  It is known that a non-local complex fermion can be written in terms of two
Majorana fermions. We exploit this fact to explain the system of two Majorana
zero modes bound to a vortex and an anti-vortex, on the surface of a
topological insulator in contact with an s-wave superconductor, as a non-local
complex fermion. Although the current density of a single zero mode vanishes,
by starting with a wave packet consisted of the positive and negative energy
complex fermions, we specify that a time-dependent oscillatory motion emerges
in the system. We also show that the amplitude and frequency of the
oscillations depend on the relative distance of those two zero modes.
Therefore, the observation of this oscillatory motion can be considered as a
signature of the Majorana zero modes. Also, as the frequency of such an
oscillatory motion depends on the distance between the two zero modes, it can
be adjusted to bring this frequency within the resolution of observations.
Furthermore, we indicate that the predicted oscillatory current is the
reminiscent of the zitterbewegung effect.
