EPW Forum

Hej experts,

first I want to thank you for all the effort and all the material that you are willing to share. Be assured, that your efforts are highly appreciated within the community. You are heros!

I want to determine Electron-Phonon-Matrix-elements, as they are written down in Felicianos Article ...
https://arxiv.org/pdf/1603.06965.pdf
... in equations (37) and (38).

I worked through the Summer-School 2021 and I see that one can compute the absolute value of these g-values for all the bands, branches and wavevectors, by setting the input-flag "prtgkk" to true and obtain quasi-infinite lists of values for the norm of the g-values for their different arguments. However, in the documentation, and on one of the exercise-sheets from the summer-school, I find the words of warning

"Since electron-phonon matrix elements are gauge-dependent, an (gauge-invariant) average of their norm over degenerate subspaces of bands and modes has been performed."

I understand that in most formulas not g itself, but |g| (or its square) appears. However... Please tell me: If I am interested in the values of g as in Felicianos article, not |g|: Can I just set g = |g|?

I would appreciate any clarification in this matter.

Med vänliga hälsningar
Sebastian Kalhöfer

Hi Sebastian,

Thanks for the appreciation and the very nice question. Indeed, the electron-phonon matrix element is a guage dependent quantity as described in the article by Prof. Feliciano Giustino. It is true that in many formulas the electron-phonon matrix appears as |g|, however, it is a complex number. Therefore, g=|g| may be ok for certain cases but in many cases the guage of "g" is important.

One of the example for such case is phonon-assisted optical absorption (https://journals.aps.org/prl/abstract/1 ... 108.167402) which can be calculated using the EPW code. The oscillator strengths are a product of "g" and the velocity matrix element "v". Hence, only g=|g| will result in error.

Therefore, g=|g| would be ok based on the particular situation you are applying your theory to.

Best regards,
Sabya.