We study the Josephson effect for a topologically nontrivial superconducting (TS) wire with Majorana fermion end states and tunnel-coupled to s-wave BCS superconducting (S) electrodes. In an S-TS junction, no supercurrent flow is possible under fairly general conditions. For the S-TS-S junction, bulk TS quasiparticles must be accessible to have a Josephson effect. In the noninteracting case, we derive the exact current-phase relation (CPR) and find \pi-periodic behavior with negative critical current for weak tunnel couplings. Charging effects then cause the anomalous CPR I(φ)=Iccosφ, where the parity-sensitive critical current I_c provides a signature for Majorana states.
@article{arxiv.1202.0438,
title = {Supercurrent blockade in Josephson junctions with a Majorana wire},
author = {A. Zazunov and R. Egger},
journal= {arXiv preprint arXiv:1202.0438},
year = {2012}
}