e-ph matrix element divergence for polar materials

General
1

Hello,
I calculated e-ph matrix elements of a polar material (cubic BN) for an electron at CBM and varied the phonon wavevector (see plot here: https://www.dropbox.com/s/7yhjyl9wzeh3tpm/g.png?dl=0 ). While the divergence of the matrix element for LO phonons near the gamma point is expected, I’m surprised by the dip in the magnitude of the matrix element right at the gamma point (the vertical green line at gamma). Shouldn’t it be undefined at the gamma point? I think I see a similar behavior in the tutorial example for GaN: http://epw.org.uk/Documentation/GaN

I’d appreciate it if someone could explain this.

Thanks!
Sridhar

2

Dear Sridhar

It should be zero as a consequence of overall neutrality of the cell. If you were to calculate the matrix elements at Gamma with ph.x you would obtain the same.

Best
Carla

3

Thank you very much for your response.
Sridhar