Majorana Bound States in Extended Topological Josephson Junctions: Disorder & Braiding Studies

Majorana bound states (MBS) have garnered significant attention in recent years, as their unique properties are fundamentally exciting and position them as potential routes toward fault-tolerant quantum computing. A highly promising candidate platform for realizing MBS is the extended topological Josephson junction, in which MBS have been theorized to bind to the cores of Josephson vortices in the presence of an external magnetic field. In this talk, we present 2D and effective 1D numerical studies of the topological Josephson junction between two p_x+ip_y superconductors, analyzing how disorder impacts the stability of the MBS. We then extend our numerical framework to simulations of a topological Josephson trijunction system, establishing presence of MBS before exploring possible braiding protocols. Lastly, we discuss how insights from these studies can translate to those derived from the Kitaev chain and to other frontrunner platforms for MBS, such as nanowires.