Proximity effects and topological superconductivity dependency on layer thickness in superconductor/ferromagnetic/semiconductor hybrid devices

We investigate the topological properties of hybrid devices made of a semiconductor wire partially covered by a ferromagnetic layer, which in turn is covered by a superconducting one (i.e., the wire and the superconductor layer are not directly in contact). We perform numerical calculations of the system including the three materials and the electrostatic environment, and we analyze how its properties change with the ferromagnetic layer width and the gate potentials. We show that both proximity effects into the wire, the induced superconductivity and the induced exchange field, strongly depends on the ferromagnetic layer thickness. We therefore find a suitable thickness range for which the system can support topological phases, and particularly the so-called Majorana bound states. We also perform the same analysis for a semiconducting 2DEG finding similar results, although the topological phases turn out to be more robust.