| Summary: | Topological matter has emerged as one of the most prominent research fronts in condensed matter physics over the past three decades. The discovery of the role of topology in materials has shaped our fundamental understanding of how the constituents of matter organize themselves to produce various phases. Topology in these systems manifests as boundary states and exotic quasiparticles, whose intriguing properties are anticipated to facilitate various technological applications. In this thesis I have contributed to the search for topological superconductivity, which is expected to support localized, particle-like excitations called Majorana bound states. Majorana bound states break the dichotomy of bosons and fermions by obeying non-Abelian exchange statistics. Hence a Majorana bound state would be a manifestation of a fundamentally new type of physics. Furthermore, Majorana braiding is envisioned to be utilized in topologically protected quantum computing, which could revolutionize the future of computing. The experimental discovery of Majorana bound states is an outstanding goal in condensed matter physics at the moment. The systems investigated in this thesis consists of magnetic adsorbed atoms (adatoms) deposited on top of a conventional superconductor. In publications I and II we investigated the appearance of Majorana bound states in adatom chains. The main result in publication I is that coupled chains are more likely to exhibit Majorana bound states than uncoupled chains. In publication II we showed that a supercurrent can be used to control the topological phase, which could be helpful for the manipulation of Majorana bound states. In publications III and IV we showed that two-dimensional adatom structures support a generalization of px+ipy superconductivity, making it an interesting addition to the list of materials with unconventional superconductivity. The complex, mosaic-like structure of the topological phase diagram is remarkably rich due to long-range electron hopping. The number of propagating ...
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