Emergent Nodal Excitations due to the Coexistence of Superconductivity and Antiferromagnetism: Cases with and without Inversion Symmetry

We argue the emergence of nodal excitations due to the coupling with static antiferromagnetic order in fully-gapped superconducting states in both cases with and without inversion symmetry. This line node structure is not accompanied with the sign change of the superconducting gap, in contrast to usual unconventional Cooper pairs with higher angular momenta. In the case without inversion symmetry, the stability of the nodal excitations crucially depends on the direction of the antiferromagnetic staggered magnetic moment. A possible realization of this phenomenon in CePt$_3$Si is discussed.