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

TL;DR

This paper demonstrates that embedding transition metal nitrides in graphene creates stable 2D topological insulators with Kane-Mele type properties, confirmed through first-principles and tight-binding models.

Contribution

It introduces a new class of 2D topological insulators based on $X$N$_4$-embedded graphene and provides a detailed theoretical analysis of their electronic and topological properties.

Findings

Embedded $X$N$_4$ in graphene opens topologically nontrivial band gaps.

The low-energy bands are accurately described by a modified Kane-Mele model.

The work presents realistic 2D materials hosting $ ext{Z}_2$ topological insulators.

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.