In the attachment, $S(\omega)$ is a transmission function, $\epsilon_1$ and $\epsilon_2$ are real and imaginary dielectric functions respectively. If we notice the equation carefully, we need $\epsilon (q, \omega)$ since the summation includes all the q points in the 1st BZ.
Normally if I do DFT using Quantum Espresso, I would get the dielectric function ($\epsilon$) over frequency ($\omega$) ranges. Are there anyway I would get dielectric function $\epsilon(\omega)$ at each q point?
The link of the paper related to the equation (9) (https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.14.024080)
Thank you in advance for your time.
Dear Prof. Md. Jahid Hasan Sagor
This is an interesting question. You can try to use an algebraic manipulator such as Maple to compare the results of DFT with your inquiry.
Creating a mesh with a finite number of q points in the first Brillouin zone with Maple is not difficult, you can add the equation you have suggested and do the sum.
Please check how it can be done for the normal and superconducting DoS in the tight-binding approximation in the reference
Article The two-dimensional density of states in normal and supercon...
Best Regards.
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