Unified picture of superconductivity and magnetism in CeRh${}_2$As${}_2$

We study the micorscopic origin of the multiple superconducting and magnetic phases observed in CeRh${}_2$As${}_2$. We exploit the existence of a van Hove singularity enforced by the nonsymmorphic symmetry to conduct a renormalization group analysis. When Fermi-surface nesting is strong, we find two closely-competing superconducting states with opposite parities, as well as an instability towards specific spin-density wave states, consistent with key features of the phase diagram of CeRh${}_2$As${}_2$.