absorption coefficient of silicon

[raul_l]

Dear all,

I'm trying to calculate the absorption coefficient of silicon and I'm confused over the meaning of some simple terms. I went through "Yambo: a quick guided tour" and reproduced the absorption plot (see calculated.jpg, left plot). What is meant by absorption? It appears to me its the imaginary part of the dielectric function (compare experiment.jpg, lower left). If that's the case then the absorption coefficient is given by alpha = w/c*sqrt(|eps|-Re(eps))*sqrt(2), where eps is the dielectric function, w is the excitation frequency and c is the universal constant (see Eq. (2) in PRL 106, 027401 (2011)). Assuming this is so I calculated the absorption coefficient (calculated.jpg, right plot). It looks qualitatively similar to the experimental curve (experiment.jpg, right plot) but seems shifted, giving strong absorption at unrealistically low photon energies. What could be the reason for that? I've already included the scissors correction. Am I missing something essential or is it simply the poor quality of my calculation (I could use higher cut-off energies, bigger brillouin zone sampling, better pseudopotentials ..)?
I've seen the calculated Im(eps) for different materials in countless papers but never the absorption coefficient (except the above-mentioned PRL paper). Is it because the absorption coefficient is too sensitive and DFT methods aren't up for that?
If it helps I could post the input files of both Yambo and Quantum Espresso.

Raul Laasner,
raullaasner@gmail.com
graduate student in University of Tartu

[Daniele Varsano]

Dear Raul,
at what level of theory are you calculating the absorption?
I suspect that you are doing Bethe-Salpeter calculations.
Please note that if you want to calculate the real part of eps, you have to use
causal green function, and if you are solving the BSE with the Tamm-Dancoff approximation,
i.e. BSresKmod and BScplKmod = none, the real part of epsilon is not calculate properly and
it will affect your calculations. Anyway, it is just a supposition, as I do not know how your input looks.

Hope it helps,

Daniele

[raul_l]

Dear Daniele,
now that I compare my Re(eps) to the experiment it appears I do have some problems. Although I'm more puzzled by my calculated Im(eps) which is non-zero at low energies. I just started learning Yambo and did everything as in the tutorial (which I assumed to be correct for silicon). Thanks for the suggestions. I'll post if I get anything interesting.

Raul Laasner

[Daniele Varsano]

DearRaul,

Although I'm more puzzled by my calculated Im(eps) which is non-zero at low energies

please note that in the plot you are using an artificial broadening: BDMrange. The results of your calculations
is an excitation energy. Lowering that values you should have a narrower peak, and consequently
zero absorption at very low energies.

Hope it helps,

Daniele

[babraram]

hello
please forgive me.
I started learning Yambo.
I run yambo -o c and then yambo command and yambo code create many (85) files with "o.eps_qX_inv_rpa_dyson" names in my save folder
i don't know which file of them is useful for plotting re(eps) and Im(eps).

Thank you very much.

babraram@yahoo.com
graduate student in university of urmia

[Daniele Varsano]

Dear Babraram,
How your input look like?
Take a look at the variable transferred momenta, may you have activated the calculation
for all your k point. In order to look at the absorption you want to look at the lim q->>0,
and hence to the first one only.

Code: Select all

% QpntsRXd
 1 | 1 |                     # [Xd] Transferred momenta
%

Cheers,
Daniele

[jmmorbec]

Dear Daniele.

What is the problem with Tamm-Dancoff approximation for the calculation of \eps_1? Should we not expected a fair agreement with the experiment?

Thank you!

[Daniele Varsano]

Dear Juliana,
I think that for silicon it should work, provided that you consider causal green function and not resonant approximation.
Best,
Daniele

[jmmorbec]

Thanks Daniele for your reply.
What do you mean by "consider causal green function and not resonant approximation"?
I am interested in other insulators, not silicon. I indeed found a fair agreement with the experiment using BSresKmod= "xc" (Yambo 3.3.0).

Thank you.

[Daniele Varsano]

Dear Juliana,
when considering resonant or causal (or time-ordered) green function, while the imaginay part of the eps is the same in for positive energies, the real part it is not.
The one with physical meaning is the causal one. When including the coupling (ie beyond the Tamm-Dancoff approx.) you consider the causal response. If you switch to the new release of the code, you can also consider causal response in Tamm-Dancoff approximation. It is possible that you do not find big differences between the two approaches, but the correct one is the causal.

Best,
Daniele