First-principles study of ferroelectricity and pressure-induced phase transitions in HgTiO$_3$

Ground-state structure is found and pressure-induced phase transitions up to 210 kbar are studied in mercury titanate from first principles within the density functional theory. It is established that the $R3c$ structure experimentally observed in HgTiO$_3$ is metastable at ambient pressure. With increasing the hydrostatic pressure, the ground-state structure changes following the $R{\bar 3} \to R3c \to Pbnm$ sequence. It is shown that the appearance of ferroelectricity in HgTiO$_3$ at $P = 0$ is associated with an unstable phonon mode. Optical and elastic properties of different phases of mercury titanate are calculated. The quasiparticle band gap calculated in the \emph{GW} approximation ($E_g = 2.43$ eV) agrees with experimental data better than the value obtained in the LDA approximation (1.49 eV). Analysis of the thermodynamic stability explains why the synthesis of mercury titanate is possible only at high pressures.