Symmetry protected line nodes in non-symmorphic magnetic space groups: Applications to UCoGe and UPd\(_2\)Al\(_3\)

Abstract

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 \(k_z=0\) or \(\pm\pi/c\) plane. Moreover, it is likely that additional Weyl point nodes exist at the axial point. On the other hand, in UPd\(_2\)Al\(_3\)-type antiferromagnetic superconductors, gap functions with \(A_g\) 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 UPd\(_2\)Al\(_3\) are candidates for unconventional superconductors possessing hidden symmetry-protected line nodes, peculiar to non-symmorphic magnetic space groups.