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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: enter image description here

The surface state was shown in below: enter image description here 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.

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    $\begingroup$ +1 perhaps you could share a plot to show what you are seeing, which may help identify the problem? $\endgroup$ Commented Feb 19, 2021 at 6:13
  • $\begingroup$ @ProfM I have already uploaded a plot for a 5atomic layers system. For other atomics layers system, the surface state are still very messy which provided no information for the material. This material was provide to have a non-trivial edge state in bulk. I have already verify the result. But I found that the result of the edge state depends on the fitting of the wannier function. For my wannier function even though the spread is a bit large, as you can see the fitted result is still very good. But it give a non-sense surface state result. $\endgroup$ Commented Feb 19, 2021 at 9:02

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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

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  • $\begingroup$ Thank you for your answer. May I ask a few more follow up question. Like you said, the wannier90 may not good at preserving the symmetry. But from the result I got, did I do anything wrong which may cause this mistake? Because by the direct inspection, the fitting is very good, even though each Wannier function is a bit larger than the Lattice constant. Is this an acceptable result ? $\endgroup$ Commented Feb 20, 2021 at 0:29
  • $\begingroup$ fitting is definitely NOT good to check symmetry... Maybe spin texture is better $\endgroup$ Commented Feb 20, 2021 at 2:58

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