  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.
