Among the different platforms to engineer Majorana fermions in
one-dimensional topological superconductors, topological insulator
nanowires remain a promising option. Threading an odd number of flux
quanta through these wires induces an odd number of surface channels,
which can then be gapped with proximity induced pairing. Because of the
flux and depending on energetics, the phase of this surface pairing may
or may not wind around the wire in the form of a vortex. Here we show
that for wires with discrete rotational symmetry, this vortex is
necessary to produce a fully gapped topological superconductor with
localized Majorana end states. Without a vortex the proximitized wire
remains gapless, and it is only if the symmetry is broken by disorder
that a gap develops, which is much smaller than the one obtained with a
vortex. These results are explained with the help of a continuum model
and validated numerically with a tight binding model, and highlight the
benefit of a vortex for reliable use of Majorana fermions in this
platform.
Fidelity in topological superconductors with end Majorana fermions
