system with a honeycomb lattice

Na₂IrO₃ is the transition-metal system with a honeycomb lattice in which five electrons per site are occupied in Ir t_2g bands. It was firstly proposed as a candidate to show the quantum spin Hall (QSH) phase because spin-orbital entangled j_eff = 1/2 bands across the Fermi level can be map into the Kane-Mele model. However, its topological phase has not been reported yet. Contrarily, Na₂IrO₃ and its isostructural systems have turned out to be Mott insulator with antiferromagnetic order. Nevertheless, the possibility of the QSH phase in these systems is still an interesting subject. State-of-the-art structural controlling with high pressure, chemical substitution, or substrate engineering can potentially manipulate their electronic kinetics and correlation effect.
In the study, we revisit the topological property of a (t_2g)⁵ system with a honeycomb lattice. We explore the topological phase transition with respect to a relative strength of two types of nearest neighboring hopping channels: the hopping mediated by edge-shared ligands with pdp bonding and the direct hopping between t_2g orbitals with ddσ bonding. Moreover, we investigate topological properties in the presence of Coulomb repulsion with help of variational cluster perturbation theory.