Conditions for fully gapped topological superconductivity in topological insulator nanowires

TL;DR

This paper demonstrates that in topological insulator nanowires, the presence of a vortex is essential for achieving a fully gapped topological superconductor with Majorana states, especially under symmetry constraints.

Contribution

It shows that vortices are necessary for a fully gapped topological phase in symmetric nanowires, and breaking symmetry via disorder can induce a smaller gap without vortices.

Findings

Vortices are required for a full gap in symmetric wires.

Disorder can induce a smaller gap without vortices.

Vortex presence enhances the robustness of Majorana states.

Abstract

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.