Triply degenerate nodal lines in topological and non-topological metals

TL;DR

This paper explores the theoretical existence of triply degenerate nodal lines in metals, revealing two types with distinct topological properties, surface states, and potential for novel quantum phenomena like the 3D quantum anomalous Hall effect.

Contribution

The study introduces two novel types of triply degenerate nodal lines in metals, expanding the understanding of topological and non-topological band structures.

Findings

Identified topologically trivial and nontrivial triply degenerate nodal lines.

Surface states depend on lattice geometry and termination.

Vortex ring of pseudospin-1 fermions exhibits Skyrmion textures and topological Fermi arcs.

Abstract

Topological nodal-line semimetals exhibit double or fourfold degenerate nodal lines, which are protected by symmetries. Here, we investigate the possibility of the existence of triply degenerate nodal lines in metals. We present two types of triply degenerate nodal lines, one topologically trivial and the other nontrivial. The first type is stacked by two-dimensional pseudospin-1 fermions, which can be viewed as an critical case of a tunable band-crossing line structure that contains a symmetry-protected quadratic band-crossing line and a non-degenerate band, and can split into four Weyl nodal lines under perturbations. We find that surface states of the nodal line structure are dependent on the geometry of the lattice and the surface termination. Such a metal has a nesting of Fermi surface in a range of filling, resulting in a density-wave state when interaction is included. The second type is a vortex ring of pseudospin-1 fermions. In this system, the pseudospins form Skyrmion textures, and the surface states are fully extended topological Fermi arcs so that the model exhibits 3D quantum anomalous Hall effect with a maximal Hall conductivity. The vortex ring can evolve into a pair of vortex lines that are not closed in the first Brillouin zone. A vortex line cannot singly exist in the lattice model if it is the only nodal feature of the system.