Characterization and braiding of Majorana bound states in planar topological Josephson tri-junctions

The extended S-I-S Josephson junction between p+ip superconductors is a promising platform for the realization and characterization of Majorana bound states (MBS). It has been shown that for a single junction geometry in the presence of an external magnetic field, MBS can be hosted at the cores of Josephson vortices. Here, we present analytical and numerical studies of MBS dynamics in a Josephson tri-junction system with three finite-sized p+ip superconducting islands. We begin by finding the locations of the MBS within the tri-junction and characterizing the current-phase relation. We also discuss and demonstrate possible braiding schemes within the system by adjusting both the applied magnetic field and the phase differences between the islands. Lastly, we relate our results to ongoing experimental efforts in S-TI-S tri-junction systems.