Nodal topological superconductivity in nodal-line semimetals

We analyze possible nodal superconducting phases that emerge from a doped nodal-line semimetal. We show that nodal-line superconducting phases are favored by interactions mediated by short-range ferromagnetic fluctuations or Hund's coupling. It is found that the leading pairing channels are momentum-independent, orbital-singlet and spin-triplet. In the pairing state, we show that the Bogoliubov-de Gennes (BdG) Hamiltonian hosts a pair of topologically protected nodal rings on the equators of the torus Fermi surface (FS). Using a topological classification for gapless systems with inversion symmetry, we find that these nodal rings are topologically nontrivial and protected by integer-valued monopole charges ν=±2. In the scenario of pairing driven by ferromagnetic fluctuations, we analyze the fate of superconductivity in the magnetically ordered phase. Based on Ginzburg-Landau free energy analysis, we find the energetically favored superconducting state is characterized by the coexistence of two pairing orders whose d-vectors are perpendicular to the magnetization axis M with their phases unfixed. In this case, each nodal loop in the pairing state splits into two, carrying a ±1 monopole charge. For bulk-boundary correspondence, these nodal rings enclose flat-band Majorana zero modes on top and bottom surface Brillouin Zones with distinct ℤ-valued topological invariants.