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Determination of the symmetry property of superconducting gaps has been acentral issue in studies to understand the mechanisms of unconventionalsuperconductivity. Although it is often difficult to completely achieve theaforementioned goal, the existence of superconducting nodes, one of the fewimportant experimental signatures of unconventional superconductivity, plays avital role in exploring the possibility of unconventional superconductivity.The interplay between superconducting nodes and topology has been activelyinvestigated, and intensive research in the past decade has revealed variousintriguing nodes out of the scope of the pioneering work to classifysuperconducting order parameters based on the point groups. However, asystematic and unified description of superconducting nodes for arbitrarysymmetry settings is still elusive. In this paper, we develop a systematicframework to comprehensively classify superconducting nodes pinned to any linein momentum space. While most previous studies have been based on the homotopytheory, our theory is on the basis of the symmetry-based analysis of bandtopology, which enables systematic diagnoses of nodes in all nonmagnetic andmagnetic space groups. Furthermore, our framework can readily provide a highlyeffective scheme to detect nodes in a given superconductor by using densityfunctional theory and assuming symmetry properties of Cooper pairs (calledpairing symmetries), which can reduce candidates of pairing symmetries. Wesubstantiate the power of our method through the time-reversal broken andnoncentrosymmetric superconductor CaPtAs. Our work establishes a unified theoryfor understanding superconducting nodes and facilitates determiningsuperconducting gaps in materials combined with experimental observations.

Symmetry-based approach to nodal structures: Unification of compatibility relations and gapless point classifications