EPW Forum

Dear all,
I am confused by the electron self-energy in phonon-assisted optical absorption calculation.

I have checked many references, but I couldn't find the calculation relationship between the absorption coefficient and the self-energy (calculated by EPW). I guess it is related to the calculation of energy levels \varepsilon .

My question is that I used the GW calculation results (which include the self-energy calculation and incorporate it into the energy level by perturbation), and now I want to know how the electronic self-energy (including electron-phonon interactions) is incorporated.

Any help will be appreciated.
Best regards.
Youzhao Lan
Zhejiang Norm. University.
China

Hi Youzhao,

Thank you for the question. I'm assuming you are talking about the broadening parameter on the denominator of the matrix elements in e.g. Phys. Rev. Lett. 108, 167402?

The short answer is, this broadening parameter should not be directly related to the electron self energy, but more as a numerical broadening to avoid divergence of the denominator. It is a limitation of second-order perturbation theory, and will happen when phonon-assisted absorption happen in the same regime direct absorption can happen. If you are in the indirect regime (for example, if one calculates the absorption coefficient of silicon in the regime of ~1.2 eV to 3 eV), one will see that the absorption will not depend on this parameter (until it becomes large).

Tricks can be used to avoid this divergence, and one example would be e.g. ACS Nano 2016, 10, 1, 957–966, Eq. 10, but it is more of numerical way. More physically what one can do is considering the quasi-degenerate perturbation theory in the indirect-direct resonant region, see: Phys. Rev. B 109, 195127. We are also considering the problem in the context of many-body perturbation theory, which may provide a way to incorporate the physical self energy into the equation but it is still in very early stages and not yet implemented into EPW.

Thanks!
Xiao