  There have been several proposals for platforms sustaining topological
superconductivity in high temperature superconductors, in order to make use of
the larger superconducting gap and the expected robustness of Majorana zero
modes towards perturbations. In particular, the iron-based materials offer
relatively large $T_c$ and nodeless energy gaps. In addition, atomically flat
surfaces enable the engineering of defect structures and the subsequent
measurement of spectroscopic properties to reveal topological aspects. From a
theory perspective, a materials-specific description is challenging due to the
correlated nature of the materials and complications arising from the multiband
nature of the electronic structure. Here we include both aspects in realistic
interacting models, and find that the correlations themselves can lead to local
magnetic order close to linear potential scattering defects at the surface of
the superconductor. Using a self-consistent Bogoliubov-de Gennes framework in a
real-space setup using a prototype electronic structure, we allow for arbitrary
magnetic orders and show how a topological superconducting state emerges. The
calculation of the topological invariant and the topological gap allows us to
map out the phase diagram for the case of a linear chain of potential
scatterers. While intrinsic spin-orbit coupling is not needed to enter the
topological state in presence of spin-spiral states, it enlarges the
topological phase. We discuss the interplay of a triplet component of the
superconducting order parameter and the spin spiral leading effectively to
extended spin orbit coupling terms, and connect our results to experimental
efforts on the Fe(Se,Te) system.

Superconductivity;Strongly Correlated Electrons