Topological Blount's theorem of odd-parity superconductors

Nontrivial nodal structures are one of the most salient features of gap functions of the unconventional superconductors. In a system with spin-orbit coupling and crystal field, the group theory plays a key role to determine the node of the gap function [1]. From the group theoretical ground, Blount proved that the line node is ``vanishingly improbable'' in spin-triplet superconductors [2]. Namely, it is impossible to create a stable line node in odd-parity superconductors. Our motivation is to compare the group theoretical result with topological stability of nodes by K-theory [3] As a result, we found that K-theory not only rebuilds the original Blount's argument but also exhibits counterexamples with the stable line node. In this talk, we will show the physical interpretation of them. [1] M. Sigrist and K. Ueda, Rev. Mod. Phys. \textbf{63}, 239 (1991). [2] E. I. Blount, Phys. Rev. B, \textbf{32}, 2935 (1985). [3] P. Horava, Phys. Rev. Lett. \textbf{95}, 016405 (2005); Y. X. Zhao and Z. D. Wang, Phys. Rev. Lett. \textbf{110}, 240404 (2013).