EPW Forum

Dear EPW community,

I am studying the following emission/absorption pair in silicon:

I start with a single k-point (0.0 0.3 0.3) and a single q-point (0.0 0.1 0.1). My kq-point is (0.0 0.4 0.4). I print g2 from transport.f90. For mode #6, g2=9.51E-9.

Then I use k-point (0.0 0.4 0.4) and q-point (0.0 -0.1 -0.1). My kq-point is (0.0 0.3 0.3). For mode #6, g2=4.11E-11.

Shouldn't the two g2 be equal? If not, how should I get the same g2 for an emission/absorption pair?

Thanks,
Vahid

Vahid Askarpour
Department of physics and atmospheric science
Dalhousie University
Halifax, Canada

Dear Vahid Askarpour:

Generally speaking, if you average the values in case of the degeneracy in energy or phonon freq. and you use the norm-conserving pseudopotential, they should be the same.
But, in real cases, they can be different and regarding its origin and how to make them equal, I just can tell you one of the reasons (and the main reason) is related to the interpolation quality.

Sincerely,

H. Lee

Dear H. Lee,

I am using a norm-conserving PSP. The coarse k-grid is 12x12x12 and q-grid is 6x6x6. These give converged EPW band structure and phonon dispersion relative to QE counterparts. I was expecting some differences in g2 but not a factor of 100.

I will dig further into the code. There might be more fundamental reasons as to why the two g2 values are so different. Meanwhile, if anyone has a single example of a case when the two g2 values are similar, I would appreciate hearing from you.

Thanks,
Vahid

Dear H. Lee,

I changed the q-grid to 12x12x12, matching the k-grid. The electron and phonon dispersions from EPW match those of QE. The PSP is norm-conserving.

After some digging into the code, I believe the mismatch between emission and absorption coupling constant comes from the phase factor exp(ik.Re) in Eq. 22 of the EPW paper (PRB76, 165108, 2007) referred to extensively inside the code (implemented in subroutine ephwan2bloch). Changing k to k' changes this phase factor resulting in a different coupling constant. Changing q to -q only affects the sign of the imaginary part of the coupling matrix not its magnitude (implemented in subroutine ephwan2blochp).

Unless I am missing something here, it seems that because of this phase factor, we cannot get the same matrix elements for emission and absorption.

Cheers,
Vahid