Engineering Majorana Kramers Pairs In Synthetic High Spin Chern Insulators

High spin-Chern-number topological phases provide a promising low-dimensional platform for realizing double-helical edge states. In this letter, we show how these edge states can host a variety of phases driven by electron interaction effects, including multi-channel helical Luttinger liquid, spin density wave, superconducting phases, and a new type of $\pi$-junction analog of the latter two, where the transitions between the phases can be controlled. The superconducting phase in the interacting system is shown to be adiabatically connected to a time-reversal-symmetric topological superconductor in the non-interacting DIII class. This connection stabilizes Majorana Kramers pairs as domain wall states at the interface between the superconducting and $\pi$-spin-density wave phases, with the latter exhibiting a time-reversal-symmetric spin-density wave phase. We discuss the possibility of realizing our proposed scheme for generating Majorana Kramers pairs in a cold-atom based platform with existing techniques, and how it could offer potential advantages over other approaches.