Majorana bound states in chains of interacting quantum dots

Abstract: This thesis concerns the creation of Majorana bound states (MBSs) -- a type of condensed matter excitations theorized to have exotic and technologically valuable properties. In particular, they could be used to store and manipulate quantum information in a protected way, forming the building blocks of a topological quantum computer. The search for MBSs has been intense since it was realized that they could be created in superconductor-semiconductor hybrid structures, such as long chains of quantum dots separated by superconductors. Majorana bound states can even appear in two-site chains, although called "poor man's" MBSs since they only appear at fine-tuned sweet spots and hence lack the protection standard MBSs offer. However, they share all other properties of MBSs, making the short quantum dot chains appealing for studying their exotic physics. In this thesis, we study the platform proposed in Ref. [1], consisting of a short chain of quantum dots where each dot is coupled to a separate superconductor. However, we consider Coulomb interactions in the system, which were neglected in the original work. We develop MBS quality measures to determine that Coulomb interactions do not destroy the possibility of creating MBSs. Furthermore, we use the quality measures to conclude that adding more sites to the chain does not necessarily improve the MBS quality. Finally, we suggest that control of the superconducting phases can be used to fine-tune the system to the sweet spot. In conclusion, this thesis finds that the quantum dot chain is a relevant platform for creating poor man's MBSs.