What This project concerns the study of so-called topological states in the iron-based superconductors. In contrast to their non-topological counterparts, topological states are unaffected by imperfections in the host material. This robustness makes them useful as fundamental constituents of electronic devices. However, topological states are elusive and suitable host materials are rare. Recent experiments have suggested that iron-based superconductors may display such topological states, which would offer a high-quality platform for their manipulation. In this project, I will investigate the mechanisms underlying the appearance of topological states in the iron-based superconductors, and how the strong electronic interactions present in these materials affect the emergence of these states. Why The scientific importance of this project is two-fold. On the one hand, putting the experimental observations on firm theoretical footing is important for efficiently implementing the materials into working devices. The theoretical foundations developed in this project will therefore have implications for the design of future devices. On the other hand, there is the more fundamental question of how the strength of the electronic interactions affect the emergence of topological states in the first place. Addressing this question will teach us whether electronic interactions help or hinder the appearance of topological states and may lead to the design of new materials. How The work will be carried out at the Niels Bohr Institute at the University of Copenhagen. The project will employ a variety of complementary theoretical approaches to address the questions posed, and will take advantage of both analytical and numerical methods. SSR The project is a piece of a much larger puzzle which concerns the understanding and design of quantum materials. Quantum materials typically refer to materials which, through quantum mechanical effects, exhibit extraordinary properties. These properties can for instance be the aforementioned topological states or the ability to conduct electricity without resistance. The ultimate goal of this endeavor is the ability to tailor materials for specific applications. On a shorter time-scale, this project will aid in the design of materials for storing and manipulating quantum information.