Resumen de 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-Tc iron-based superconductors, and on two-dimensional materials, like the recent magic-angle twisted bilayer graphene or the itinerant ferromagnet Fe3GeTe2.
In the first chapter, I will briefly review the band theory and Fermi liquid theory for solid systems. In certain situations, the long-range character of the Coulomb interaction can be safely ignored, and short-range Coulomb interaction will result in various interesting behaviors, such as the Mott insulator and the Hund metal, which can change the expectations from band theory. I will constraint to onsite (local) correlations, i.e. those between electrons sitting in the same lattice site. I will also briefly review some of the most important properties of unconventional superconductors and two-dimensional materials.
In the second chapter, I will review the effects of local correlations in multiorbital systems. I will compare with experimental results for high-Tc iron-based superconductors with the expectations given by local correlations, arguing that the iron superconductors are in the Hund metal regime, in which the Hund’s coupling plays a major role.
Last chapters are dedicated to the work done during this thesis. I studied the effects of local correlations in various high-Tc iron superconductors, as well as in the magic-angle twisted bilayer graphene. A brief chapter about my ongoing work in Fe3GeTe2 is presented at the end of the thesis. Through this thesis, I used the Slave-Spin Mean-Field technique to address the local correlations behavior in these multiorbital systems.
In the third chapter, we proposed to search a new family of high-Tc superconductors in the chromium analogues of iron-based superconductors. We argue that, due to the similar strength of electronic correlations, plus a superconducting instability driven by magnetic fluctuations, chromium-based pnictides and chalcogenides could host unconventional superconductivity. This argument is based on the fact that iron-based superconductors can be viewed as electron-doped Mott insulators, where the strength of correlations increases when doping these iron superconductors with holes, and decreases when doping them with electrons. In this picture, chromium pnictides and chalcogenides will be the hole-doped Mott insulator, and we found a similar trend: electronic correlations increase when doping the cromium-based systems with electrons (and decrease when doping with holes).
In the fourth chapter, I studied the strength of local correlations in the quasi-1D two-leg ladder iron-based superconductor BaFe2S3 for two different pressures. Contrary to other iron-based superconductors, BaFe2S3 (and related materials) is an insulator. Other have pointed out that these quasi-1D systems are Mott insulators. In this chapter, I calculated the strength of local correlations to check the behavior of these systems at T = 0K. I found a metallic behavior instead, so that we concluded by stating that the insulating behavior could be driven by finite temperature effects. I found a substantial Fermi surface reconstruction due to local correlations, contrary to what happen in other iron-based superconductors.
In the fifth chapter, I studied the nature of the insulating states in magic-angle twisted bilayer graphene. I implemented the Zeeman effect in the Slave-Spin Mean-Field formalism to address the behavior of the insulating states when varying an onsite magnetic field in the local correlations picture. I found that the behavior is opposite to the experimental evidences. We argued that local correlations by themselves cannot explain the insulating states in magic-angle twisted bilayer graphene. We reviewed the last works done in non-local correlations in other lattices, concluding that the insulating states in magic-angle twisted bilayer graphene could be explained by using the non-local correlations picture.
In the sixth chapter, I obtained the band structure and tight-binding model of the 2D itinerant ferromagnet Fe3GeTe2. This is a brief chapter about the current status on my work in this system.
A final chapter is devoted to the conclusions and a final overview that can be extracted from this thesis. Various appendices indicate the details of the techniques used during this thesis, as well as some interesting mathematical proofs.
