Characterizing Majorana bound states in extended disordered Josephson junctions

In this talk, we consider the emergence of Majorana bound states (MBS) in extended S-TI-S Josephson junctions between p+ip superconductors. In a single junction geometry, it has been shown that the cores of Josephson vortices can host MBS when an external magnetic field is present within the junction. Here, we present analytic and numerical studies of MBS dynamics in a single Josephson junction system formed by two finite-sized p+ip superconducting islands. We focus primarily on the interplay between flux and disorder in the system by first developing an effective 1D-model for the system before examining the spectrum for the full 2D-lattice model. We discuss potential implications of our results in experimentally relevant S-TI-S junction systems and the extension of this analysis to a tri-junction system, in which braiding of MBS can occur.