Size Constraints on Majorana Beamsplitter Interferometer: Majorana Coupling and Surface-Bulk Scattering

Topological insulator surfaces in proximity to superconductors have been proposed as a way to produce Majorana fermions in condensed matter physics. One of the simplest proposed experiments with such a system is Majorana interferometry. Here, we consider two possibly conflicting constraints on the size of such an interferometer. Coupling of a Majorana mode from the edge (the arms) of the interferometer to vortices in the centre of the device sets a lower bound on the size of the device. On the other hand, scattering to the usually imperfectly insulating bulk sets an upper bound. From estimates of experimental parameters, we find that typical samples may have no size window in which the Majorana interferometer can operate, implying that a new generation of more highly insulating samples must be explored.