[Wannier] [SUSPECT ATTACHMENT REMOVED] PW vs Wannier interpolated bandstructure of Silicon

[Marc Höppner]

Hi Samuel,

the issue is not the wannierization, but the disentanglement of the band 
structure with respect to your chosen local basis set. Wannier90 uses 
two steps in order to obtain the Wannier Hamiltonian / Wannier Functions:

1) Disentanglement.
2) Wannierization / Optimization of the local basis set to obtain 
maximally localized functions.

The first step is choosing the number of "effective" bands you are 
interested in. In case that your bands are not entangled, i.e. the 
number of local basis orbitals equals the number of bands, you skip this 
step. In case of entanglement, it is always an approximation to the band 
structure. Wannier90 tries to obtain an "effective" band structure based 
on the weights of each Kohn-Sham eigenvalue for your given initial local 
projections (a simple example: if the expansion of the Kohn-Sham 
eigenfunction in your local basis is complete, the eigenvalue is taken 
as it is; however, if some weight is missing other Kohn-Sham eigenvalues 
have a partial contribution as well and the weighted average of all the 
eigenvalues with partial weights is taken). You can always circumvent 
disentanglement by enlarging your basis, i.e. choosing the number of 
basis orbitals such that they equal the number of bands.

The second step is merely a unitary basis transformation, i.e. does not 
change the band structure at all. However, since the transformations are 
not limited to on-site basis orbitals only, but are inherently 
multi-site transformations, you will loose all exact symmetries 
(especially in conjunction with disentanglement; I once patched w90 v1.2 
to on-site transformations only).

So, how to proceed in your case? The wannierization is not the problem, 
but the disentanglement.

a) make "clever initial projections" and choose the fixed window wisely 
in case you want to use disentanglement.

b) As Jesse already pointed out, the disentanglement itself has a tricky 
dependency on k-points. However, more is not necessarily better.

-- 
Kind regards,
Marc Höppner

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On 11.12.2016 21:39, Samuel Ponce wrote:
> Dear Wannier team,
>
> I have a small question about Wannier90.
>
> Somehow I find it very difficult to get very good Wannierization of
> Silicon. I'm interested in the top of the VB and the bottom of the CB
> (between G-X).
>
> I can get okish one but when I try to improve them, I do not manage.
>
> Attach to this email is a comparison between the L-G-X path of Silicon
> with PW/bands.x (in green) VS Wannier90 in red.
>
> As you can see, the Wannier code fail to reproduce the second branch of
> the CBM (on the right), which is problematic. The wannier seems to have
> some unphysical oscillation in the CB.
>
> Attach to this email are all the file needed to obtain both plots and
> even the line needed to do the gnuplot (you have to scale them). In each
> of them I've place a README file with all the steps for convenience.
> I've also placed the psp.
> The calculations are very fast.
>
> Maybe its something very stupid.
>
> So far, I've try:
> - increasing the nscf grid (you can see a comparison between 8x8x8 and
> 10x10x10 grid. The latest 10x10x10 gives dramatic oscillations)
> - changing the number of bands
> - playing with the frozen windows
> - increasing the number of Wannier iteration
>
> Nothing made it better than that.
>
> Would you have any suggestions?
>
> PS: The lattice parameter is slightly lower (10.17 Bohr) than the DFT
> one (10.208 Bohr) on purpose but is the same in both case. In the case
> of the DFT lattice 10.208 similar issues exists but its slightly better.
>
> PPS: I also noticed that the Wannierzation was breaking the symmetries.
> For example doubly degenerate bands along G-X were slightly lifted. As a
> results, effective masses are quite bad. Is there a way to impose
> crystal symmetries?
>
> Thank you,
>
> Samuel
>
>
>
>
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