Mapping the topological phase diagram of multiband semiconductors with supercurrents.

We show that Josephson junctions made of multiband semiconductors with strong spin-orbit coupling carry a critical supercurrent Ic that contains information about the nontrivial topology of the system. In particular, we find that the emergence and annihilation of Majorana bound states in the junction is reflected in strong even-odd effects in Ic at small junction transparency. This effect allows for a mapping between Ic and the topological phase diagram of the junction, thus providing a dc measurement of its topology.