Topological properties of the [110] SnTe nanowires

SnTe materials are know to be a platform for realization of various strong and symmetry protected topological phases in one, two and three spatial dimensions. We study symmetry-protected topological states in $[110]$ SnTe nanowires in the presence of various combinations of Zeeman field, $s-$wave superconductivity, inversion-symmetry-breaking field and the thickness of the wire. In the normal state we find a Weyl semimetal phase protected by a twofold screw axis symmetry and a topological insulating phase characterized by a $\mathbb{Z}$ invariant protected by a mirror symmetry. In the presence of superconductivity, we find inversion-symmetry-protected gapless phase which becomes fully gapped and topologically non-trivial by introducing an inversion-symmetry-breaking field. Consequently, we find topologically protected localized Majorana zero modes appear at the ends of the wire. We find that this Majorana phase is much easier to achieve in a $[110]$ SnTe nanowire than in a $[001]$ one.