## absorption onset of a small gap 2D system is missing!

Questions and doubts about the spin-dependent version of Yambo.

Moderators: Davide Sangalli, andrea marini, Conor Hogan, myrta gruning

### Re: absorption onset of a small gap 2D system is missing!

Dear Martin,
OK, the IP spectrum at least is meaningful.
The negative peak instead means that you have negative eigenvalues in the BSE as you pointed out in your first post.
This is not physical, but if I well understood you are doing BSE on top of KS electronic structure instead of GW, which is not consistent.
An opening of the gap, by using GW eigenvalues or some empirical shift should solve the problem. Now it looks that the binding energy is rather big in comparison of the small gap.
Next here in this case also the convergences parameters, even if they do will not solve the problem, I think they could play a role.

Best,
Daniele

PS: I will be not online in the next 3-4 days.
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

Daniele Varsano

Posts: 1948
Joined: Tue Mar 17, 2009 2:23 pm

### Re: absorption onset of a small gap 2D system is missing!

Dear Daniele,

I will perform BSE on top of GW and further converge the parameters.

Since in VASP I also did not converge the parameters and performed BSE on top of the KS structure, I was just a bit wondering about the inconsistencies.
In VASP I do not get such a negative peak. Any way my problem is to a large extent solved.

I thank you very much and take care.

Best wishes,
Martin
Martin Spenke, PhD Student
Theoretisch-Physikalisches Institut
Universität Hamburg, Germany
martinspenke

Posts: 149
Joined: Tue Apr 08, 2014 6:05 am

### Re: absorption onset of a small gap 2D system is missing!

Dear Martin,
your result is not so strange to me. You have a system with a small gap, in 2D, where the interaction is poorly screened. When you include the eh interaction in the BSE the binding energy is bigger than the gap.

I think it is an artefact of the missing QP corrections. Moreover you should cut the long range coulomb interaction in 2D.

I find instead strange the VASP result ...

D.
Davide Sangalli, PhD
CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit) and MaX Centre
http://www.ism.cnr.it/en/davide-sangalli-cv/
http://www.max-centre.eu/

Davide Sangalli

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### Re: absorption onset of a small gap 2D system is missing!

Dear Davide,

The problem was the following : when I changed the BSEmod from resonant to retarded with a very small broadening of 0.01 eV, I had in Yambo some negative energies, as shown in the plot in the previous post.
However, with BSEmod = resonant and a very small broadening of 0.01 eV, every thing was fine and I obtained no negative energies and had a nice absorption onset.

I was just puzzled by negative excitation energies for IP approximation at that time.

VASP has somehow no long range Coulomb interaction cutting procedure like in Yambo which is indeed quite strange, but for this 2-D system I never got any negative energies in VASP
when I performed the calculation on top of KS wave functions and energies.

Best wishes
Martin
Martin Spenke, PhD Student
Theoretisch-Physikalisches Institut
Universität Hamburg, Germany
martinspenke

Posts: 149
Joined: Tue Apr 08, 2014 6:05 am

### Re: absorption onset of a small gap 2D system is missing!

Dear Martin,
just a small remark, inspecting the plot you posted times ago, looking at the column showed in that plot, the red line (column 1:2) it is the BSE result and not the IP which
is given by the column (1:4) green line.

Happy new Year,

Daniele
Dr. Daniele Varsano
S3-CNR Institute of Nanoscience and MaX Center, Italy
MaX - Materials design at the Exascale
http://www.nano.cnr.it
http://www.max-centre.eu/

Daniele Varsano

Posts: 1948
Joined: Tue Mar 17, 2009 2:23 pm

### Re: absorption onset of a small gap 2D system is missing!

With the "resonant" approximation only the poles
Code: Select all
1/(w-E+i\eta)

are represented.
If you have a pole with negative energy you simply do not spot it unless
(i) you plot the absorption spectrum also in the negative side of the energy axis or
(ii) you have a broadening big enough, so that the tail of the negative energy peak enters the positive energy region

If instead you choose the "retarded" approximation the expression becomes (some minus maybe wrong, I'm writing by heart)
Code: Select all
1/(w-E+i\eta)+1/(w+E+i\eta)

i.e. you have both the resonant and the anti-resonant peaks.
Then a negative pole appears as a negative energy peak in the positive energy range of the spectrum, since it comes from the anti-resonant peak.

Best,
D.
Davide Sangalli, PhD
CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit) and MaX Centre
http://www.ism.cnr.it/en/davide-sangalli-cv/
http://www.max-centre.eu/

Davide Sangalli

Posts: 314
Joined: Tue May 29, 2012 4:49 pm
Location: Via Salaria Km 29.3, CP 10, 00016, Monterotondo Stazione, Italy

### Re: absorption onset of a small gap 2D system is missing!

Dear Daniele and Davide,

many thanks. Yes, you are right with the columns, since I check results with different codes, you sometimes forget which column was what.

Then a negative pole appears as a negative energy peak in the positive energy range of the spectrum, since it comes from the anti-resonant peak.

This is the point. In VASP when I activated anti-resonant contributions, I didn't have the negative energies in the positive range!!!
This was exactly puzzling me at that time.

For systems with a gap I think these anti-resonant contributions are not important for optical properties.

Happy new year
Martin
Martin Spenke, PhD Student
Theoretisch-Physikalisches Institut
Universität Hamburg, Germany
martinspenke

Posts: 149
Joined: Tue Apr 08, 2014 6:05 am

### Re: absorption onset of a small gap 2D system is missing!

What if you try to plot the negative energy range with both yambo and VASP ?

Best,
D.
Davide Sangalli, PhD
CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit) and MaX Centre
http://www.ism.cnr.it/en/davide-sangalli-cv/
http://www.max-centre.eu/

Davide Sangalli

Posts: 314
Joined: Tue May 29, 2012 4:49 pm
Location: Via Salaria Km 29.3, CP 10, 00016, Monterotondo Stazione, Italy

### Re: absorption onset of a small gap 2D system is missing!

I don't get the negative range in VASP or at least I don't know how to do it with VASP. What I get is the positive range, and there I had no negative excitation energies when including the anti-resonant contributions.

Then a negative pole appears as a negative energy peak in the positive energy range of the spectrum, since it comes from the anti-resonant peak.

This is however non-physical for the positive range, right?

Best,
Martin
Martin Spenke, PhD Student
Theoretisch-Physikalisches Institut
Universität Hamburg, Germany
martinspenke

Posts: 149
Joined: Tue Apr 08, 2014 6:05 am

### Re: absorption onset of a small gap 2D system is missing!

This is however non-physical for the positive range, right?

Yeah, this is my understanding.
If there exist a negative energy solution of the BSE (which, by the way, is usually a hint that you are starting from the wrong GS), then you should have a negative peak in the positive energy part of absorption if the anti-resonant contribution is included.

Notice that the peak is negative if the absorption is constructed from the "retarded" four point propagator.
If the T-ordered four points propagator were instead used, than the peak intensity would be positive.
However the physical quantity is the retarded function. The T-ordered is just a mathematical tool needed for deriving equations.

I would say that there is also a straightforward physical interpretation to this. If you have a negative energy solution, you can think that what you are considering as the GS is instead an excited state.
The system can emit light to reach the lower energy ground state. The dielectric function contains both absorption and stimulated emission (we usually call it "absorption" just because the emission channel is always zero from the ground state). Then, if light is emitted, the dielectric function must be negative at that energy.

Best,
D.
Davide Sangalli, PhD
CNR-ISM, Division of Ultrafast Processes in Materials (FLASHit) and MaX Centre
http://www.ism.cnr.it/en/davide-sangalli-cv/
http://www.max-centre.eu/

Davide Sangalli

Posts: 314
Joined: Tue May 29, 2012 4:49 pm
Location: Via Salaria Km 29.3, CP 10, 00016, Monterotondo Stazione, Italy

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