Critical current anomaly at the topological quantum phase transition in a Majorana Josephson junction

Majorana bound states in topological Josephson junctions induce a 4π period current-phase relation. Direct detection of the 4π periodicity is complicated by the quasiparticle poisoning. We reveal that Majorana bound states are also signaled by the anomalous enhancement on the critical current of the junction. We show the landscape of the critical current for a nanowire Josephson junction under a varying Zeeman field, and reveal a sharp step feature at the topological quantum phase transition point, which comes from the anomalous enhancement of the critical current at the topological regime. In multi-band wires, the anomalous enhancement disappears for an even number of bands, where the Majorana bound states fuse into Andreev bound states. This anomalous critical current enhancement directly signals the existence of the Majorana bound states, and also provides a valid signature for the topological quantum phase transition.