Robust topological superconductivity in spatially modulated planar Josephson junctions

Semiconductor-superconductor planar Josephson junctions are promising platforms for realizing topological superconductivity and Majorana zero modes. We purpose a spatially modulated structure consisting of a planar Josephson junction with periodically modulated width. Based on detailed numerical calculations for a low-energy effective model of the proposed device, we demonstrate that the topological gap characterizing the modulated structure is enhanced significantly, which, in turn, enhances the robustness of the associated Majorana zero modes. The enhancement of the topological gap is the result of a stronger effective spin-orbit coupling generated by the periodic potential induced by the spatial modulation of the junction. In addition, we find that the proposed structure supports a low-field topological superconducting phase within a significant range of electrostatic control parameters, in the absence of a superconducting phase difference across the junction. The optimal regime for operating the device can be achieved by tuning the electrostatic potential in the junction region.