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Electronic Correlations in Multiorbital Systems Electronic correlations in multiorbital systems by José María Pizarro Blanco Submitted to the Department of Condensed Matter Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics at the UNIVERSIDAD AUTÓNOMA DE MADRID PhD Supervisor: Dr. Elena Bascones Fernández de Velasco Instituto de Ciencia de Materiales de Madrid Consejo Superior de Investigaciones Científicas Madrid, Mar 2019 Acknowledgements Para comenzar, me gustaría agradecer a mi directora, Leni Bascones, por la oportunidad de realizar esta tesis junto a ella. Gracias por haber tenido tanta paciencia y haberme enseñado tanto en estos años. Gracias también por haberme dado la oportunidad de viajar e intercambiar conocimientos con otros compañeros de profesión en diferentes conferencias y escuelas. Y gracias también por haberte preocupado por mi presente y futuro y para que pudiese salir adelante. Aprovecho y también te doy las gracias junto a Maria José Calderón y Belen Valenzuela por haberme permitido ayudar a fomentar la Ciencia y la Física de Materiales en diferentes eventos de divulgación. También quiero agradecer a mi familia el apoyo durante estos años. A mis hermanos (y sobrinos), a mis tíos (en especial a mi tía Marisa) y demás por preocuparse por mí. Gracias a mi padre por todo el apoyo que me ha brindado durante años y por la confianza en que lograría ser un buen científico. Gracias también a Enrique y Mila. Gracias a los compañeros y compañeras que me han ido acompañando en mi carrera científica. Gracias a Fer, Teje, a otro Fer, Carol, Gloria, Nadia, Miguel Ángel, Carlos, Jordi. Gracias también a los compañeros del ICMM por haber hecho este camino más ameno: Mónica, Fernando, Sigmund, Bea, Álvaro, José Carlos, Jorge, Guillem, Jesús y Jordi (otra vez). I would also like to thank all of the co-workers from Frankfurt: Ying, Sananda, Emanuelle, Hendrik, Karim, Fabian, Vladislav, Steve, Kira, Anand, Thomas. Y por supuesto, gracias a Roser Valentí por acogerme en su grupo y permitirme aprender tantas cosas. Por último, quiero dar las gracias a Laura por haber estado ahí durante todos estos años. Muchas gracias por haber estado ahí todos estos días y por haberme escuchado y animado. Y gracias por haberme ayudado en la escritura y revisión de esta tesis. Sin tí, esta tesis no habría salido adelante. iv Para Laura v Electronic correlations in multiorbital systems by José María Pizarro Blanco Abstract 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 con- sidering 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 F e3GeT e2. 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 F e3GeT e2 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 super- conductivity. 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 elec- trons. 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 BaF e2S3 for two different pressures. Contrary to other iron-based superconductors, BaF e2S3 (and related materials) is an insulator. Other authors have pointed out that these quasi-1D systems are Mott insulators. In this chapter, I calcu- lated the strength of local correlations to check the behavior of these systems at T = 0 K. 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 sur- face 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 itin- erant ferromagnet F e3GeT e2. 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. Keywords: Unconventional superconductivity, strongly correlated electron systems, Mott insulator, multiorbital systems, Hund metal, metal-to-insulator transition, many-body tech- niques, Slave-Spin Mean Field formalism, local correlations, magic-angle twisted bilayer graphene. Correlaciones electrónicas en sistemas multi-orbitales por José María Pizarro Blanco Resumen Las correlaciones electrónicas en Física de la Materia Condensada juegan un papel fundamen- tal en varios sistemas importantes, como son los materiales magnéticos, los superconductores, los materiales topológicos, las redes ópticas, etc. Las correlaciones electrónicas son aquellas que modifican el movimiento de electrones individuales cuando se considera su interacción con otros electrones dentro del material. Dentro de los sistemas disponibles para estudiar los efectos de las correlaciones electrónicas, en esta tesis voy a centrarme en los superconductores no convencionales, específicamente en los superconductores de alta Tc basados en hierro, y en sistemas bidimensionales, como el recientemente descubierto grafeno bicapa rotado en ángulo mágico o el ferromagneto itinerante F e3GeT e2. En el primer capítulo, resumiré brevemente la teoría de bandas y la teoría del líquido de Fermi para sistemas sólidos. En ciertas situaciones, el cáracter de largo alcance de la interacción de Coulomb puede ignorarse, y la interacción de Coulomb de corto alcance resulta en varios comportamientos interesantes, tales como el aislante de Mott y el metal de Hund, los cuales cambian las expectativas dadas por la teoría de bandas. Me centraré en las correlaciones en el mismo sitio (locales), es decir, aquellas entre electrones que están localizados en el mismo sitio de la red. También resumiré brevemente algunos de las propiedades más importantes de los superconductores no convencionales y de los materiales bidimensionales. En el segundo capítulo, repasaré los efectos de las correlaciones locales en sistemas multi- orbitales. Compararé los resultados experimentales para los superconductores de alta Tc basados en hierro con las expectativas dadas por las correlaciones locales, y argumentaré que los superconductores de hierro están en el régimen del metal de Hund, en el cual el acoplo Hund juega un papel esencial. Los últimos capítulos están dedicados a los trabajos
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