Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators

TL;DR

This paper explores unique vortex and surface phase transitions in superconducting higher-order topological insulators, revealing new phenomena that could aid in identifying HOTIs and realizing Majorana zero modes.

Contribution

It uncovers two distinct phase transitions in HOTIs involving surface and vortex states, with numerical evidence showing dependence on vortex position, advancing understanding of topological superconductivity.

Findings

Vortices on gapped surfaces exhibit two phase transitions as doping varies.

Surface transition involves competition between superconducting and $ ext{T}$-breaking gaps.

Critical doping for vortex phase transition varies with vortex position.

Abstract

Topological insulators (TIs) having intrinsic or proximity-coupled s-wave superconductivity host Majorana zero modes (MZMs) at the ends of vortex lines. The MZMs survive up to a critical doping of the TI at which there is a vortex phase transition that eliminates the MZMs. In this work, we show that the phenomenology in higher-order topological insulators (HOTIs) can be qualitatively distinct. In particular, we find two distinct features. (i) We find that vortices placed on the gapped (side) surfaces of the HOTI, exhibit a pair of phase transitions as a function of doping. The first transition is a surface phase transition after which MZMs appear. The second transition is the well-known vortex phase transition. We find that the surface transition appears because of the competition between the superconducting gap and the local $\mathcal{T}$-breaking gap on the surface. (ii) We present numerical evidence that shows strong variation of the critical doping for the vortex phase transition as the center of the vortex is moved toward or away from the hinges of the sample. We believe our work provides new phenomenology that can help identify HOTIs, as well as illustrating a promising platform for the realization of MZMs.