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

I will talk about a scheme for engineering a magnetic field-free, one-dimensional topological superconductor hosting unpaired Majorana zero-energy modes. We consider an all electric setup with a spin-orbit coupled wire in proximity to an s-wave superconductor and subject to a spatially modulated electric field. The required crossing of the Fermi level by a single spin-split energy band is ensured by the 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. The resulting helical liquid state can be driven, through superconducting pairing, to a topological superconducting phase. As the scheme calls for the assistance of electron-electron interactions, the microscopic Hamiltonian is cast in a low-energy effective bosonized description amenable to a renormalization group analysis. I will show the resulting phase diagram and provide the minimum practical conditions for sustaining the topological phase in the lab.