Odd parity and line nodes in nonsymmorphic superconductors

Group theory arguments have been invoked to argue that odd-parity order parameters cannot have line nodes in the presence of spin-orbit coupling. In this Rapid Communication we show that these arguments do not hold for certain nonsymmorphic superconductors. Specifically, we demonstrate that when the underlying crystal has a twofold screw axis, half of the odd-parity representations vanish on the Brillouin-zone face perpendicular to this axis. Many unconventional superconductors have nonsymmorphic space groups, and we discuss implications for several materials, including UPt₃, UBe₁₃, Li₂Pt₃B, and Na₄Ir₃O₈.