Disorder Effects in Planar Topological Josephson Junctions

Disorder has emerged as one of the main obstacles toward the realization, and unambiguous detection, of Majorana bound states in superconductor-semiconductor heterostructures. In recent years a lot of work, both theoretical and experimental, has been done to address the effects of disorder in quasi one-dimensional superconductor-semiconductor nanowires. Planar Josephson junctions based on InAs and Al are another promising platform for the realization of Majorana bound states for which the effects of disorder, so far, have not been studied in depth. In this talk I will present some of the recent results that we have obtained to quantitatively estimate the dominant sources of disorder in planar topological Josephson junctions, and their effects on the robustness and detection of the Majorana bound states that can be realized in such junctions.