Dual nature of the ferroelectric and metallic state in LiOsO${}_3$

Using density functional theory we investigate the lattice instability and electronic structure of recently discovered ferroelectric metal LiOsO${}_3$. We show that the ferroelectric-like lattice instability is related to the Li-O distortion modes while the Os-O displacements change the d-p hybridization as in common ferroelectric insulators. Within the manifold of the d-orbitals, a dual behavior emerges. The ferroelectric transition is indeed mainly associated to the nominally empty e${}_g$ orbitals which are hybridized with the oxygen p orbitals, while the t${}_{2g}$ orbitals are responsible of the metallic response. Interestingly, these orbitals are nominally half-filled by three electrons, a configuration which suffers from strong correlation effects even for moderate values of the screened Coulomb interaction.