I used first principle calculations to study the thin film model. An obvious crossing was shown to appear at the gamma point when the edge state was calculated, which was originally predicted to be the evidence of quantum spin hall phases. The edge state occur at the Gamma point but it is not the location of of VBM. Therefore when I use the recursive green function method to calculate the edge state, the crossing appear inside the bulk band region. If we use the non-Abelian Berry connection method to calculate the $Z_2$, is it possible to get a $Z_2$ = 0 result in this situation?

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    $\begingroup$ +1. I made substantial attempts to improve the grammar, but still this sentence "But unfortunately where the gamma point is not the location of valence band maxima which another bulk band will be folded and cover the original pocket at the gamma point when the edge state was calculated" confuses me a bit. Perhaps you can try to re-word that sentence. $\endgroup$ Jun 22 '21 at 17:35
  • $\begingroup$ @NikeDattani Thanks for your reminder and help . I've already modified the place where you suggested in my post $\endgroup$
    – JensenPang
    Jun 23 '21 at 15:48
  • $\begingroup$ I am not sure what you mean by "thin film model". However, the presence of an edge state is no proof of topological order, you can have edge states in topologically trivial materials. The calculation of Z2 is a robust way of determining topological order. $\endgroup$
    – ProfM
    Jun 26 '21 at 8:00