We investigate the Josephson effect in TNT and NTN junctions, consisting of
topological (T) and normal (N) phases of semiconductor-superconductor 1D
heterostructures in the presence of a Zeeman field. A key feature of our setup
is that, in addition to the variation of the phase of the superconducting order
parameter, we allow the orientation of the magnetic field to change along the
junction. We find a novel magnetic contribution to the Majorana Josephson
coupling that permits the Josephson current to be tuned by changing the
orientation of the magnetic field along the junction. We also predict that a
spin current can be generated by a finite superconducting phase difference,
rendering these materials potential candidates for spintronic applications.
Finally, this new type of coupling not only constitutes a unique fingerprint
for the existence of Majorana bound states but also provides an alternative
pathway for manipulating and braiding topological qubits in networks of wires.Comment: references and a note were added in v2; 6 pages, 2 figures; v1 had
been submitted for the ICM2012 proceedings on the 31st of May 201