Topological edge states in correlated honeycomb materials with strong spin-orbit coupling

We study the topological nature of single layers of correlated honeycomb materials $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}₃$ and ${A}₂{\mathrm{IrO}}₃$ $(A=\text{Li},\text{Na})$ with strong spin-orbit coupling. An effective tight-binding model based on first principles band structure calculations including Hubbard and spin-orbit coupling is derived. Two pairs of propagating edge modes centered at the zone center and zone boundary are found when their one-dimensional boundary forms a zigzag shape, while the bulk has a gap with trivial time-reversal ${Z}₂$ invariants. The effects of strong electronic interactions and doping on the edge modes in these Mott insulators are discussed. We further suggest a heterostructure of $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}₃/{\mathrm{IrCl}}₃$ to search for the proposed topological Mott phase.