  Majorana bound states in topological Josephson junctions induce a 4? period
current-phase relation. Direct detection of the 4? 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.
