Materials predicted to be topological insulators in hypothetical structures assumed by theorists might be trivial insulators in their stable phases*

The quest for new topological insulators (TIs) has motivated numerous {\em ab initio} calculations of the topological metric $Z_{2}$ of candidate compounds in hypothetical crystal structures, or in assumed pressure or doping conditions. However, TI-ness might destabilize certain crystal structures that would be replaced by other structures, which might not be TIs. Here, we discuss such false-positive predictions recurrent in the {\em ab initio} search for new TIs: (i) Various ABX compounds, predicted to be TIs in the assumed ZrBeSi-type structure that turns out to be unstable, become trivial insulators in their stable structures. (ii) Band-inversion-inducing structure perturbations destabilize the system which is instead trivial at equilibrium: examples of this scenario are the cubic $A^{\textrm{III}}$BiO$_{3}$ perovskites that transform from topological to trivial when they relax to their equilibrium structures. (iii) Doping destabilizes the band-inverted system that relaxes to a trivial atomic configuration (orthorhombic band-inverted BaBiO$_{3}$ becomes trivial upon electron doping). This shows the need of performing total energy along with $Z_{2}$ calculations to predict stable TIs.