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

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.

6 pages, 4 figures