Synthesizing Majorana zero-energy modes in a periodically gated quantum wire

We explore a scheme for engineering a one-dimensional spinless $p$-wave superconductor hosting unpaired Majorana zero-energy modes, using an all-electric setup with a spin-orbit-coupled quantum wire in proximity to an $s$-wave superconductor. The required crossing of the Fermi level by a single spin-split energy band is ensured by employing a periodically modulated Rashba interaction, which, assisted by electron-electron interactions and a uniform Dresselhaus interaction, opens a gap at two of the spin-orbit shifted Fermi points. While an implementation in a hybrid superconductor-semiconductor device requires improvements upon present-day capabilities, a variant of our scheme where spin-orbit-coupled cold fermions are effectively proximity coupled to a BEC reservoir of Feshbach molecules may provide a ready-to-use platform.