Detecting topological superconductivity by using a dc-SQUID

We theoretically investigate the current and phase response of a dc-SQUID composed of two Josephson junctions (JJs) in parallel. The JJs are exposed to an in-plane magnetic field and their chemical potential and Rashba spin-orbit coupling strength are tuned by top gates acting separately on each of the junctions. By tuning the system parameters, each JJ can individually be driven from the trivial to the topological phase and vice versa. We investigate the 3 possible dc-SQUID configurations: the two junctions are topological, one junction is trivial and the other topological, and the two junctions are trivial. We perform theoretical simulations of the phase difference and critical current of the dc-SQUID for the 3 different configurations, and by comparing them we identify the signatures of the topological superconducting phase and its dependence on junction transparency, magnetic field, and spin-orbit coupling.