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 $3times 3$ 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.