Nodes calculation of semimetals with supercell

[Md Islam]

Hi,

I am interested to calculate nodes of Na3Bi Dirac semimetals. It produces expected result, two Dirac nodes and zero chirality, when I use conventional unit cell.  But I am trying to calculate what happens to the nodes when I add impurity. So I created a 1 × 1 × 2 supercell and added an impurity. Strangely, it gives hundreds of nodes with non-zero chirality for N+1 and also for N-1 occupied Wannier functions. Just to check, I repeated calculation for the same supercell but with no impurity i.e. a pure 1 × 1 × 2 supercell.  It should have produced the same result as the conventional unit cell but unfortunately, it is also showing very large number nodes, which doesn’t make sense. The DFT and the Wannier90 bands are in good match, so I am wondering if there is any special requirement for supercell calculation with WannierTools. Or do I need to provide any additional information in the wt.in file for Nodes calculation.

 

Regards,

Fhokrul

 

[Brook]

Hi Fhokrul,

I think the problem is about the band folding. When you use the supercell to perform the calculation.  the energy band will fold which leading to a nodal line. You can plot the nodes together.  If you introduce the impurity, then the impurity could induce a gap to the nodal line which caused by the band folding.

You could plot the energy bands in a k plane to check how the bands touch together close to the Fermi level by setting BulkBand_plane_calc=T and setting KPLANE_BULK.

for example

KPLANE_BULK

0 0 0

1 0 0

0 1 0

 

Then WannierTools will get a 2D energy bands in a k plane centered at (0, 0, 0).

 

QuanSheng

[Md Islam]

Hi QuanSheng,

Thank you for your quick reply. I also thought about band folding but I don’t know if I can separate their contribution. I also have done another calculation with the same supercell but added 2 impurity atoms such that inversion symmetry is preserved (so it is still a Dirac semimetal). In this case, however, it produces the expected result and I don’t see any additional node for N+1 WFs. That’s why I am confused why a pure supercell, which presumable has inversion symmetry didn’t reproduce the same result. But I will follow your suggestion and calculate bands on a plane. Hopefully, I will get some better insight.

 

Regards,

Fhokrul

 

[Brook]

Could you compare the band structure from Wannier TB and DFT close to the nodes that you found? Maybe you need to increase the kmesh when constructing the WFs.

[Md Islam]

Most of the nodes are above the Fermi level (0.2 eV or more) and at general k-points, not close to any high symmetry axes. So it is not easy to see from the bandstructure. We are checking the ones that are close to the Fermi level, which are probably more relevant for the physics. For me the most confusing issue is that almost all those nodes are showing non-zero chirality, which is quite odd.

 

Fhokrul

 

 

 

[Brook]

If the gap at the isolated node is exactly zero, then usually, the chirality should not be zero. In the inversion symmetric system, there should not be Weyl points. The only possibility is that your Wannier tight binding model is not symmetric so that the inversion symmetry is broken. You can symmetrize it with a tool in the WannierTools package. See the documentation about the symmetrization of the TB model.

 

[Md Islam]

Yes, there is no Weyl node for inversion symmetric system. In fact, when I add impurities in a supercell by preserving inversion symmetry, I get the expected result. But you might be right that symmetry is broken in the Wannier TB model. I will check if it solves the problem. Thanks for the suggestion.

 

Fhokrul

 

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