PhD Thesis: Electronic correlations in multiorbital systems

The role of electronic correlations in Condensed Matter is at the heart of various important systems, like magnetic materials, superconductors, topological materials, optical lattices, etc. Electronic correlations are those which change the motion of individual electrons when considering the interaction with other electrons in the material. Among the available systems to study electronic correlation effects, in this thesis I focus on unconventional superconductors, specifically in high-$T_c$ iron-based superconductors, and on two-dimensional materials, like the recent magic-angle twisted bilayer graphene or the itinerant ferromagnet $Fe_3GeTe_2$. In the introduction, I explained in detail the importance of electronic correlations, and how their strength can be modeled by the quasiparticle weight $Z$. I briefly reviewed the most important aspects of the Fermi Liquid Theory. Chapter 2 is devoted to explain in detail the role of electronic correlations in multiorbital systems, with a special attention to the role played by the Hund's coupling $J_H$. Chapters 3 to 6 describe the calculations done in various real systems. During this thesis, I used a combination of ab-initio and modelling, plus slave-spin many-body approaches to study the effect of the Hubbard interaction $U$ and the Hund's coupling $J_H$ in various real systems. A detailed description of the techniques can be found in the appendixes.