Topological properties of spin-triplet superconductors and Fermi surface topology in the normal state

We report intimate relations between topological properties of full-gapped spin-triplet superconductors with time-reversal invariance and the Fermi surface topology in the normal states. An efficient method to calculate the ${\mathit{Z}}_2$ invariants and the winding number for the spin-triplet superconductors is developed and connections between these topological invariants and the Fermi surface structures in the normal states are pointed out. We also obtain a correspondence between the Fermi surface topology and gapless surface states in the superconducting states. The correspondence is inherent to spin-triplet superconductivity.