Quantum Spin Hall Effect in a Transition Metal Oxide ${\mathrm{Na}}_2{\mathrm{IrO}}_3$

We study theoretically the electronic states in a $5d$ transition metal oxide ${\mathrm{Na}}_2{\mathrm{IrO}}_3$, in which both the spin-orbit interaction and the electron correlation play crucial roles. A tight-binding model analysis together with the first-principles band structure calculation predicts that this material is a layered quantum spin Hall system. Because of the electron correlation, an antiferromagnetic order first develops at the edge, and later inside the bulk at low temperatures.

Figure 1

(a) The honeycomb lattice of Ir atoms in ${\mathrm{Na}}_2{\mathrm{IrO}}_3$ viewed from the $c$ axis. A large black circle shows an Ir atom surrounded by six O atoms (red small circles). (b) The transfer integrals on the honeycomb lattice. A black solid line shows $-t$, while blue short-dashed, red dash-dotted, and green long-dashed arrows indicate $i{t}^{\prime }{\sigma }_x$, $i{t}^{\prime }{\sigma }_y$, $i{t}^{\prime }{\sigma }_z$, respectively.

Figure 2

(a) and (b) The relativistic DOS including the SOI in two different ranges of energy. Black thick solid, red thin solid, green dashed, and blue dotted lines indicate Ir $j_{\mathrm{eff}}=1/2$, Ir $j_{\mathrm{eff}}=3/2$, Ir $e_g$, and O $p$ bands, respectively. The Fermi energy is set to zero. (c) The first-principles band structure (thin lines) and the extended tight-binding model with typical parameters $t=310\mathrm{K}$, $t^{\prime }=100\mathrm{K}$, $t_0^{\prime }=-130\mathrm{K}$, and $t_{\perp }=60\mathrm{K}$ (thick lines). (d) The interlayer coupling $t_{\perp }$ is indicated by black dashed lines, while the other transfer integrals are shown in Fig. 1b. Because of the monoclinic crystal structure, layers are not stacked in the simple way as in $AB$-stacked graphene.