Unified Picture of Superconductivity and Magnetism in CeRh_{2}As_{2}.

We propose a theory for the microscopic origin of the multiple superconducting and magnetic phases observed in CeRh_{2}As_{2} based on the existence of Van Hove singularities near the Fermi energy. The nonsymmorphic symmetry of this material implies that these singularities are located away from high-symmetry momenta; i.e., they have so-called type-II character. This allows us to include the significant Rashba spin-orbit coupling in CeRh_{2}As_{2} in a parquet renormalization group approach. When Fermi-surface nesting is strong, our analysis reveals two closely competing superconducting states with opposite parities, as well as an instability toward spin-density wave states that support both of them, consistent with the phase diagram of CeRh_{2}As_{2}. Type-II Van Hove singularities are generic to nonsymmorphic space groups, and so our theory implies that many other compounds may support closely competing even- and odd-parity superconductivity.