Majorana fermions from Shiba states in an antiferromagnetic chain on top of a superconductor

We propose a new mechanism for topological superconductivity based on an antiferromagnetically ordered chain of magnetic atoms on the surface of a conventional superconductor. In a weak Zeeman field, a supercurrent in the substrate generates a staggered spin-current, which converts the preexisting topologically-unprotected Shiba states into Majorana fermions (MFs). The two experimental knobs can be finely tuned providing a platform with enhanced functionality for applications. Remarkably, the electronic spin-polarization of the arising edge MF wavefunctions depends solely on the parity of the number of magnetic moments, which can serve as a distinctive signature of the MFs. We introduce the basic concepts within a minimal model and make contact with experiments by a microscopic analysis based on the Shiba states.