## Optical matrix elements

Run-time issues concerning Yambo that are not covered in the above forums.

Moderators: myrta gruning, andrea marini, Daniele Varsano, Conor Hogan

Guo_BIT
Posts: 28
Joined: Tue Jun 06, 2023 2:55 am

### Re: Optical matrix elements

Dear Daniele:
First of all, thank you for your help in the previous topic
Actually, we are very interested in the formulas I mentioned in these two topic, and I am trying to understand the the physics behind these parameters. This is also the reason why I am asking these questions.

Allow me to share my understanding, if you don’t mind.
(1) with

Code: Select all

``ypp -e a -b 1 -F ypp_nodipoles.in``
we can get the |Aeh|^2 in this equation

It represents the weights (contributions) at each K-points for a specified excitonic state.
(2) with

Code: Select all

``ypp -e a -b 1 -d exc -F ypp_withdipoles.in``
we get |Aeh*<e|D|h>|^2 in

In which <e|D|h> is optical matrix elements (‘dipoles’), and the value of dipoles determines whether excitons are bright or dark.
(3) Considering this equation, I speculate that Aeh should have a similar form to dipole (but as you mentioned, it should be a scalar). We are curious if it’s possible to use Yambopy to read Aeh over the entire Brillouin zone.
Or, Aeh is a real number, and I only need to take the square root of the amplitude in the o-amplitude?

Jingda Guo
Beijing Institute of Technology

palful
Posts: 62
Joined: Tue Jan 26, 2016 11:23 am
Location: Modena and Milan

### Re: Optical matrix elements

Dear Jingda,

Yes, you can read the excitonic weights / coefficients A_l^{vck} using yambopy. In particular, if you check this tutorial, you can inspect the sample user script called exc_read.py.

You will see that when the exciton data are loaded with YamboExcitonDB, you then have access to the attribute YamboExcitonDB.eigenvectors. This is a complex-valued numpy array with shapes [N_excitons, N_transitions] and contains all the A-coefficients. Thus, eigenvectors[l,t] means the A-value for exciton l at transition t="vck". The "vck" index is an aggregate transition index: you can see how to extract the individual k, v and c indices from t from the same exc_read.py script.

Have a look also at this post, where some things about the relationship between dipoles, excitonic weights and "residuals" (better called excitonic dipoles) in Yambo is clarified.

Cheers,
Fulvio
Dr. Fulvio Paleari
S3-CNR Institute of Nanoscience and MaX Center
Modena, Italy

Guo_BIT
Posts: 28
Joined: Tue Jun 06, 2023 2:55 am

### Re: Optical matrix elements

Dear Fulvio:
Thank you very much for your reply! This is exactly what I wanted, and I will try it right away.
Furthermore, is my understanding accurate, please?
with ypp -e a -b 1 -F ypp_nodipoles.in
we get |Aeh*<e|D|h>|^2 in

In which <e|D|h> is optical matrix elements (‘dipoles’), and the value of dipoles determines whether excitons are bright or dark.
Update: I found that the dipole file was calculated in step GW, so it should not be related to BSE.
Can I obtain this<e|D|h> by Yambopy?
Jingda Guo
Beijing Institute of Technology

Daniele Varsano
Posts: 3926
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Optical matrix elements

Dear Jingda,

yes you can read the dipoles and this is explained in the same tutorial indicated by Fulvio:
https://www.yambo-code.eu/wiki/index.ph ... absorption
see YamboDipolesDB

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/

Guo_BIT
Posts: 28
Joined: Tue Jun 06, 2023 2:55 am

### Re: Optical matrix elements

Dear Daniele:
You may have misunderstood my question. I have already successfully read the dipole data by dipoles_plot.py.
(1) Please forgive my foolishness, but I still want to know if the dipole of excitons is <e | D | h> in

(2) We attempted to use this dipole data, combined with Aeh obtained from YamboExcitonDB, to reproduce the oscillator strength. However, our calculated results clearly did not match the oscillator strength provided by o * exc_qpt_1. We believe this discrepancy arises because the dipole we obtained is the dipole in a single-particle picture (from hole to electron, not exciton). Therefore, can we obtain the dipole of excitons using yambopy?
Jingda Guo
Beijing Institute of Technology

Daniele Varsano
Posts: 3926
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Optical matrix elements

Dear Jingda,

the exciton dipole is obtained as a linear combination of the singl-particle ones.
1) The oscillator strength in o.exc* is normalized to its maximum, normalization factor is reported.
2) The strenght is defined as:
Residuals(:)*real(spin_occ,SP)/(2._SP*pi)**3*d3k_factor*4._SP*pi/q_norm*HA2EV

where:
Residual=\Sum_cv |Acv<c|d|v>|^2
d3k_factor=Vol_bz/Nk
q_norm=q^2, for q=0 is the q0 limit and q0=1e-5
HA2EV=27.2113834_SP

Essentially is the numerator (for a given lambda) of slide 11a in the Yambo cheatsheet:
https://www.yambo-code.eu/wiki/images/c ... et-5.0.pdf

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/

Guo_BIT
Posts: 28
Joined: Tue Jun 06, 2023 2:55 am

### Re: Optical matrix elements

Dear Daniele:
Please let me give an example.
If my ground state exciton is basically formed by one single transition (k,c,v = Γ,11,10), the exciton dipole of this exciton is solely determined by the single-particle(hole and electron) dipole of this transition. This single-particle dipole can be obtained from ydip.dipoles [0, *,10.9]. If the value of the dipoles is very small, the exciton would be dark.
If an exciton formed by two transition, the exciton dipole is the weighted sum of single-particle dipoles of these two transition.
Right?
Jingda Guo
Beijing Institute of Technology

Daniele Varsano
Posts: 3926
Joined: Tue Mar 17, 2009 2:23 pm
Contact:

### Re: Optical matrix elements

Dear Jingda,
yes that's correct.

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/

Guo_BIT
Posts: 28
Joined: Tue Jun 06, 2023 2:55 am

### Re: Optical matrix elements

Dear Daniele:
Thank you very much for your patience and explanation！
I have benefited a lot from it
Jingda Guo
Beijing Institute of Technology