yambo calculate the exciton lifetime

[Jagjit Kaur]

Dear all,

I was trying to calculate the exciton lifetime of a 3D material using the following formula:

radiative decay rate = \frac{8\sqrt{\pi\epsilon}e^2\hbar p_{s}^{2}}{3\epsilon_0 m^2 V E_s(0)^2}(\frac{E_s(0)^2}{2M_s m c^2k_BT})^{3/2}, and the excitonic lifetime is inverse of radiative decay rate.

Here, e is electron charge 1.60217663 × 10-19C, m is electron mass is 9.1093837 × 10-31 kg, \epsilon_0 is permitivity in vaccuum is 8.8541878128×10−12, k_B is boltzmann constant which is 8.617333262×10−5eV/K, \hbar is planck's constant which is 6.652119x10^-16 eVs, c is speed of light which is 3x10^8 m/s, T is temperature which is 300K, \pi is 22/7. \epsilon which is dielectric constant is unitless, p_{s}^{2} which is oscillator strength in units of eV, E_s(0) which is exciton energy in unit of eV, M_s which is exciton effective mass in the units of electron rest mass energy, V is the volume of the material in m^3

I am getting the lifetime in the order of e-55 ps which is too less. Basically the order of lifetime is coming out to be wrong.

Can the yambo community help me whether the units and the values of different parameters are correct?

Regards

[Ponnappa]

Dear Qxiao

N_k is needed since you have a sum over k in the numerator. See also the formula for the macroscopic dielectric function in the
first paper of yambo https://doi.org/10.1016/j.cpc.2009.02.003 to see what I am speaking about.
In any case if you want to obtain mu_S^2 from the residuals^2 written by yambo
in the o*exc*E_sorted file do in this way:
take the second column of the file and multiply by the Maximum Residual Value you read at the beginning of the file
these are the modulus square of the residuals now not normalized to 1.
From them to obtain the modulus square of excitonic dipoles
mu_S^2 = residuals^2*Omega*N_k/(4*pi*HA2EV*n_spin)
where Omega is the volume of the cell in real space, HA2EV is the conversion from Hartree to eV and n_spin=2 for non spin-polarized case and 1 for soc, spin-polarized .

Best
Maurizia

Dear Developers,
I was trying to match the units of mu_s^2. While trying to do so, I had few queries.

1) Why is the term HA2EV multiplied? residulals^2 has the units of eV. Except that I do not find any term having energy units( Hartree). So why is it divided?

2) After trying to match the units I could find mu_s^2 has the units Coloumb^2*Length^2 as per the above equation. But I suppose mu_s^2 needs to have the units of Length^2. Are we supposed to divide the above equation (ms-s^2) by e^2.


Awaiting your response. Thank you in advance!

[nilesh12]

Dear Ponnappa,
Please follow this article. I hope that it can be useful for you.
https://pubs.aip.org/aip/jcp/article/16 ... properties

[Ponnappa]

Dear Nilesh,

Thank you for your reply. As per the above mentioned paper, I could see \mu_s is given by (\epsilon_0*V/e^2)*residulas^2. This expression matches the units. However, N_k and HA2eV terms are missing in this expression. Can you please let me know why it is not considered? Once again, thank you for the recommended paper and waiting for the response.

Thank you,
Ponnappa K. P.

[nilesh12]

Dear Ponnappa,
Probably, you misunderstood the expression. the correct expression is $\mu^2 = $\frac{\epsilon_0 V}{e^2}$\texttt{Strengths}, where strengths = oscillator strength*residuals.
N_k will not be include in expression because it's already implemented with oscillator strength (we confirmed it after reading ypp source file). Further, this expression is for SI units, that's why HA2eV factor is not there. If you want to do it in HA units, you can convert it accordingly. i hope you'll get it now.

Best Regards
Nilesh K.

[Ponnappa]

Dear Nilesh,
Thank you for the response; I found this really useful in clearing my doubts.

Regards,
Ponnappa K. P.