dimension of electron-phonon coupling strength

[jiachen]

Dear Experts,

I have a native question about dimension of electron-phonon coupling strength and the expression of it in tutorial section. It seems to me electron-phonon coupling strengths usually are reported as dimensionless in literature. Looking at the tutorial "electron-phonon coupling" of this website. It reads like:
\lambda = 1/{N_F \omega} \sum |g^{SE}|^2 \delta \delta
As far as I can see, two delta functions pick up which |g^{SE}|^2 to sum up. |g^{SE}|^2 has dimension energy^2. Density of states N_F has dimension energy^{-1} and frequency has dimension energy. So, this expression of \lambda seems to me has dimension energy^2, instead of being dimensionless. Can you point out where are my mistakes? Appreciate your help.

Cheers

[carla.verdi]

Hi,

The delta functions have the dimension of en^(-1) - they are usually calculated using a gaussian function with a specified broadening for example.

Best
Carla

[jiachen]

Dear Carla,

This is very helpful. Thank you very much!