Majorana fermions in nanowire-superconductor systems in periodic magnetic fields and their resonant manipulation*

The nanowire-superconductor structures with a helical magnetic field are known to host Majorana fermions. We show that the structures built in Si can support Majorana fermions even for the field shapes that are very different from helical ones. We discuss various shapes and imperfections of the magnetic field, and present phase diagrams for a wide range of experimental parameters.

Preliminary results of a separate project indicate the possibility to achieve the Majorana braiding in a 1D structure. The idea is to employ resonant manipulation that brings Majoranas to the first excited delocalized state that serves as a common bus for localized states. Tuning modulations on 4 gates, we aim to achieve an arbitrary unitary transformation on Majorana subspace.