Browsing by Author "Westström, Alex"

Majorana quasiparticles are zero-energy modes theorised to exist at the boundaries of topological superconductors. Due to their topological protection and non-Abelian exchange statistics, Majorana quasiparticles have in recent years garnered much interest within the condensed matter community as a promising platform for fault tolerant quantum computing. To this end, theorists constantly attempt to come up with new experimentally feasible models that can host these quasiparticles. In this thesis, we investigate a recent proposal for realising an effective topological superconductor with Majorana quasiparticles, namely the helical Shiba chain. The system consists of a one-dimensional array of magnetic impurities deposited on a conventional superconductor, such that the overall magnetic texture is helical. A single impurity hosts a bound electron state with an energy within the superconducting gap. For many impurities, these so called Shiba states hybridise and form energy bands, that for a certain range of parameters support topological superconductivity and Majorana bound states at the ends of the chain. Prior to this work, the Shiba chain has only been studied in the deep-dilute limit where the energies of the individual Shiba states are assumed to be very close to the centre of the gap, and the magnetic impurities are placed sufficiently far away from each other as to keep the resulting bands deep within the gap. By re-expressing the problem in terms of a non-linear eigenvalue equation, we go beyond this limit and extend the study of the topological properties of the Shiba chain to a novel domain of experimental interest — a domain which has until now remained unexplored. We compare our results with previous work and observe an agreement between our more general theory and the deep-dilute limit in the expected parameter regime. However, qualitative differences emerge when the coherence length of the underlying superconductor becomes very large.