High spin-Chern-number topological phases provide a promising low-dimensional platform for realizing double-helical edge states. Here we show how these edge states can host a variety of phases driven by electron interaction effects, including multichannel 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 noninteracting 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.

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• Cold gases in optical lattices
• Domain walls
• Edge states
• Majorana bound states
• Quasiparticles & collective excitations
• Symmetry protected topological states
• Topological superconductors
• 1-dimensional systems
• Thin films
• Ultracold gases
• Luttinger liquid model
• Quantum field theory (low energy)
• Renormalization group