Topological Josephson Junctions

The Josephson effect in conventional superconductors has led to a variety of extensions and applications from SQUID magnetometers to pairing symmetry detection using planar junctions.  It is therefore interesting to extend the discussion to topological Josephson junctions where Majorana fermions, and not just Cooper pairs, can tunnel through the junction. In this talk I will consider a setup made of a ring of topological superconducting wires separated by Junctions and coupled to a quantum dot.  The coupling to the quantum dot serves as a knob which tunes the periodicity of the current in the junction as a function of external flux.  The periodicity can change from one flux quantum (h/2e), expected from a conventional junction, to that of a topological junction, h/e. This tuning ability can distinguish between a topological junction and a dirty non-topological junction. I will also discuss phase slips and the suppression of 2pi phase slips in topological Josephson junctions.