negative binding energy

[xjxiao]

Dear all,
I noticed that in the hBN example provided on the Yambo official website(https://wiki.yambo-code.eu/wiki/index.p ... 022_school), the file o-3D_BSE.exc_qpt1_E_sorted shows that excitons 3 and 4 (which are degenerate and have the highest intensity) have an excitation energy of 5.02167761 eV.

Code: Select all

   
#    E [ev]             Strength           Index
#
     4.97959425        0.240329831E-5      1.00000000
     4.97977116        0.109951277E-4      2.00000000
     5.02167761        0.328193780E-1      3.00000000
     5.02199662         1.00000000         4.00000000

However, the file o-3D_BSE.exc_weights_at_3 reveals that the single-particle transition energies of the electron-hole pairs composing this exciton are 4.35248947 eV and 4.81094742 eV.

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# Band_V          Band_C          Kv-q ibz        Symm_kv         Kc ibz          Symm_kc         Weight          Energy
#    
  7.00000000      10.0000000      14.0000000      2.00000000      14.0000000      2.00000000     0.395135850      4.35248947   
  7.00000000      10.0000000      14.0000000      1.00000000      14.0000000      1.00000000     0.394993663      4.35248947   
  8.00000000      9.00000000      14.0000000      2.00000000      14.0000000      2.00000000     0.391943455      4.35241365   
  8.00000000      9.00000000      14.0000000      1.00000000      14.0000000      1.00000000     0.391800284      4.35241365   
  7.00000000      10.0000000      13.0000000      2.00000000      13.0000000      2.00000000     0.745555162E-1   4.81094742   
  7.00000000      10.0000000      13.0000000      1.00000000      13.0000000      1.00000000     0.745274872E-1   4.81094742   
  8.00000000      9.00000000      13.0000000      2.00000000      13.0000000      2.00000000     0.739243180E-1   4.81087065   
  8.00000000      9.00000000      13.0000000      1.00000000      13.0000000      1.00000000     0.738964081E-1   4.81087065 

Since 5.02167761 eV is larger than both of these values, does this imply that the exciton has a negative binding energy? Additionally, given that there are two distinct single-particle transition energies, how should the binding energy be calculated in this case?

Another question: I noticed that when using Yambo 5.3.0 to calculate BSE cases with rim_cutoff(https://wiki.yambo-code.eu/wiki/index.p ... al_systems), only o-...alpha files are generated, while eps and eel files are missing. Is this normal?

Thank you very much for your patient assistance!
Xiao

[Daniele Varsano]

Dear Xiangjun,

However, the file o-3D_BSE.exc_weights_at_3 reveals that the single-particle transition energies of the electron-hole pairs composing this exciton...

These are Kohn-Sham energy differences, i.e. without the GW correction.

Another question: I noticed that when using Yambo 5.3.0 to calculate BSE cases with rim_cutoff(https://wiki.yambo-code.eu/wiki/index.p ... al_systems), only o-...alpha files are generated, while eps and eel files are missing. Is this normal?

Yes, macroscopic dielectric function is not a well-defined quantity in reduced dimension systems. The meaningful quantity is the polarizability alpha.
This is reported in the FAQ: https://www.yambo-code.eu/learn/#FAQs and extensively discuused in the forum see e.g.:
viewtopic.php?p=8333&sid=2144508e1d78c0 ... 2bf2#p8333

Best,

Daniele