Face centered cubic SnSe as a $\mathbb{Z}_2$ trivial Dirac nodal line material

Abstract

The presence of a Dirac nodal line in a time-reversal and inversion symmetric system is dictated by the $\mathbb{Z}_2$ index when spin-orbit interaction is absent. In a first principles calculation, we show that a Dirac nodal line can emerge in $\mathbb{Z}_2$ trivial material by calculating the band structure of SnSe in a face centered cubic lattice as an example. We qualitatively show that it becomes a topological crystalline insulator when spin-orbit interaction is taken into account. We clarify the origin of the Dirac nodal line by obtaining irreducible representations corresponding to bands and explain the triviality of the $\mathbb{Z}_2$ index. We construct an effective model representing the Dirac nodal line using the {\bf k}$\cdot${\bf p} method, and discuss the Berry phase and a surface state expected from the Dirac nodal line.