Signatures of flux-dependent Majorana zero modes in a finite-width topological Josephson junction

In the presence of an applied magnetic field, an extended Josephson junction between topological superconductors can host Majorana zero modes (MZMs) in its Josephson vortices. The MZMs in a multiply connected network of such junctions can be moved and braided by applying currents, voltages, and phase differences. We present a theoretical study of MZMs and Josephson currents in a junction between two finite-sized p_x+ip_y superconductor islands, where a key role is played by a delocalized MZM on the system’s outer boundary. Our main result is a parity-dependent splitting of the critical current diffraction pattern. On the way, we characterize the sub-gap quasiparticle spectrum and the equilibrium positions and dynamics of the MZMs under external biases. We connect our results to ongoing experiments on topological superconductors in extended junction geometries, such as those being carried out by the group of Van Harlingen.