Exploring Signatures of Majorana States in the Current-Phase Relation of Lateral S-TI-S Josephson Junctions

Current developments toward topologically protected quantum computing rely heavily on verifying the existence of Majorana bound states (MBS). In Superconductor-Topological Insulator-Superconductor lateral Josephson junctions, it is predicted that MBS are nucleated at the cores of Josephson vortices where the local phase difference is an odd multiple of π. We study the current-phase relation (CPR) of these junctions, which is theoretically modified to include a 4π-periodic contribution due to the presence of MBS. We describe and present results from two experiments designed to measure the current-phase relation directly via phase-sensitive Josephson interferometry in two regimes. The first uses a SQUID interferometer circuit that allows measurement of the CPR in the absence of an applied magnetic field and is sensitive to extended Majorana states in the junction. The second uses transport measurements of the magnetic field dependence of the critical current in asymmetric SQUIDs that yields the CPR of the smaller junction and is sensitive to localized Majorana states.