Higher-order topological superconductivity of spin-polarized fermions

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 formulas for the topological invariants characterizing the higher-order topology of centrosymmetric superconductors. Based on the formulas, 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 another avenue for future topological quantum computations using Majorana zero modes.