Realization of Kane-Mele Model in $X{\mathbf{N}}_4$-Embedded Graphene ($X$=Pt, Ir, Rh, Os)

Abstract

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

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