Helical topological superconductivity in a magnetic field through spin-orbit coupling and superlattice potential

One of the approaches to engineering topological superconductivity (TSC) which supports gapless Majorana edge modes is to expose a 2D superconductor in a spin-orbit coupled material to a magnetic field. We investigate this question in a mean-field theory which obtains the superconducting order parameter, and hence the topology of the system, as well as the nature of the Abrikosov lattice, in a self-consistent fashion. We find small regions of TSC in parameter space. The region of TSC is greatly enhanced by the addition of a superlattice potential. The TSC is associated with either a disortion of the Abrikosov lattice or an Abrikosov lattice of giant vortices which carry two superconducting flux quanta. To find the lowest energy solution, it is essential to employ helical order parameters, although we find that the helical solutions do not carry a net supercurrent. Finally, we consider the experimental feasibility of this model.