Asking for help about the relationships bwtween alpla_2D(w) and alpha=-X/q^2

[Luo Yan]

In official website tutorial http://www.yambo-code.org/wiki/index.ph ... al_systems, it shows that “For a 2D system， the macroscopic polarizability (called here 'o-2D_WR_WC.alpha_q1_diago_bse') which is a well defined quantity strictly related to optical conductivity, or absorbance, is defined as attachment below” However, I find some topics show that "including the coulomb cutoff yambo print in output alpha defined as alpha=-X/q^2 where X is the response function."
Question 1: What's the relationship between two equations ?? I can't find more detailed derivation process about them, especially for the equation in the attachment below .
Question 2: Is the imaginary part of the GW and BSE polarizabilities obtained from "o-2D_WR_WC.alpha_q1_diago_bse" obtained via dielectric function Epsilon ε(q) = 1 + 2πα_2D|q|[PHYS. REV. B 84, 085406 (2011)] ? If not, how can I obtain the imaginary part of dielectric function in a 2D system ? If yes, the q tends to be 0, and the Epsilon is alway 1 ?
Thanks for your attentions. Best wish to you !

[lyzhao]

Dear Luo,
The following posts should be helpful for you.
Real part of the dielectric function is absolutely one
viewtopic.php?t=1663&sid=10bd0adae13efd ... 5806ef1c30
Real part of the dielectric function
viewtopic.php?t=1858
Bethe salpether diago/inversion output
viewtopic.php?t=1715

Best regards.

[Luo Yan]

Dear Lan,
I am very grateful for your quick reply. I will study these files.
Looking forward to further discussions with you!
Thank you once again.

[Daniele Varsano]

Dear Luo,

If not, how can I obtain the imaginary part of the dielectric function in a 2D system? If yes, the q tends to be 0, and the Epsilon is alway 1 ?

Yes, the dielectric function behaves as you say, having a supercell with increasing vacuum to isolate the system, you are simulating a layered system with the interlayer distance increasing and in the limit, you obtain the eps of vacuum.

You can anyway define an eps_2d from the alpha_2d (see e.g. Rasmussen et al. PHYSICAL REVIEW B 94, 155406 (2016), Eq. 6 and text above where alpha_2d is defined).
In Yambo, alpha_2d is calculated in that way propto -X/q^2.
Alternatively you can evaluate it by discarding the coulomb cutoff potential and extracting it from Eq. 16 of PHYSICAL REVIEW B 84, 085406 (2011) you were mentioning, performing different calculations with increasing vacuum .

Best,
Daniele

[Luo Yan]

Dear Daniele,
Thanks four your detailed helps. Could you offer me more deduced informations about the response function X used in Yambo ?
Thank you !

[Daniele Varsano]

Dear Luo,

you can have a look at the yambo cheatsheet to look on how X and many other quantities are calculated.

http://www.yambo-code.org/wiki/index.ph ... heatsheets


Best,
Daniele