Dirac Line Nodes in Inversion-Symmetric Crystals

TLDR

The letter discusses the effects of spin‑orbit interactions, symmetry breaking, and experimental implications. The authors propose and characterize a new ${\mathbb{Z}}_{2}$ class of topological semimetals with negligible spin‑orbit coupling. They construct ${\mathbb{Z}}_{2}$ invariants from parity eigenvalues at high‑symmetry points to predict Dirac line nodes. The study finds bulk 1D Dirac line nodes and nearly flat 2D surface states protected by inversion and time‑reversal symmetries, and predicts such DLNs in doped Cu₃N near the Fermi level.

Abstract

We propose and characterize a new ${\mathbb{Z}}_{2}$ class of topological semimetals with a vanishing spin-orbit interaction. The proposed topological semimetals are characterized by the presence of bulk one-dimensional (1D) Dirac line nodes (DLNs) and two-dimensional (2D) nearly flat surface states, protected by inversion and time-reversal symmetries. We develop the ${\mathbb{Z}}_{2}$ invariants dictating the presence of DLNs based on parity eigenvalues at the parity-invariant points in reciprocal space. Moreover, using first-principles calculations, we predict DLNs to occur in ${\mathrm{Cu}}_{3}\mathrm{N}$ near the Fermi energy by doping nonmagnetic transition metal atoms, such as Zn and Pd, with the 2D surface states emerging in the projected interior of the DLNs. This Letter includes a brief discussion of the effects of spin-orbit interactions and symmetry breaking as well as comments on experimental implications.