Possible Strong Topological Insulator Phase in Li$_{2}$IrO$_{3}$

Recently Na$_{2}$IrO$_{3}$, a layered 5$d$ transition metal oxide compound, was suggested to be a possible topological insulator (TI) based on the $j_{eff}=1/2$ states induced by the strong spin-orbit coupling of Ir 5$d$ states, but its realization has not been clarified yet. In search of the TI phase in transition metal oxides, we propose Li$_{2}$IrO$_{3}$ to be a candidate for the three-dimensional strong TI. By carrying out Wannier function analysis based on first-principles calculations, we constructed a low energy effective Hamiltonian, which leads to a three-dimensional extension of the Kane-Mele model with third-nearest-neighbor hopping within the Ir honeycomb layer and a significant inter-layer coupling. The nature of spin-orbit coupled states near the Fermi level depends on the change of the trigonal crystal field driven by the lattice deformations. A competition between the third next-nearest-neighbor hopping parameter and the trigonal crystal field is found to play a key role in determining the topological character of Li$_{2}$IrO$_{3}$.