Helical topological superconductivity in intrinsic quantum Hall superconductors

One of the approaches to engineering topological superconductivity in a two dimensional electron gas with spin-orbit coupling is to proximity-couple it to an s-wave type-II superconductor with a non-standard Abrikosov flux lattice that is neither triangular or square but has an even number of superconducting flux quanta per unit cell. Here we ask whether exposing an intrinsic two-dimensional superconductor with spin orbit coupling to a perpendicular magnetic field -- an intrinsic quantum Hall superconductor -- can give rise to topological superconductivity. We investigate this question in a mean-field theory and obtain, in a self-consistent fashion, the real space configuration of the superconducting order parameter, which encodes information about the topology of the superconductivity as well as the nature of the Abrikosov lattice. We find small regions of topological superconductivity in the parameter space, which can be greatly enlarged by the addition of a superlattice potential. Topological superconductivity is seen to be correlated with the presence of either a distorted Abrikosov lattice or an Abrikosov lattice of giant vortices which carry two superconducting flux quanta. To identify the lowest energy solution, it is essential to employ helical order parameters. Finally, we discuss the experimental feasibility of this proposal