Symmetry-Protected Line Nodes in Non-symmorphic Magnetic Space Groups: Applications to UCoGe and UPd2Al3

We present the group-thoretical classification of gap functions in superconductors coexisting with some magnetic order in non-symmorphic magnetic space groups. Based on the weak-coupling BCS theory, we show that UCoGe-type ferromagnetic superconductors must have horizontal line nodes on either kz=0 or ±π/c plane. Moreover, it is likely that additional Weyl point nodes exist at the axial point. On the other hand, in UPd₂Al₃-type antiferromagnetic superconductors, gap functions with Ag symmetry possess horizontal line nodes in antiferromagnetic Brillouin zone boundary perpendicular to c-axis. In other words, the conventional fully-gapped s-wave superconductivity is forbidden in this type of antiferromagnetic superconductors, irrelevant to the pairing mechanism, as long as the Fermi surface crosses a zone boundary. UCoGe and UPd₂Al₃ are candidates for unconventional superconductors possessing hidden symmetry-protected line nodes, peculiar to non-symmorphic magnetic space groups.