The determination of the symmetry properties of superconducting gaps has been a central issue in the study of unconventional superconductivity. Although fully resolving this question remains challenging, the presence of superconducting nodes and their topological characteristics is crucial for uncovering unconventional pairing. Several comprehensive databases of topological materials in the normal phases have been established, but there is no equivalent database for topological superconductors—primarily because detailed information on the pairing symmetries of real materials is still lacking.
Sidestepping this issue, we tackle an alternative problem: the predictions of topological and nodal superconductivity in materials for each possible pairing symmetries. In this talk, we first discuss a framework to comprehensively classify superconducting nodes pinned to any line in momentum space, which results in a complement of the symmetry-indicator theory. Next, we combine this classification with symmetry-indicator theory to demonstrate a systematic diagnosis of both topological and nodal superconducting states. Finally, we discuss recent progress in detecting topological features in superconductors using Fermi-surface formulas.

References
– S. Ono & K. Shiozaki, Phys. Rev. X 12, 011021 (2022)
– F. Tang, S. Ono, X. Wan, and H. Watanabe, Phys. Rev. Lett. 129, 027001 (2022)
– Z. Zhang, K. Shiozaki, C. Fang, S. Ono, arXiv:2407.20231