Topological crystalline insulators and Dirac octets in antiperovskites

We predict a class of topological crystalline insulators in the antiperovskite material family with the chemical formula $A_{3}BX$. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a “Dirac octet.” Our work suggests that antiperovskites are a promising venue for exploring the cooperative interplay between band topology, crystal symmetry, and electron correlation.

Figure 1

(a) Crystal structure of the antiperovskite $A_{3}BX$. (b) Band structure of TCI ${\mathrm{Sr}}_3\mathrm{PbO}$ in which the orbital character of valence and conduction bands within a Dirac octet is inverted ($\pm$ denotes the parities of the band orbitals). The inset depicts a fit with the $kp$ theory described in the main text. There is a small avoided crossing along the $\Gamma X$ direction. (c) ${\mathrm{Sr}}_3\mathrm{SnO}$ is near a topological phase transition with gap closing at $\Gamma$. (d) ${\mathrm{Ca}}_3\mathrm{SnO}$ is a trivial insulator.

Figure 2

Topological phase diagram for the minimal quadratic $kp$ theory describing a Dirac octet, for the (100) mirror plane. The three phases have different mirror Chern numbers $\left(n_M\right)$. Each inset is a schematic band structure depicting bulk states in light blue and surface states in dark blue, cutting through the bulk gap. The existence of the surface states is dictated by $n_M$.

Figure 3

Topological phase diagram for the minimal quadratic $kp$ theory of the $\left(1\overline{1}0\right)$ mirror plane. The numbers $n_M$ are the mirror Chern numbers.