Topological states in a transition metal oxide Na2IrO3

The electronic state of an Ir oxide, Na$_2$IrO$_3$ with the honeycomb structure is analyzed theoretically as a representative system where both the spin-orbit interaction and the electron correlation play important roles. The $5d$ electrons of Ir$^{4+}$ form the effective $J_{\rm eff} = 1/2$ states, leading to the effective Hubbard model with the complex spin-dependent hopping integrals. We propose that this system can realize the quantum spin Hall effect close to room temperature. At much lower temperature, antiferromagnetic order first develops at the edge, and then inside the bulk, leading to fractionally charged states on the dynamic domain walls along the edge.