Optical matrix elements

[Daniele Varsano]

Dear Shudong,
it is not clear to me what do you mean by "transition dipoles including e-h pairs?
What are you interested in exactly?

Daniele

[sdwang]

Dear Daneile,
I want to know the BSE exciton transition dipole of the system.

Thanks!

SD

[Daniele Varsano]

Dear Shudong,
sorry, but I don't get it. Transition dipoles are calculated on the basis of KS wave function.
What you want are the dipole moments for a given excitation weighted by the BSE eigenstate?
i.e.
for a given excitation lambda:
|\sum_cv Acv_lambda*<c|r|v>|^2

Daniele

[sdwang]

Dear Daniele,
I think you are right. Waht I need is the the dipole moments for a given excitation. For example, I want to know the dipole of the first exction in the BSE absorption. Where I can get it?

Thanks!

SD

[Daniele Varsano]

Dear Shudong,

ok, correct if I've not well understood, you want to look at the intensity (oscillator strength of the excitation), so the expression I reported above, which is built as a linear combination of dipole moments weighted by the BSE eigenvector right?

This is calculated by ypp when sorting excitation and reported as intensity (o.exc_I_sorted).
In the output file, the values are normalized to the max value of the intensity, in the recent versions of yambo the max value is reported in the output as:

Code: Select all

 Maximum Residual Value=

Best,
Daniele

[sdwang]

*Short explanation:
Read the dipole variable i<v|r|c> and <v|P|c>.
The dipole variable has 4 indexes that are:
1: Valence index from 1 to Nv (python index start from 0)
2: Conduction index from 0 to Nc (0 is the first conduction band up to the last calculated)
3: Direction 0,1,2 --> x,y,z
4. 0/1. real and imaginary part

Dear Daniele,
Just a question for sure. In the script you mentiond, 1 means the VBM, and 2 is VBM-1, 3 is CBM and 4 is CBM+1? Right?

Thanks!

Best
Shudong

[Daniele Varsano]

Dear Shudong,
actually I do not know of what script you are talking about, anyway if the script it is meant to read dipoles databases,
is sound strange to me that it could be:

1 means the VBM, and 2 is VBM-1

as valence bands are ordered from the first band computed to the VBM, while for conduction the index runs from CBM to the last band computed.
Best,
Daniele

[sdwang]

Dear Daniele,
Thank you for the quick reply. Yes I mean the read dipole script.
I extend the script to include more valence and conduction bands (in current scriot is 2v+2c).
My sytem has 16 valence bands, so if I want to konw the dipole between VBM and CBM, I shoud giveit as:
print ("<16|p|17>=",DIP_P[15,0,0],DIP_P[15,0,1],DIP_P[15,0,2],sqrt(abs(DIP_P[15,0,0])**2+abs(DIP_P[15,0,1])**2+abs(DIP_P[15,0,2])**2))

Am I right?

Thanks!

Shudong

[Daniele Varsano]

Dear Shudong,
yes, it seems correct.

Daniele

[sdwang]

Dear Daniele,
I got the dipole moments of 2 layer MoS2 and it is as:
Dipole P
('<52|p|53>=', (4.8576367e-05+0.00028422844j), (-0.00020457263+3.4868885e-05j), (-8.9401248e-05+1.5234437e-05j), 0.0003666550846841008)
In which the modules is 0.0003666550846841008. And I used it to compare with the μS^2(I used as 0.0003666550846841008X27.2114^2 eV to transfer it into the unit of eV,right?), which is the square modulus of the BSE exciton transition
dipole using Yambo in paper "Exciton Radiative Lifetimes in Two-Dimensional Transition Metal Dichalcogenides, Nano Lett. 2015, 15, 2794−2800". and it seems
my results here is several orders of magnitude less than the published paper. But my absoption and quasiparticle quantites are almost the same as that in the paper.
What's the problem?

Thanks!

Best wishes,

Shudong