Topological Quantum Phase Transition in $5d$ Transition Metal Oxide ${\mathrm{Na}}_2{\mathrm{IrO}}_3$

We predict a quantum phase transition from normal to topological insulators in the $5d$ transition metal oxide ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, where the transition can be driven by the change of the long-range hopping and trigonal crystal field terms. From the first-principles-derived tight-binding Hamiltonian, we determine the phase boundary through the parity analysis. In addition, our first-principles calculations for ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ model structures show that the interlayer distance can be an important parameter for the existence of a three-dimensional strong topological insulator phase. ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ is suggested to be a candidate material which can have both a nontrivial topology of bands and strong electron correlations.

Figure 1

Hopping parameters considered in our tight-binding model: (a) the indirect hopping ($t_{pd}$) mediated by the oxygen $2p$ orbital and two kinds of direct hoppings ($t_{d{d}_1}$ and $t_{d{d}_2}$), (b) the second-nearest-neighbor hopping ($t_{n_1}$) and the third-nearest-neighbor hopping ($t_{n_2}$), and (c) the band structure of first-principles (solid lines) and tight-binding (dashed lines) calculations with spin-orbit coupling.

Figure 2

One-dimensional energy bands for armchair strip in the (a) NI phase with $t_n=-0.075$ and (b) TI phase with $t_n=0$.

Figure 3

TB band structure with the variation of $t_n$. The solid (red) ($t_n=0$) lines belong to the TI, and the dot-dashed (blue) ($t_n=-0.040$) and double-dashed (orange) ($t_n=-0.075$) lines belong to the NI. Note that, at the transition point, i.e., $t_n=-0.021$, the dispersion is linear.

Figure 4

Phase diagram as a function of $t_n$ and SOC for several values of $\Delta$. The pink circle indicates where the reality exists. $|t_c|=0.062$ is the asymptotic line in the case of $\Delta =0.6$.