Currently I met a problem when I calculate the surface state of a topologically non-trivial thin film system. I did a DFT calculation and fit the result with wannier function. The fitting looks pretty good around the band gap region. Then I use tight binding to calculate the surface state. I found that the band structure along -X -> G -> X didn't preserve the time reversal symmetry (E(k) is not equal to E(-k) and it become a trivial edge state. For a system without magnetisation and external B-field, the time reversal symmetry can be preserved. So the relation of E(k) = E(-k) should be always true? I can't find any reason for my result. Is there any people who did similar things before and have some suggestion ?
For the band gap region:
The surface state was shown in below:
For the notation of R in the surface state plot, it is -X. So it is the plot from -X -> G -> X. and it didn't contain the time reversal symmetry.