Controlling Majorana states in topologically inhomogeneous superconductors

Majorana bound states have been recently observed at the boundaries of one-dimensional topological superconductors. Yet, controlling the localization of the Majorana states, which is essential to the realization of any topological quantum device, is an ongoing challenge. To this end, we introduce a mechanism which can break a topologically homogeneous state via the formation of topological domains, and which can be exploited to control the position of Majorana states. We found in fact that in the presence of amplitude-modulated fields, contiguous magnetic domains can become topologically inequivalent and, as a consequence, Majorana states can be pinned to the domain walls of the magnetic structure. The formation of topological domains and the position of Majorana states can be externally controlled by tuning an applied field (e.g., magnetic or gate).