  We propose a setup involving Majorana bound states (MBS) hosted by a vortex
on a superconducting surface of a 3D Topological Insulator (TI). We consider a
narrow channel drilled across a TI slab with both sides covered by s-wave
superconductor. In the presence of a vortex pinned to such a channel, it acts
as a ballistic nanowire connecting the superconducting surfaces, with a pair of
MBS localized in it. The energies of the MBS possess a 4\pi-periodic dependence
on the superconductive phase difference \phi between the surfaces. It results
in the appearence of an anomalous term in the current-phase relation, I_a(\phi)
for the supercurrent flowing along the channel between the superconductive
surfaces. We have calculated the shape of the 4\pi-periodic function I_a(\phi),
as well as the dependence of its amplitude on temperature and system
parameters.
