Topological Nodal Line Semimetal and Dirac Semimetal State in Antiperovskite Cu$_3$PdN

TL;DR

This paper predicts that the antiperovskite Cu$_3$PdN can host a 3D topological nodal line semimetal state without SOC, which transitions into a Dirac semimetal with SOC and becomes a topological insulator when symmetry is broken.

Contribution

It introduces Cu$_3$PdN as a new material hosting a topological nodal line semimetal state and describes the evolution into Dirac semimetal and topological insulator phases.

Findings

Nodal line semimetal state protected by symmetry without SOC.

Transition to Dirac points when SOC is included.

Gapping of Dirac points leading to a topological insulator.

Abstract

Based on first-principles calculation and effective model analysis, we propose that the cubic antiperovskite material Cu$_3$PdN can host a three-dimensional (3D) topological nodal line semimetal state when spin-orbit coupling (SOC) is ignored, which is protected by coexistence of time-reversal and inversion symmetry. There are three nodal line circles in total due to the cubic symmetry. "Drumhead"-like surface flat bands are also derived. When SOC is included, each nodal line evolves into a pair of stable 3D Dirac points as protected by C$_4$ crystal symmetry. This is remarkably distinguished from the Dirac semimetals known so far, such as Na$_3$Bi and Cd$_3$As$_2$, both having only one pair of Dirac points. Once C$_4$ symmetry is broken, the Dirac points are gapped and the system becomes a strong topological insulator with (1;111) Z$_2$ indices.