplay between Hund¿s coupling and spin-orbit interactions relevant for 5d oxides, like iridates