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.

7 pages, 2 figures

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• Nodal lines and nodal loops in non-symmorphic odd-parity superconductors
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Topological d-wave superconductivity in two dimensions
• Enhancement of superconductivity by pressure-induced critical ferromagnetic fluctuations in UCoGe
• Topological gapless points in superconductors: From the viewpoint of symmetry
• Supercurrent-Induced Weyl Superconductivity
• Tunable zero-energy Dirac and Luttinger nodes in a two-dimensional topological superconductor
• Unveiling the superconducting scenario in multiphase superconductor CeRh${}_2$As${}_2$ from space-group symmetry analysis and DFT calculations