Chiral symmetry classes and Dirac nodal lines in three-dimensional layered systems

TL;DR

This paper investigates the formation and stability of Dirac nodal lines in layered three-dimensional systems with chiral symmetry, revealing their topological nature and conditions for annihilation.

Contribution

It introduces a model of layered graphene with external potentials, demonstrating the emergence of spiraling Dirac nodal lines protected by chiral symmetry.

Findings

Dirac nodal lines form in layered systems with chiral symmetry

Nodal lines approach and annihilate as potential increases

Topological invariants explain the stability and annihilation of nodal lines

Abstract

We study the existence and stability of Dirac nodal lines in three-dimensional layered systems, whose layers individually have Dirac nodal points protected by chiral (sublattice) symmetry. The model system we consider is the rhombohedral stack of graphene layers with each layer subjected to a uniform external potential that respects either AIII or BDI classes. From the Hamiltonians in either classes, a pair of nontrivial spiraling Dirac nodal lines can be derived. The results are reasonable in accord to the topological classification of gapless phases for codimension $2$. The nodal lines approach each other as the magnitude of the potential increases, revealing their annihilation due to the fact that regarding the full system their topological invariants are cancelled out.