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### Static dielectric function from ndb.em1s

Posted: Fri Nov 18, 2022 2:50 pm
Hello,

I would like to know how you can compute the static dielectric function eps^{-1} (q, G,G') from the ndb.em1s databases.
I found in a yambopy script that the following quantity is stored in the ndb.em1s files: sqrt(v(q+G)) chi(G,G') sqrt(v(q + G')).
To isolate the epsilon, I have to compute eps^{-1} (q, G,G') = delta_{G,G'} + v(q+G) chi(G,G') for G .ne. G'

But in order to do so, I need to exactly know how you build your Coulomb interaction, especially in the limits of q -> 0 or G -> 0 or both.

Edit:
I am additionally using the RIM as well as the truncated Coulomb potential within a box z geometry to properly treat the 2D systems of study.
Thus, I also have the ndb.RIM and ndb.cutoff that I probably need to correctly construct v(q, G).

Best,
Franz Fischer

### Re: Static dielectric function from ndb.em1s

Posted: Fri Nov 25, 2022 1:00 pm
Dear Franz,

What you write about the contents of the ndb.em1s database is correct.
The Coulomb interaction v is just the standard 4\pi/|q+G|^2 if no Coulomb cutoff is used, otherwise it is the cutoffed version according to the chosen geometry.
So you don't need ndb.cutoff in order to reconstruct epsilon.

By the way, if you have a 2D system I would suggest using the "slab z" geometry instead of "box z". In this way, an analytical expression for v is used and you don't need to specify a CUTBox parameter anymore. In addition, the RIM Monte Carlo integral will be calculated on the analytical cutoffed version instead of the 3D version of v, which is more consistent.

The RIM is not included in the v stored in ndb.em1s. It is a kind of averaging for very small q-points and a few G-vectors normally used to accelerate convergence of integrals over momentum space. If you want the exact values of epsilon_GG'(q) in that region you probably don't need to add it, but for good samplings you might need to use a very dense k/q-mesh.

Cheers,
Fulvio

### Re: Static dielectric function from ndb.em1s

Posted: Fri Nov 25, 2022 4:21 pm
Dear Fulvio,

thanks a lot for your reply. But I want to add a naive follow-up question to your answer concerning the correct construction of the inverse dielectric function eps^{-1}_{GG'}(q).
As I can tell, what is stored is the matrix M_GG'(q) = sqrt(v_{G}(q)) * chi^0_{GG'}(q) * sqrt(v_{G'}(q)).
So for a given q, I could compute eps_{GG'}(q) = delta_{GG'} - M_{GG'}(q), and then invert the matrix eps_{GG'}(q) to get the inverse dielectric function. I have experimented with this approach, but it seems to result in wrongful values for Gx = Gx' = Gy = Gy' = 0 for Gz = Gz' > 0
(For monolayer MoTe2 at q=0, these values are far greater than 1, which contradicts most references, e.g. [1]).
What would be the correct way to handle this issue or did I took a wrong turn at some point?

Best,
Franz Fischer

[1] Screening and many-body effects in two-dimensional crystals: Monolayer MoS2,
Diana Y. Qiu, Felipe H. da Jornada, and Steven G. Louie,
Phys. Rev. B 93, 235435 (2016)

### Re: Static dielectric function from ndb.em1s

Posted: Mon Dec 05, 2022 9:08 am
Dear Franz,

please note that what is stored in ndb.em1s is vX and *not* vX^0, so that
\epsm1=1+vX

Best,

Daniele

### Re: Static dielectric function from ndb.em1s

Posted: Thu Dec 08, 2022 2:22 pm
Dear Daniele and dear Fulvio,

thanks for your replies. I computed the inverse dielectric function as you suggested, i.e.: eps^-1_GG'(q) = delta_GG' + v_G(q) X_GG'(q) for a monolayer of MoS2 to compare the results with the ones presented in literature [1].
I tried two different cases a) using the bare Coulomb interaction and b) using the truncated Coulomb interaction.
The inverse dielectric function for case a) is in perfect agreement with the literature, see 'em1s_bare.png' in the attachments.
The issue is that the inverse dielectric function in case b) is correct, if Gx=Gy=Gz=0, but not, if we set Gx=Gy=0 and Gz .neq. 0 (see em1s_trunc.png).
I will furthermore attach the report file for the calculation of case b).
I also tried the suggestion of Fulvio to not use the "box z" cutoff geometry, but the "slab z" geometry instead.
Doing so, the Coulomb interaction was not truncated at all. Maybe the "slab" geometry is not implemented in the yambo version that I am using (v4.5.2).

What is causing the unexpected behaviour using the truncated Coulomb interaction?

[1] Screening and many-body effects in two-dimensional crystals: Monolayer MoS2,
Diana Y. Qiu, Felipe H. da Jornada, and Steven G. Louie,
Phys. Rev. B 93, 235435 (2016)

### Re: Static dielectric function from ndb.em1s

Posted: Thu Dec 08, 2022 6:42 pm
Dear Franz,

as suggested by Fulvio I would avoid the box shape (which is not analytical and can also present negative components) and I would switch to the slab geometry "slab z".
Yes, the slab is present starting from the 5.X release. I strongly suggest you update to the last release of the code.

Best,
Daniele

### Re: Static dielectric function from ndb.em1s

Posted: Tue Dec 13, 2022 4:14 pm
Dear Daniele,

I updated to the yambo version 5.1.0 and repeated the calculation and found that using the "slab z" option solves my issues.
For completeness I attach the corresponding eps^-1 file plotted against |q| for different out-of-plane G's of MoS2 that shows the exact same behaviour as reported in the source I cited earlier.