  We consider core-shell nanowires with prismatic geometry contacted with two
or more superconductors in the presence of a magnetic field applied parallel to
the wire. In this geometry, the lowest energy states are localized on the outer
edges of the shell, which strongly inhibits the orbital effects of the
longitudinal magnetic field that are detrimental to Majorana physics. Using a
tight-binding model of coupled parallel chains, we calculate the topological
phase diagram of the hybrid system in the presence of non-vanishing transverse
potentials and finite relative phases between the parent superconductors. We
show that having finite relative phases strongly enhances the stability of the
induced topological superconductivity over a significant range of chemical
potentials and reduces the value of the critical field associated with the
topological quantum phase transition.
