Unconventional transport of Cooper pairs in topological Josephson junctions.

It is well known that Josephson junctions (JJs) in the presence of a perpendicular magnetic field exhibit qualitatively different interference patterns depending on the length of the junction and the current density profile. Two paradigmatic scenarios are the SQUID and the Fraunhofer patterns, corresponding to a current density sharply peaked at the edges of the junction or to a homogeneous current density profile, respectively. In these simple cases the electrons within the Cooper pair (CP) can be treated effectively as a single entity. However, it is not hard to run into physical mechanisms under which this assumption does not hold, leading to new features in the pattern. An example is the even-odd effect in SQUID patterns due to a non-local transmission of CPs, with the two electrons travelling along opposite edges. In fancier JJs, such as in the presence of inter-edge tunnelling or broadened edge states, the two electrons can propagate and explore the junction independently. We analyse the consequences of a major role acquired by the single-electron physics in the superconducting context: the relevant flux quantum doubles, introducing unexpected periodicities, and new patterns arise.