Topological Blount's theorem of odd-parity superconductors

Blount's theorem prohibits the existence of line nodes for odd-parity superconductors (SCs) in the presence of spin-orbit coupling (SOC). We studied the topological stability conditions of line nodes under inversion symmetry by generalizing the original statement and establishing a relation to surface zero-energy states. The topological instability of line nodes in odd-parity SCs implies the disappearance of corresponding flat zero-energy surface dispersions due to surface Rashba SOC, which provides an experimental means to distinguish line nodes in odd-parity SCs from those in other SCs.