Simulation of Majorana Bound States in Multi-Band Josephson Junction Nanowires

Abstract: Majorana bound states can be created at the ends of semiconducting nanowires using a combination of proximity-induced superconductivity, spin-orbit coupling and a magnetic eld. By adding a Josephson junction to this nanowire, four Majorana bound states can exist at the same time in the system. In this thesis I aim to examine the impact that the barrier in Josephson junctions has on the energy states in multi-band nanowires. This is done through simulations using a tight-binding model. The thesis will focus on how Majorana bound states in the system will be influenced by different widths and heights of the Josephson junction barrier through calculations of the Majorana coupling energy and the energy gap to the nearest excited state. By choosing a larger barrier width the system will require a smaller voltage to achieve four Majorana bound states, but be more susceptible to changes in the excited states. This result will only appear in multi-band models. The study indicates that Majorana bound states will behave differently in different energy bands and that the choice of barrier width is non-trivial in order to avoid influences from excited states.