An anomalous band inversion protected by symmetry in a topological insulator of the Kane-Mele model

Depositing Au on a graphene derivate, which involves substituting four C atoms with three N atoms in a $3\times 3$ cell graphene, we realized a topological insulator of the Kane-Mele model with a gap of 50~meV surrounding the Dirac point of graphene. In this material, we observed an anomalous band inversion (BI) protected by the symmetry with character $e$ of group C$_{\rm 3V}$. The symmetry constrains two $e$ bands with mirror-symmetry combination (MSC) and mirror-antisymmetry combination (MAC) of Au and N orbitals degenerate at $\Gamma$, whereas the interaction of $\pi^*$ of graphene on the $e$-MAC band tends to lift this degenerate, resulting in that the $\pi^*$ and $e$-MAC band exchange their orbital components near $\Gamma$, causing thus a discontinued BI.