# Effect of Zeeman coupling on the Majorana vortex modes in iron-based topological superconductors

## TL;DR

This paper investigates how Zeeman coupling influences Majorana vortex modes in iron-based topological superconductors, explaining the observed differences in vortex zero-energy states and their localization properties.

## Contribution

It demonstrates the effects of Zeeman coupling on different pairing symmetries and explains the experimental dichotomy of vortex states in FeTeSe superconductors.

## Key findings

- Weak Zeeman fields suppress intra-orbital pairing, localizing vortex states.
- Orbital-triplet pairing remains stable but causes delocalized Majorana modes.
- Zero-bias peaks disappear with increasing magnetic field due to Zeeman effects.

## Abstract

In the superconducting regime of FeTe$_{(1-x)}$Se$_x$, there exist two types of vortices which are distinct by the presence or absence of zero energy states in their core. To understand their origin, we examine the interplay of Zeeman coupling and superconducting pairings in three-dimensional metals with band inversion. Weak Zeeman fields are found to suppress the intra-orbital spin-singlet pairing, known to localize the states at the ends of the vortices on the surface. On the other hand, an orbital-triplet pairing is shown to be stable against Zeeman interactions, but leads to delocalized zero-energy Majorana modes which extend through the vortex. In contrast, the finite-energy vortex modes remain localized at the vortex ends even when the pairing is of orbital-triplet form. Phenomenologically, this manifests as an observed disappearance of zero-bias peaks within the cores of topological vortices upon increase of the applied magnetic field. The presence of magnetic impurities in FeTe$_{(1-x)}$Se$_x$, which are attracted to the vortices, would lead to such Zeeman-induced delocalization of Majorana modes in a fraction of vortices that capture a large enough number of magnetic impurities. Our results provide an explanation to the dichotomy between topological and non-topological vortices recently observed in FeTe$_{(1-x)}$Se$_x$.