Phonon-Assisted Absorption Mismatch

Running EPW
1

Dear all,
I’m studying Si optical absorption. Used scissor flag (0, 0.44 eV) in EPW instead of BGW eigenvalues; results don’t match tutorial. Attached: inputs, band structure, absorption plots. Kindly help me to match the results with the scissor flag.

Attached

  1. Bandstructure
    Si_Abs_comparison.jpg
  2. Absorption
    Si_BS_comparison.jpg
  3. Inputs
    inputs.zip (3.6 KB)
2

Hello,

When you apply a scissor shift, you need to renormalize the oscillator strengths. This is not performed automatically in EPW and is an additional step you need to perform. Check page 11 of https://journals.aps.org/prb/abstract/10.1103/PhysRevB.109.195127 for details.

In a nutshell, you need to multiply your imaginary dielectric constant with ((omega/(omega-delta))^2; here omega is the photon frequency and delta is the scissor shift.

Best regards,
Sabya.

3

Hi,

Just as to add to Sabya’s point: this renormalization is performed in the case of reading an external eigenvalue. Therefore, it is mostly recommended to use that option as much as possible instead of using a scissor. If you would like use a scissor shift, one way to have EPW does the renormalization is to supply a .eig file where the scissor shift is already applied.

The other thing to be careful with is to make sure in either case (eig_read or a scissor), the Fermi level is correctly set. It looks possible that you Fermi level is set to something very close to the VBM or CBM in the scissor case of your plot. If that’s the case, you may see some sub-gap contributions like what you are seeing in ~0.5 eV because of intraband absorption due to partially occupied bands.

Best!
Xiao

4

Dear Sabya and Xiao,

Thank you so much for your valuable suggestions!

  1. I learned about the necessity of renormalisation, but I couldn’t understand how it was implemented from the paper. In Python, I tried renormalising and got the subsequent result (which I don’t think is the proper way to do it).

If possible, could you tell or guide me with literature on how to find oscillator strengths?

hcut = 6.582e-16
c = 3e10 
n_r = 3.4
scissor = 0.4403

#Before Renormalisation
alpha = (data[:,0] / (hcut * c * n_r)) * data[:,7] 

#After Renormalisation
alpha_renom = (data[:,0] / (hcut * c * n_r)) * data[:,7] * (data[:,0]/(data[:,0]-scissor))**2

Scissor_forum_approach.jpg
2. As Xiao said, I had used the VBM value as the Fermi Energy. On shifting it properly (mid of VBM and CBM), I got the following result: close to the BGW eig file’s absorption.
Si_BS_scissor.jpg
fermishift_forum_approach.jpg

5

Dear Agathyan,

For the renormalization of the velocity matrix elements, see Eq.30 in https://doi.org/10.1103/PhysRevB.62.4927.

Thanks!
Xiao