Interplay of Domain Walls and the Supercurrent in a Topological Josephson Junction

We consider an interferometer based on chiral Majorana and Dirac modes in a hybrid superconductor/ferromagnet/superconductor Josephson junction on top of a topological material. These one-dimensional bound chiral modes can carry Josephson current, which results in an unusual current-phase relation. Domain walls in the magnetic layer may influence the supercurrent. We demonstrate that the supercurrent depends on the distance between the domain walls, and on the other hand, it controls the interaction of the domain walls and thus the dynamics of the magnetic layer.