Time reversal invariant topological 1D and 2D superconductors: doubling the Sau-Luchtin-Tewari-Sarma and Oreg-Refael-von Oppen proposals

In this work we present a doubled version of the Sau-Luchtin-Tewari-Sarma and Oreg-Refael-von Open proposals thereby obtaining time reversal invariant p-wave superconductivity in both 1D and 2D. This construction is much like the Kane-Mele spin Hall model which is a time reversal invariant doubling of the Haldane model. We show that the low energy effective action for these doubled versions of the Sau-Luchtin-Tewari-Sarma and Oreg-Refael-von Open models corresponds to a single band p-wave time reversal invariant superconductors with pseudo spin degree of freedom instead of spin degree of freedom. There are Majorana fermions at the ends of wires or in vortex cores of these superconductors. Furthermore these are shown to be stable to small perturbations. In the supplement we present physical realization of the system with cold atoms and show a related "no-go" theorem given in Haim et. al. (2019) has too restrictive assumptions to apply to this proposal.
Comment: Comments welcome, V2: minor typos corrected, V3 Minor clarifications