Effect of strain and doping on the polar metal phase in LiOsO$_3$

We systematically investigate the effect of strain and doping on the polar metal phase in lithium osmate, LiOsO$_3$, using first-principles calculations. We demonstrate that the polar metal phase in LiOsO$_3$ can be controlled by biaxial strain. Based on density functional calculations, we show that a compressive biaxial strain enhances the stability of the polar $R3c$ phase. On the other hand, a tensile biaxial strain favors the centrosymmetric $R\overline{3}c$ structure. Thus, strain emerges as a promising control parameter over polar metallicity in this material. We uncover a strain-driven quantum phase transition under tensile strain, and highlight intriguing properties that could emerge in the vicinity of this polar to non-polar metal transition. We examine the effect of charge doping on the polar metal phase. By means of electrostatic doping as well as supercell calculations, we find that screening from additional charge carriers, expected to suppress the polar distortions, have only a small effect on them. Rather remarkably, and in contrast to conventional ferroelectrics, the polar metal phase in LiOsO$_3$ remains robust against charge doping up to large doping values.