Topological edge states in single layers of honeycomb materials with strong spin-orbit coupling

We study possible edge states in single layers of honeycomb materials such as $\alpha$-RuCl$_3$ and A$_2$IrO$_3$ (A=Li, Na) with strong spin-orbit coupling (SOC). These two dimensional systems exhibit linearly dispersing one-dimensional (1D) edge states when their 1D boundary forms a zig-zag shape. Using an effective tight-binding model based on first principles band structure calculations including Hubbard U and SOC, we find degenerate edge states at the zone center and zone boundary. The roles of chiral symmetry and time-reversal symmetry are presented. The implications to experimental signatures and the effects of disorder are also discussed.