Binding energy+ nature of excitons

[lamia]

Dear Developers,
I want to estimate the binding energy of exciton which is defined as: "bandgap - first exciton peak" is it correct? To this goal, I run "ypp -e s" to precise the nature of the first exciton.
Is the nature of exciton depend on the nature of the band gap? For example, if it is an indirect band gap the first exciton peak should be dark (zero or very small intensity) and if it is direct the first exciton peak is bright (intensity).
I calculate the band gap and it is indirect with the value of 4.9 eV (GW) and the first bright peak is 4.3572 eV extracted from imaginary part using BSE. The results of ypp -e s " o.exc_E_sorted" is mentioned below:
# E [ev] Strength Index
#
4.354979 1.000000 1.000000
4.355045 0.417641 2.000000
4.679 0.4272E-4 3.000
4.6796 0.0070 4.0000
4.67963 0.02002 5.00000
4.777322 0.283423 6.000000
4.777348 0.139316 7.000000
4.790 0.1264E-7 8.000
4.905 0.5877E-2 9.000
4.905 0.6082E-2 10.00
4.96 0.379E-09 11.0
4.974 0.7883E-2 12.00
4.975 0.3231E-2 13.00

Based on these results how can I deduce the dark or bright excitons then the binding energy?

[Daniele Varsano]

Dear Lamia,

the binding energy of exciton which is defined as: "bandgap - first exciton peak" is it correct?

Correct.

For example, if it is an indirect band gap the first exciton peak should be dark (zero or very small intensity) and if it is direct the first exciton peak is bright (intensity).

It depends, if you are solving a q=0 BSE, i.e. optics. In this case you need to look at the direct gap to estimate the binding energy. If the excitations are dark or bright will depend on ite intensity (dipoles) independently on the nature of the gap.

If you look at finite momentum excitations, all the excitations are dark as cannot be excited by light (q~0). Nevertheless they can be "active" as can be detected by EELS or IXS experiments.

Best,
Daniele

[lamia]

Dear Daniele,
Thank you very much for your reply!
Could you give me more details , please?
Could you help me to deduce the nature of the excitons (dark or bright) from the example below?:
I calculate the band gap and it is indirect with a value of 4.9 eV (GW) and the first bright peak is 4.3572 eV extracted from imaginary part using BSE. The results of ypp -e s " o.exc_E_sorted" is mentioned below:
# E [ev] Strength Index
#
4.354979 1.000000 1.000000
4.355045 0.417641 2.000000
4.679 0.4272E-4 3.000
4.6796 0.0070 4.0000
4.67963 0.02002 5.00000
4.777322 0.283423 6.000000
4.777348 0.139316 7.000000
4.790 0.1264E-7 8.000
4.905 0.5877E-2 9.000
4.905 0.6082E-2 10.00
4.96 0.379E-09 11.0
4.974 0.7883E-2 12.00
4.975 0.3231E-2 13.00

Best,
Lamia

[Daniele Varsano]

Dear Lamia,
if you did an absorption spectrum calculation (i.e q=0) you are looking at vertical transition so you should consider the direct gap and not the indirect one in order to evaluate the biding energy.

The excitations are bright or dark according to their strengths, here the first 2 are bright.

The excitations are the ones you reported in your post, the fact you see a peak at slighter higher energy is due to the fact the spectrum is built as a summation of the excitation energies with their strength with a Lorentzian broadering you set in the input files.
If you reduce him you would have peaks corresponding to the excitation energies reported below.

Best,

Daniele

[lamia]

Dear Daniele,

is it normal to get the 2 first peaks bright while the gap is indirect which means a dark exciton ?


Best,

Lamia

[Daniele Varsano]

Dear Lamia,
Indirect excitons are all darks, but you need to calculate the finite q excitons. Are you solving finite q bse?

Having said that, even if you solve finite q bse you can have finite strenght, which does not means they are bright to light excitations but they are detectable by eels or ixs experiments.

Best,
Daniele

[lamia]

Dear Daniele,

Thank you very much for your patience!
If you mean by q=0 BSE optical absorption spectrum, I have already done it and the results are presented in figures:


best,

Lamia