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Monolayer graphene embedded with transition metal nitride (i.e., $X$N$_4$)has been experimentally synthesized recently, where a transition metal atomtogether with four nitrogen atoms as a unit are embedded in graphene to form astable planar single-atom-thick structure. We provide a systematic study on thestructural, electronic and topological properties of these $X$N$_4$-embeddedgraphene by utilizing both first-principles calculations and tight-bindingmodel. We find that $X$N$_4$-embedded graphene ($X$=Pt, Ir, Rh, Os) can opentopologically nontrivial band gaps that host \emph{two-dimensional}$\mathbb{Z}_2$ topological insulators. We further show that the low-energybands near the band gaps can be perfectly captured by a modified Kane-Melemodel Hamiltonian. Our work not only provides concrete two-dimensionalmaterials that are very rare to realize \emph{two-dimensional} $\mathbb{Z}_2$topological insulators, but also makes the graphene system to be realistic inhosting Kane-Mele type $\mathbb{Z}_2$ topological insulators.

Realization of Kane-Mele Model in $\pmb X\bf{N_4}$-Embedded Graphene ($\pmb X$=Pt, Ir, Rh, Os)