# Higher-Order Topological Superconductivity of Spin-Polarized Fermions

## TL;DR

This paper develops a theoretical framework for higher-order topological superconductivity in spin-polarized ferromagnetic metals, identifying promising materials and pairing mechanisms for realizing Majorana modes.

## Contribution

It derives generalized parity formulas for higher-order topological invariants and classifies band structures capable of hosting such superconductivity in ferromagnetic systems.

## Key findings

- Doped ferromagnetic nodal semimetals are promising platforms.
- Odd-parity pairing induces various higher-order topological phases.
- Potential for topological quantum computation with Majorana modes.

## Abstract

We study the superconductivity of spin-polarized electrons in centrosymmetric ferromagnetic metals. Due to the spin-polarization and the Fermi statistics of electrons, the superconducting pairing function naturally has odd parity. According to the parity formula proposed by Fu, Berg, and Sato, odd-parity pairing leads to conventional first-order topological superconductivity when a normal metal has an odd number of Fermi surfaces. Here, we derive generalized parity formulae for the topological invariants characterizing higher-order topology of centrosymmetric superconductors. Based on the formulae, we systematically classify all possible band structures of ferromagnetic metals that can induce inversion-protected higher-order topological superconductivity. Among them, doped ferromagnetic nodal semimetals are identified as the most promising normal state platform for higher-order topological superconductivity. In two dimensions, we show that odd-parity pairing of doped Dirac semimetals induces a second-order topological superconductor. In three dimensions, odd-parity pairing of doped nodal line semimetals generates a nodal line topological superconductor with monopole charges. On the other hand, odd-parity pairing of doped monopole nodal line semimetals induces a three-dimensional third-order topological superconductor. Our theory shows that the combination of superconductivity and ferromagnetic nodal semimetals opens up a new avenue for future topological quantum computations using Majorana zero modes.