Topological odd-parity superconductors

Abstract

We investigate topological phases of full-gapped odd-parity superconductors without or with time-reversal invariance. For odd-parity superconductors, a combination of the inversion and the $U\left(1\right)$ gauge symmetry is manifestly preserved, and the combined symmetry enables us to characterize the topological phases from the knowledge of the electron dispersion. Topologically protected gapless boundary states are predicted from the Fermi-surface topology. Simple criteria for topological odd-parity superconductors, in particular, that for a non-Abelian topological phase supporting a non-Abelian anyon are provided. Implications for nodal odd-parity superconductors are also discussed.