Yambo Community Forum

Dear friends:
I am a novice who use yambo to calculate the character of exciton,recently ,i have a question about calculating the lifetime of exciton.
The formulate calculate the lifetime in an article:Ab initio calculations of exciton radiative lifetimes in bulk crystals, nanostructures, and molecules.
In that article,i know that Rs2D(0) as the recombination rate for Q=0,Rs2D(0)=((e^2)*(Ps^2))/[(8.854187817 × 10-12)*(m^2)*c*A*Es(0)].
the m is the quality of electron,the permittivity of vacuum is t0=8.854187817 × 10-12,c is the spead of light，A is the area of the system in the xy plane,e is the electron charge,Es(0) is the exciton energy,Ps is the exciton transition dipole. So I want to know how to calculate the Ps by using yambo.
In addition,i have read another article:Exciton Radiative Lifetimes in Two-Dimensional Transition Metal Dichalcogenides.the recombination rate for Q =0,could be expressed as :(8*Π*(e^2)*Es(0)*Us^2)/((h/2Π）*c*A),Us^2 is the square modulus of the BSE exciton transition dipole divided by the number of unit cells in 2D in the system.(i.e., the number of 2D k-points employed in the calculation),so how to calculate the Us^2?

what is the relation between exciton transition dipole and the strenth in the document which called ~.exc_E_sorted？
Thanks for your read，please help me to understand that.
I hope you are well and in good health!
Best wishes!
Quxiao

Dear Qxiao

the two formulas are the same beyond a factor 2 due to a wrong normalization to sqrt(2) instead of 1 in the first derivation.
see the discussion at pag 3842 before eq. 11 of this paper H.Chen et al Nano Letters https://doi.org/10.1021/acs.nanolett.8b01114
In the first paper we used CGS in the second and in Phys. Rev. B 100, 075135 we used MKS
The factor A is the area of the unit cell multiplied by the number of k-points used in the BSE simulation.
Yes in principle you can use the o*sorted file but pay attention because in that file the oscillator strength (= the modulus square of the excitonic dipole)
is normalized to the maximum value but you can find this maximum value at the beginning of the file.

Best
Maurizia

Dear Palummo Maurizia:
Thank you so much for your reply!
However,I still have some questions。
Fistly，I want to ensure that if the Us^2 of the formular is the oscillator strength？My understanding about your reply is that the Us^2 is equal to the oscillator,right？

Secondly,I read your reply :"the oscillator strength is normalized to the maximum value",so I use the maximum value multiply the strength.

Then, as you said, "in principle you can use the o*sorted file",so you don not use that method,maybe you have another file to get that Us^2?or I understand that mistakely?

The last question:I make calculation of the MoS2,the oder of magnitude is not correct,so I suppose that if the unit of the strength were not the MSK?maybe that need some transition about the unit?

Sincere thanks for your help and guidance!
Best wishes!
Qu Xiao
BIT

Dear Qxiao

we implemented a routine in ypp in one old version of yambo that is not available anymore.
yes you can use the o*sorted* file and yes , mu_s^2. (that I imagine is your Us^2 right?) is what is written inside o*exc* file beyond the normalization.
so yes you can take those numbers and multiply them with the maximum.
The order of magnitude should be similar, so yes I suspect a problem of units.

Best
Maurizia

Dear Qxiao,
the dipole units in yambo are in bohr!

Best,
Daniele

Dear Palummo Maurizia:
I am so exciting to get your reply,it is so useful that solve my puzzle！
Thank you for all your assistance！
Best wishes！
Quxiao

Dear Daniele Varsano:
Firstly,thanks for your help!I learn that "the dipole units in yambo are in bohr!'from your reply,it is important for me to ensure that ,the units of the oscillator strength is the squre of bohr(bohr^2),is it?
Finally，thanks for your help again！And thanks for the guidance from Prof.Palummo Maurizia ！
Best wishes
Quxiao

Dear Quxiao,
the strengths reported in the o*sorted file should have the unit of energy. And if I'm not wrong is already in eV.
You can have a look to this thread.

Best,
Daniele

Dear Daniele Varsano:
I understand that units after reading the link you shared
Thanks for your patient!
Best Wishes!
Quxiao
BIT

Palummo Maurizia wrote: ↑Sun Mar 28, 2021 5:53 pm Dear Qxiao

the two formulas are the same beyond a factor 2 due to a wrong normalization to sqrt(2) instead of 1 in the first derivation.
see the discussion at pag 3842 before eq. 11 of this paper H.Chen et al Nano Letters https://doi.org/10.1021/acs.nanolett.8b01114
In the first paper we used CGS in the second and in Phys. Rev. B 100, 075135 we used MKS
The factor A is the area of the unit cell multiplied by the number of k-points used in the BSE simulation.
Yes in principle you can use the o*sorted file but pay attention because in that file the oscillator strength (= the modulus square of the excitonic dipole)
is normalized to the maximum value but you can find this maximum value at the beginning of the file.

Best
Maurizia

Dear  Palummo Maurizia
I also want to ensure that，when I solve the BSE，the number of k-points what I used would reduced due to the symmetry,so which the number I choose to multiplied? The number of k-points in the whole brillouin zone，or in the irreducible?" The factor A is the area of the unit cell multiplied by the number of k-points used in the BSE simulation."
Thanks so much for your help
Best wishes!
BIT Quxiao