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

In the superconducting regime of FeTe(1−x)Sex, two types of vortices which are distinct by the presence or absence of zero energy states in their core are observed. To understand their origin, we examine the interplay of Zeeman coupling and superconducting pairings in three-dimensional metals with band inversion. 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, leads to delocalized zero-energy Majorana modes. In contrast, the finite-energy vortex modes remain localized at the vortex ends for both types of pairings. 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)Sex, 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)Sex