Semi-metal and Topological Insulator in Perovskite Iridates

The two-dimensional (2D) layered perovskite Sr$_2$IrO$_4$ was proposed to be a spin-orbit (SO) Mott insulator, where the effect of Hubbard interaction is amplified on a narrow J$_{eff}$=$\frac{1}{2}$ band due to strong spin-orbit coupling. On the other hand, the three-dimensional (3D) orthorhombic perovskite SrIrO$_3$ remains metallic. We construct a tight-binding model for SrIrO$_3$ to understand the physical origin of the metallic behaviour and study possible metal-insulator transitions. In particular, we identify possible perturbations that turn the material into a topological insulator.