Can exciton wavefunction plotted via ypp be periodic?

[xueshanxihua]

Dear all:

I'm using "ypp -e w" to plot the exciton wavefunction with a finished G0W0-BSE result. The hole position has been fixed by considering the orbital component of VBM. However, when setting the supercell to be extremely large, I find that the exciton wavefunction comes out to be periodic in real space, i.e., locally the wavefunction is still an envelope with finite size, but these "localized" envelopes repeat periodically in a larger scale.

So can anyone tell me how this happens? Have I done something wrong?

Many thanks~!

[Daniele Varsano]

Dear Zeyu,
Nothing wrong, Yambo is a plane wave code.
if you look the expression of the excitonic wave function in real space as obtained by FFT, you realize that it is periodic after a distance given by 1/deltaK, where deltaK is the smaller K-K' available in your sampling. If you see that the exciton wave function touch the border of your build supercell given by Nk*Lside, it means that probably your calculation is not converged with respect your kpoint grid
and you need a larger k point grid.

Best,

Daniele

[Reza_Reza]

Dear Daniele,

I’m currently calculating the exciton wavefunction, but its behavior seems unusual — there is noticeable density at the edges of the cell.
Could this indicate that the k-point grid is not yet converged?
I attached it.

Best regards,
Reza

[Daniele Varsano]

Dear Reza,

exactly, you should note that the exciton wavefunction is periodic with a period given by 1/dq where dq is the spacing of your grid.
If you want to include more cells in the plot you need to enlarge your k point sampling.

Best,

Daniele

[Reza_Reza]

Dear Daniele,

Thank you for your response.

I have computed the optical absorption using k-points = 50 and 100. In both cases, the optical absorption shows exactly the same behavior. However, the excitonic wavefunction is completely different.

Attached is the excitonic wavefunction for the case with 100 k-points.

Best,
Reza

[Daniele Varsano]

Dear Reza,

1. please check the hole position in the two cases, not in the input file but in the report file, as the hole is placed in the position closest to the one indicated in the input allowed by the FFT grid.

2. Be sure you are using the same isosurface value.

3. Have a look at the excitonic wavefunction in the k space (e.g. exploring the weight file) for the two cases, larger the sampling you will have more transitions participating in the exciton.

4. Check if the exciton is degenerate or there are exciton levels nearby. By default, ypp groups degenerate excitons according to an energy threshold, which in some cases can be a bit large. You can tune it from input file setting the Degen_Step variable.

Best,

Daniele

[Reza_Reza]

Dear Daniele,

1. please check the hole position in the two cases, not in the input file but in the report file, as the hole is placed in the position closest to the one indicated in the input allowed by the FFT grid.

For k-points = 50, the hole position is: (168.33 23.93 0.00000)
For k-points = 100, the hole position is: (305.00 23.93 0.00000)
This shift seems reasonable due to the increased number of grid points in the larger k-point sampling.

2. Be sure you are using the same isosurface value.

Yes, I confirm that the isosurface value is the same in both cases.

3. Have a look at the excitonic wavefunction in the k space (e.g. exploring the weight file) for the two cases, larger the sampling you will have more transitions participating in the exciton.

I have attached the output file.

4. Check if the exciton is degenerate or there are exciton levels nearby. By default, ypp groups degenerate excitons according to an energy threshold, which in some cases can be a bit large. You can tune it from input file setting the Degen_Step variable.

Degen_Step = 0.001 for both

I have also attached the exciton report files for both cases for comparison.

Best,

Reza

[Daniele Varsano]

Dear Reza,

It seems that different transitions are participating in the excitations in the two cases.
I do not know if different excitons have been merged, I suggest you to set Degen_Step = 0.0 eV to be sure you are analyzing single excitons, even if it seems this is already the case as reported in the weight file: Degen_Step= 0.000000

States= "0 - 3"

Please note, states indexes starts from 1 and not from 0.

Be sure that you are placing the hole in a region of space where the valence wavefunction density is not too small, this will avoid noise.

In general, real space excitonic wavefunction depends on the hole positions, and provides you qualitative information on the localization, k space representation is in general more informative, e.g. projected on bands. Here you can find a tutorial using yambopy:

https://wiki.yambo-code.eu/wiki/index.p ... _databases

Best,

Daniele

[Reza_Reza]

Dear Daniele,

I have calculated the k-space representation using different numbers of k-points: 50, 100, and 150. The results appear to be converged at 100 k-points. However, the exciton wavefunction in real space is still somewhat questionable.

I’ve attached the results, including the k-space representation and the real-space exciton wavefunction, where I placed the hole in different positions.

Best regards,
Reza

[Daniele Varsano]

Dear Reza,

yes, the k space excwf is converged and meaningful. The real space wfs indeed is a two variable function, and it depends on the hole position. In your case, this is really evident, and I'm wondering if you are placing the hole in a nodal point of the valence wavefunction.

You can try to slightly displace a bit the hole from the plane of the polymer, i.e. no setting it in 0.00 but just a bit above/below.

Best,
Daniele