Quantum transport of planar Josephson junctions with Majorana bound states

We investigate the transport features of a planar Josephson junction which was recently proposed and verified as a host of Majorana bound states (MBSs). With finite phase difference, MBSs can be gapped from the excited states at moderate Zeeman field. A considerable amount of current density develops at the stripe edges due to the presence of the MBSs. More interestingly, we note that in detecting MBSs via scanning tunneling spectroscopy (STM), a conductance minimum is observed at the peak position of the MBS local density of states. We ascribe this discrepancy to the fact that the penetration of the pair potential decays away the superconducting/normal interface. These results are instructive in not only for identifying MBSs in planar Josephson junction via STM measurement, but also for the detection of MBSs in platforms with nonuniform pair potentials.