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, $s\text{−}\mathrm{wave}$ 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 nontrivial 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.

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• Symmetry protected topological states
• Topological insulators
• Chalcogenides
• Nanowires
• Topological materials
• Discrete symmetries
• Tight-binding model