Semimetal and Topological Insulator in Perovskite Iridates

The two-dimensional layered perovskite Sr${}_{2}$IrO${}_{4}$ was proposed to be a spin-orbit Mott insulator, where the effect of Hubbard interaction is amplified on a narrow $J$${}_{\mathrm{eff}}=1/2$ band due to strong spin-orbit coupling. On the other hand, the three-dimensional orthorhombic perovskite (Pbnm) SrIrO${}_{3}$ remains metallic. To understand the physical origin of the metallic state and possible transitions to insulating phases, we construct a tight-binding model for SrIrO${}_{3}$. The band structure possesses a line node made of $J$${}_{\mathrm{eff}}=1/2$ bands below the Fermi level. As a consequence, instability toward magnetic ordering is suppressed, and the system remains metallic. This line node, originating from the underlying crystal structure, turns into a pair of three-dimensional nodal points on the introduction of a staggered potential or spin-orbit coupling strength between alternating layers. Increasing this potential beyond a critical strength induces a transition to a strong topological insulator, followed by another transition to a normal band insulator. We propose that materials constructed with alternating Ir- and Rh-oxide layers along the (001) direction, such as Sr${}_{2}$IrRhO${}_{6}$, are candidates for a strong topological insulator.