Vortex-line topology in iron-based superconductors with and without second-order topology

TL;DR

This paper investigates how second-order topological phases in iron-based superconductors influence vortex line topology and Majorana modes, revealing conditions under which vortex lines are trivial or nontrivial, and connecting theory with recent experiments.

Contribution

It provides a detailed analysis of vortex line topology in second-order topological superconductors, highlighting the effects of Zeeman fields and inhomogeneity on Majorana modes and vortex states.

Findings

Vortex lines far from hinges are topologically nontrivial in weakly doped regimes.

Hybridization near helical Majorana hinge states can trivialize vortex lines.

Large Zeeman fields lead to chiral Majorana hinge modes and trivial vortex lines.

Abstract

The band topology of a superconductor is known to have profound impact on the existence of Majorana zero modes in vortices. As iron-based superconductors with band inversion and $s_{\pm}$-wave pairing can give rise to time-reversal invariant second-order topological superconductivity, manifested by the presence of helical Majorana hinge states in three dimensions, we are motivated to investigate the interplay between the second-order topology and the vortex lines in both weak- and strong-Zeeman-field regimes. In the weak-Zeeman-field regime, we find that vortex lines far away from the hinges are topologically nontrivial in the weakly doped regime, regardless of whether the second-order topology is present or not. However, when the superconductor falls into the second-order topological phase and a topological vortex line is moved close to the helical Majorana hinge states, we find that their hybridization will trivialize the vortex line and transfer robust Majorana zero modes to the hinges. Furthermore, when the Zeeman field is large enough, we find that the helical Majorana hinge states are changed into chiral Majorana hinge modes and thus a chiral second-order topological superconducting phase is realized. In this regime, the vortex lines are always topologically trivial, no matter how far away they are from the chiral Majorana hinge modes. By incorporating a realistic assumption of inhomogeneous superconductivity, our findings can explain the recent experimental observation of the peculiar coexistence and evolution of topologically nontrivial and trivial vortex lines in iron-based superconductors.