Current-phase relationship of planar Josephson junctions mediated by the surface states of a topological insulator

It is predicted that the presence of Majorana fermions manifests itself with a $4\pi$ periodic current-phase relation (CPR) in planar Josephson junctions formed with topological weak links. To test this proposal, we have fabricated planar junctions by depositing Nb leads on exfoliated Bi$_{2}$Se$_{3}$ single crystals. The temperature and magnetic field dependence of the proximity-induced supercurrent have been examined in various doping regimes accessed via top gating. The critical current modulation with magnetic field deviates from the usual Fraunhofer diffraction pattern, suggesting modifications to a sinusoidal CPR consistent with a $sin(2\phi)$ component. We are corroborating those results with direct measurements of the CPR using a phase-sensitive SQUID interferometry technique.