Fig. attached show the imaginary part of bulk system with GW and GW+BSE calculation.
Present optical gap (GW) is 1.38 eV. Can we call these peaks (P1, P2, P3 appear at 1.45, 1.65 and 1.98 eV, resp.) as excitonic peaks, if yes, then how to estimate exciton binding energy? As I know people discuss only near or before optical band gap peaks but not others like this. Does anyone know Ref. for same. I observer 150-meV red shift in the prominent absorption peak (at 2.82 eV) with the e-h interactions. Can I conclude that this shift is due to the weak excitonic effect in this system.
Thank you in advance !
Dear Mukesh,
first of all, congratulations to the nice results. Your calculations confirms the importance to include electron-hole interaction (excitonic effects) via solving the Bethe-Salpeter equation (BSE)) when discussing the shape of the imaginary part of the dielectric function (DF).
And now to your question. In general, a clculated independent-particle DF (i.e. without excitonic effects) from Fermi's golden rule mirrors the critical points of the band structure but it deviates from the experimental data. The differences become particular pronounced for materials with high band gaps (see for example our work on cubic AlN, Roppischer et. al.). The inclusion of excitonics effects solve the prblem, we find a prouounced redistribution of oscillator strength and peaks in the excitonic DF towards lower energies in the high energy range. A mor detailed analysis is presented in the work of A. Riefer et.al.
The bahaviour around the band gap is easier to understand. For an direct band-gap material, one would expect a square-root increase of epsilon 2 above the gap when disregarding excitonic effects. The inclusion of excitonic effects leads to two pronounced changes; (1) discrete ecitonic line below the fundamental band gap (hydrogen-like series), and (2) strongly enhanced absorption at and above the gap (the exciton continuum, or Sommerfeld enhancement, described already be Elliot's exciton theory). Corresponding experimental data and analysis applying this theory can be found in the work of M. Feneberg (e.g. as attached).
It means, that the e-h interaction enhences strongly the absorption above the gap. It is also evident in your data (what you call exciton lines above the gap). Why do you see only three lines and not more. I think that you included not enough k-points. When you will refine the k-grid to get mor data points, you will increase the number of peaks merging finally in a continuum.
Best regards, Ruediger
http://dx.doi.org/10.1063/1.3239516
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Dear Prof. Rüdiger Goldhahn,
Greetings.
Thank you very much for a kind detailed answer. You cleared many doubts in your above explanation and also through attached papers.
Regards
Mukesh
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