  To guide the search for the Majorana fermion, we theoretically study
superconductor/topological/superconductor (S/TI/S) junctions in an
experimentally relevant regime. We find that the striking features present in
these systems, including the doubled periodicity of the Andreev bound states
(ABSs) due to tunneling via Majorana states, can still be present at high
electron densities. We show that via the inclusion of magnetic layers, this 4pi
periodic ABS can still be observed in three-dimensional topological insulators,
where finite angle incidence usually results in the opening of a gap at zero
energy and hence results in a 2pi periodic ABS. Furthermore, we study the
Josephson junction characteristics and find that the gap size can be controlled
and decreased by tuning the magnetization direction and amplitude. These
findings pave the way for designing experiments on S/3DTI/S junctions.
