Nodal topological superconductivity in nodal-line semimetals

TL;DR

This paper investigates nodal-line superconducting phases in doped nodal-line semimetals, revealing topologically protected nodal rings with Majorana surface modes, driven by ferromagnetic fluctuations or Hund's coupling.

Contribution

It identifies the favored pairing channels, topological properties of nodal rings, and the impact of magnetic order on superconductivity in nodal-line semimetals.

Findings

Nodal-line superconducting phases are favored by ferromagnetic fluctuations or Hund's coupling.

Topologically protected nodal rings with monopole charges $ u = ext{±}2$ are found on the Fermi surface.

Majorana zero modes are enclosed by nodal rings on the surface Brillouin zones.

Abstract

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 $\nu = \pm 2$. 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 $\bf d$-vectors are perpendicular to the magnetization axis $\bf M$ with their phases unfixed. In this case, each nodal loop in the pairing state splits into two, carrying a $\pm 1$ monopole charge. For bulk-boundary correspondence, these nodal rings enclose flat-band Majorana zero modes on top and bottom surface Brillouin Zones with distinct $\mathbb{Z}$-valued topological invariants.