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 ?
Wannier90 might not be good at preserving the symmetry. But they probably include a few new methods to enforce symmetry in Wannier90.v.3.1.0. Maybe you can check this. http://www.wannier.org/features/
Also, WannierTools can symmetrize the hr.dat, but from my personal experience it sometimes gives you worse results than the original hr.dat. http://www.wanniertools.com/symmetrization.html