Symmetry enforced line nodes in unconventional superconductors

We classify line nodes in superconductors with strong spin-orbit interactions and time-reversal symmetry, where the latter may include non-primitive translations in the magnetic Brillouin zone to account for coexistence with antiferromagnetic order. We find four possible combinations of irreducible representations of the order parameter on high symmetry planes, two of which allow for line nodes in pseudo-spin triplet pairs and two that exclude conventional fully gapped pseudo-spin singlet pairs. We show that the former can only be realized in the presence of band-sticking degeneracies, and verify their topological stability using arguments based on Clifford algebra extensions. Our classification exhausts all possible symmetry protected line nodes in the presence of spin-orbit coupling and a (generalized) time-reversal symmetry. Implications for existing non-symmorphic and antiferromagnetic superconductors are discussed.