We present simultaneous measurements of Josephson inductance and DC transport characteristics of ballistic Josephson junctions based upon an epitaxial Al-InAs heterostructure. The Josephson inductance at finite current bias directly reveals the current-phase relation. The proximity-induced gap, the critical current and the average value of the transparency $\bar{ \tau}$ are extracted without need for phase bias, demonstrating, e.g.,~a near-unity value of $\bar{ \tau}=0.94$. Our method allows us to probe the devices deeply in the non-dissipative regime, where ordinary transport measurements are featureless. In perpendicular magnetic field the junctions show a nearly perfect Fraunhofer pattern of the critical current, which is insensitive to the value of $\bar{ \tau}$. In contrast, the signature of supercurrent interference in the inductance turns out to be extremely sensitive to $\bar{ \tau}$.
Categories: cond-mat.supr-con