Structural distortions and ferroelectricity in antiperovskite oxides with tetrel elements

Antiperovskites share the same structure as perovskites, but allow completely different chemistries and nominal charge states of anions to be stabilized. This gives rise to many interesting phenomena, including septet superconductivity and topological crystalline insulating phases in these systems. Despite this, the work on the crystal structural trends in these compounds is more limited compared to perovskites. In this study, we consider the family of antiperovskite oxides with tetrel elements (Si, Ge, Sn, Pb) and alkaline earth metals (Ca, Sr, Ba), and perform a detailed study of their crystal structures using first-principles density functional theory. We show how tolerance factor arguments can be constructed to predict their structure in a way parallel to the perovskites, and furthermore, how heterostructuring (or cation-order) can be used to induce ferroelectricity in these systems which may provide an experimental knob to modify electronic structure. We conclude with a discussion of the electronic structure of antiperovskites, and show that they display interesting trends not observed in regular perovskites, including significant antibonding interactions between face-center ions, which might need to be taken into account when building effective electronic models of these compounds.