Joint measurement of current-phase relations and transport properties of hybrid junctions using a three junctions SQUID

We propose a scheme to measure both the current-phase relation and differential conductance $dI/dV$ of a superconducting junction, in the normal and the superconducting states. This is done using a dc Superconducting Quantum Interference Device (dc SQUID) with two Josephson junctions in parallel with the device under investigation and three contacts. As a demonstration we measure the current-phase relation and $dI/dV$ of a small Josephson junction and a carbon nanotube junction. In this latter case, in a regime where the nanotube is well conducting, we show that the non-sinusoidal current phase relation we find is consistent with the theory for a weak link, using the transmission extracted from the differential conductance in the normal state. This method holds great promise for future investigations of the current-phase relation of more exotic junctions.