The few reported members of the antiperovskite structure class $A{e}_{3}P{n}_{A}P{n}_B$ of alkaline-earth ($Ae=\mathrm{Ca}$, Sr, Ba) pnictide ($Pn=\mathrm{N}$, P, As, Sb, Bi) compounds are all based on the $B$-site anion $P{n}_B=\mathrm{N}$. All can be categorized as narrow-gap semiconductors, making them of interest for several reasons. Because chemical reasoning suggests that more members of this class may be stable, we provide here a density functional theory (DFT)-based survey of this entire class of $3\times 5\times 5$ compounds. We determine first the relative energetic stability of the distribution of pairs of $Pn$ ions in the $A$ and $B$ sites of the structure, finding that the $B$ site always favors the small pnictogen anion. The trends of the calculated energy gaps versus the $Ae$ cation and $Pn$ anions are determined, and we study effects of spin-orbit coupling as well as two types of gap corrections to the conventional DFT electronic spectrum. Because there have been suggestions that this class harbors topological insulating phases, we have given this possibility attention and found that energy gap corrections indicate the cubic structures will provide at most a few topological insulators. Structural instability is addressed by calculating phonon dispersion curves for a few compounds, with one outcome being that distorted structures should be investigated further for thermoelectric and topological character. Examples of the interplay between spin-orbit coupling and strain on the topological nature are provided. A case study of ${\mathrm{Ca}}_3\mathrm{BiP}$ including the effect of strain illustrates how a topological semimetal can be transformed into a topological insulator and Dirac semimetal.

• Received 10 October 2017

DOI:https://doi.org/10.1103/PhysRevB.97.035202