Majorana fermions in superconducting nanowires without spin-orbit coupling

We study nanowires with proximity-induced s-wave superconducting pairing in an external magnetic field that rotates along the wire. Such a system is equivalent to nanowires with Rashba-type spin-orbit coupling, with strength proportional to the derivative of the field angle. For realistic parameters, we demonstrate that a set of permanent magnets can bring a nearby nanowire into the topologically nontrivial phase with localized Majorana modes at its ends. This occurs even for a magnetic field configuration with nodes along the wire and alternating sign of the effective Rashba coupling.