A phase diagram for band inversion of topological materials as a function of interactions between two involved bands

Based on first principles calculations, we predicate that Bi on a graphene derivate, $g$-C$_{14}$N$_3$, which involves a $3\times 3$ unit cell of graphene with four C atoms substituted by three N atoms, is a topological insulator with a gap of 50~meV. With the help of maximally localized Wannier functions, we find that the band inversion gap can be determined by examining a pair of interaction parameters between the two involved bands. Accordingly, a phase diagram for band inversion of topological materials as a function of the interactions is obtained. The conclusion also holds for Sb, Ir and Rh on $g$-C$_{14}$N$_3$. These materials are topological nontrivial either insulator or semimetal, indicating that $g$-C$_{14}$N$_3$ is a good platform for conceiving topological materials.