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High-temperature unconventional superconductivity is arguably one of the most studied but least understood phenomena in solid-state physics. Indeed the discovery of the first high-temperature superconductor, a copper oxide compound (cuprate), already dates back more than 35 years. Yet, there is no consensus concerning the mechanism behind superconductivity in those materials. Recently, also nickel oxide superconductors (nickelates), which are isostructural to cuprates, were discovered. This thesis focuses on applying advanced numerical tools to study these two families of superconductors. One aspect responsible for the complexity of cuprates and nickelates is the strong Coulomb interaction between the 3d electrons. As a result, they become strongly correlated, and simple mean-field theories no longer capture the relevant physics. Most methods that can treat strong correlations non-perturbatively are, however, restricted to a few orbitals and/or sites. One way to address these methodological shortcomings is a two-step procedure: first, obtain an approximate solution of the exact many-body Hamiltonian and subsequently use it to construct an approximate Hamiltonian which can be solved (more) exactly.Within this thesis, we adopt this approach and start by briefly reviewing density-functional theory and how to construct effective low-energy Hamiltonians. Following this, the many-body Green’s function formalism, which forms the basis for the methods used to study the previously obtained effective models, is introduced. Our method of choice is the dynamical vertex approximation, a Feynman diagrammatic extension of the dynamical mean-field theory.The remainder of this thesis deals with the physics of cuprates and nickelates, with aparticular focus on their respective models. Cuprates are first introduced, and a parameter region where the density of states displays a depression at the Fermi energy,commonly known as “pseudogap”, is studied. Based on calculations of the Hubbard model, we unveil how the imaginary part of the spin-fermion vertex can lead to the formation of the pseudogap. Furthermore, we show that the pseudogap can be understoodas a momentum-selective insulator, where the Fermi surface at the antinode becomes gapped. At the same time, coherent states remain at the node.The next sections focus on the “new kids on the block” of high-temperature superconductors: nickelates. Currently, there is no consensus regarding the minimal model for superconductivity in nickelates within the community. Hence, the first section reviews the electronic structure and establishes our view on the minimal model: a single-band Hubbard model. Subsequently, this model is tested by comparing the calculated superconducting transition temperature and magnetic response to experimental measure-ments. Additionally, we extend our framework to finite-layer nickelates and identify“superconductivity without rare-earth pockets”.The last part of this thesis focuses on hydrogen defects in nickelate superconductors.Intercalating hydrogen during the synthesis process of infinite-layer nickelates is en-ergetically favorable. Hence, it is crucial to determine possible ways of detecting itspresence in samples and understand how it influences their physics. |
