# Topological odd-parity superconductors

## TL;DR

This paper characterizes topological phases of full-gapped odd-parity superconductors using Z_2 invariants derived from Fermi surface topology, providing criteria for various dimensions and implications for nodal cases.

## Contribution

It introduces a method to evaluate Z_2 invariants in odd-parity superconductors based on symmetry and Fermi surface structure, linking topological invariants to Fermi surface topology.

## Key findings

- Z_2 invariants can be evaluated from Fermi surface data.
- Criteria for topological phases in various dimensions are established.
- Implications for nodal odd-parity superconductors are discussed.

## Abstract

In this letter, we investigate topological phases of full-gapped odd-parity superconductors, which are distinguished by the bulk topological invariants and the topologically protected gapless boundary states. Using the particle-hole symmetry, we introduce Z_2 invariants characterizing topological odd-parity superconductors without or with time-reversal invariance. For odd-parity superconductors, a combination of the inversion and the U(1) gauge symmetry is manifestly preserved, and the combined symmetry enables us to evaluate the Z_2 invariants from the knowledge of the Fermi surface structure. Relating the Z_2 invariants to other topological invariants, we establish characterization of topological odd-parity superconductors in terms of the Fermi surface topology. Simple criteria for topological odd-parity superconductors in various dimensions are provided. Implications of our formulas for nodal odd-parity superconductors are also discussed.