Influence of the Majorana nonlocality on the supercurrent

We study the equilibrium Josephson current between an $s$-wave superconductor and a topological superconducting nanowire with Majorana bound states (MBS) at its ends. Within a low-energy model, we show analytically that the nonlocality of the MBS allows for a finite supercurrent to flow that otherwise would vanish. In particular, we find the critical current to be a function of the difference in the spin-canting angles of the Majorana wave functions at the location of the tunnel contact. We complement our analytical calculations by numerically solving the full tight-binding model and show how to extract the main features of the low-energy model from the critical current using available experimental techniques.