Spin-forbidden and momentum-forbidden dark excitons

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Sumit
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Joined: Wed Jun 09, 2021 12:10 pm

Spin-forbidden and momentum-forbidden dark excitons

Post by Sumit » Sat May 07, 2022 3:37 am

Dear developers,

As the dark excitons can be either by spin-forbidden direct transitions or momentum-forbidden indirect transitions. So, Is this Yambo code giving us both types of dark exciton information. If yes so, how can we distinguish between these using the code?
Additionally, even without spin-orbit calculation, we are getting dark exciton information as in the given example hBN. So are these dark excitons only momentum-forbidden or something I am not getting?
One more thing, as in the Yambo wiki it is written q-index = 1 (optical limit q=0). So here, Is q-index = 1 means finite momentum excitons, so then how the spin-forbidden excitons are included ….?
Kindly guide me to make a fundamental understanding of these confusions about the code.

Thank You !

Regards
Sumit Kukreti
PhD Physics
Indian Institute of Technology Jodhpur INDIA

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Daniele Varsano
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Re: Spin-forbidden and momentum-forbidden dark excitons

Post by Daniele Varsano » Sun May 08, 2022 11:05 am

Dear Sumit,
qindex=1 is the optical limit so zero momentum.
In the optical limit, you can have dark exciton because they are dipole forbidden.

When calculating exciton with finite momentum iq > 1, they are all optically dark. Nevertheless, yambo reports strengths given by generalized dipoles:
see eq.8 of Phys. Rev. Materials 6, 034009 (2022) available here: https://arxiv.org/abs/2204.11105
as they give you the strengths in EELS or IXS spectra.

About spin forbidden excitons, in spin-polarized case (collinear) spin-flip transitions are not included (unless you calculate magnons, but here I'm not an expert and I could be wrong). You can nevertheless calculate triplet excitons (which are dark). In non-collinear cases, all transitions are included.

Best,
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/

Sumit
Posts: 20
Joined: Wed Jun 09, 2021 12:10 pm

Re: Spin-forbidden and momentum-forbidden dark excitons

Post by Sumit » Mon May 09, 2022 8:57 am

Dear Daniele sir,

Really the suggested PRM paper is very informative for me.

But I have few different doubts which i am raising humbly:

1. As you suggest in optical limit dark exciton are dipole forbidden so means direct transition between same parity orbitals? Can you illustrate me little bit?
How can we calculate triplet exciton using the code?

2. I have another doubt related 3D hBN example withing "How to analyses exciton - ICTP 2022 school" section in WIKI where two peaks of bright exciton are shown at around 4.3 eV and 4.8 eV but those bright excitons lies around energy in 5.02 eV in o-3D_BSE.exc_qpt1_E_sorted file. So what these numbers (4.3eV and 4.8eV) represents?

3. In the suggested PRM paper sigma and pi character are shown how you determine these computing charge density or something else.

4.How you determine this momentum resolved momentum band structure as shown in paper fig 7. using the yambo output.


Thank You!

Regards
sumit Kukreti
PhD scholar Physics
Indian Institute of Technology Jodhpur
INDIA

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Daniele Varsano
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Re: Spin-forbidden and momentum-forbidden dark excitons

Post by Daniele Varsano » Mon May 09, 2022 1:09 pm

Dear Sumit,

1) as illustrated in the paper I suggested to you, dark excitons are formed by transition with zero dipole (ie zero oscillator strength): \Sum_cvk A_vck <vk|r|ck>=0

Triplet excitons are calculated by setting to zero the exchange term (see PRB 62, 4297 (2000) Eq.25 and text below).

2) The peaks 4.3 and 4.8 are not the absorption peak but the amplitude of the degenerate exciton with indexes 3 and 4 (excitation energy 5.02). The peaks correspond to the KS energies of the transition forming the exciton.

3) By inspecting the electronic wavefunctions (charge density)

4) By calculating the excitons having momentum Q along the path. ( BSEQptR variable in input). Then you inspect the eigenvalues.

Best,
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/

Sumit
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Joined: Wed Jun 09, 2021 12:10 pm

Re: Spin-forbidden and momentum-forbidden dark excitons

Post by Sumit » Thu May 19, 2022 10:05 am

Dear Daniele sir,

As you said that q>1 considers finite momentum excitons. Is this information given by the QpntsRXd tag? And what number we should pick for this tag.
In your suggest recent PRM paper on graphene like C3N ( in Fig6 ), you have shown the Loss function for different values of the transferred momentum along the gamma-M direction. Is this path is along the valence band mean I am unable to get what this transferred momenta means?
"We observe that the low-energy peak goes down in energy for q moving away from gamma, as expected for an indirect gap system. This indicates the presence of a dispersive excitonic band reaching a minimum of ∼0.8 eV at q = M in correspondence of the indirect gap." Can you please explain this?
I would also like to explore these finite momentum excitons using Yambo that's why I would like to know how to analyze this using Yambo?

Thank You

Regards
Sumit Kukreti
Ph.D. scholar
IIT Jodhpur INDIA

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Daniele Varsano
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Re: Spin-forbidden and momentum-forbidden dark excitons

Post by Daniele Varsano » Thu May 19, 2022 11:41 am

Dear Sumit,

The variable to set for finite-Q BSE is BSEQptR. You provide the index corresponding to the Q point indicated in the report file.
The finite Q exciton is formed by transitions having hole and electrons in different points of the BZ, k and k+Q respectively.
"We observe that the low-energy peak goes down in energy for q moving away from gamma, as expected for an indirect gap system. This indicates the presence of a dispersive excitonic band reaching a minimum of ∼0.8 eV at q = M in correspondence of the indirect gap."
From the explanation above this should be clear, as the minimum transition energies are found in the correspondence of the indirect gap, where you have a hole at M and an electron at Gamma, resulting in an exciton with momentum Q=M.

Best,
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/

Sumit
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Joined: Wed Jun 09, 2021 12:10 pm

Re: Spin-forbidden and momentum-forbidden dark excitons

Post by Sumit » Mon May 23, 2022 11:27 am

Dear Daniele sir,

As suggested, I did two calculations with finite-Q BSE by giving BSEQptR tag
One calculation with
% BSEQptr
1| 27| ( considering all irreducible Brillouin zone points)
Then I ran the command for exciton analysis (expecting that it will list all direct and indirect excitons with strength);
ypp -J 2D -e s 1
The output is attached herewith
sent.tar.gz
.

This output is the same as for the other calculation with

Another calculation
% BSEQptr
1 | 1
and then running
ypp -J 2D -e s 1

1. Can you please tell me if the output is fine (as seen in several negative formation energy excitons and a bright exciton also) Should I change some parameters?
2. By doing exciton analysis why the output is same in both cases? Is it because I considered index 1 in ypp command? if yes so how do we consider all the index for a single output file?
3. Can a bright exciton can have negative formation energy?

I have attached my BSE input file and output file of the exciton analysis. Kindly suggest to me what wrong I am doing.

Thank You

Regards
Sumit Kukreti
PhD Scholar
IIT Jodhpur INDIA
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Daniele Varsano
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Re: Spin-forbidden and momentum-forbidden dark excitons

Post by Daniele Varsano » Mon May 23, 2022 4:28 pm

Dear Sumit,

the correct syntax for analyzing exciton is:

Code: Select all

ypp -e s -b #iq
where #iq you assign the q index of the momentum you want to analyze. You need then analyze one by one (or build a simple script to run over the #iq index).

1) You should not have negative energy, check if the scissor you considered is correct, your system has a so small GW correction < 100meV ?

Best,
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/

Sumit
Posts: 20
Joined: Wed Jun 09, 2021 12:10 pm

Re: Spin-forbidden and momentum-forbidden dark excitons

Post by Sumit » Tue May 24, 2022 3:33 am

Dear Daniele sir,

Yes, my strained-2D system has low scissor correction around ~100 meV (difference between GW0 - PBE bandgap). I am looking for an excitonic insulator. According to you, this peak can't reside below 0 eV. Kindly suggest to me what appropriate can be done to compute proper BSE spectra.

However, I found an article predicting bright exciton-based excitonic insulators with electric field modulated structures. I attached the reference
DOI: 10.1103/PhysRevB.104.085150 They predicted an increase in oscillator strength in the EI phase. Can you comment on it?

Additionally, I set BSE spectra to range from -1 to 4 eV. Is it fine or I should select only 0 to 4 eV or above.
% BEnRange
-1.00000 | 4.00000 |

Thank You

Regards
Sumit Kukreti
PhD Scholar
IIT Jodhpur INDIA

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Daniele Varsano
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Re: Spin-forbidden and momentum-forbidden dark excitons

Post by Daniele Varsano » Tue May 24, 2022 8:31 am

Dear Sumit,
what the authors claim is that the exciton forming the exc-ins is bright. You can explore this by looking at the optical properties before the phase transition.
Next, the authors also look at the oscillator strength after the transition, in my opinion, this is problematic. Once the transition has occurred, you have a many-body gap. The ground state is qualitatively different from the one used to calculate the excitation and its oscillator strength. You would need a response theory on the new ground state. Note this is my vision, the authors (and referees) clearly have different thoughts: for this reason, better to address in the forum questions related to the code theory and usage.

Best,
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/

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