questions about two-dimensional polarizability alpha_2D

[HaozheLi]

Dear all,

I am currently engaged in a research project identifying whether some two-dimensional materials are excitonic insulators (EI). The two-dimensional polarizability alpha_2D is an important parameter to describe the screened Coulomb interaction in some theoretical models of EI, which also can be find in the excellent paper Nature Nanotechnology volume 15, 367–372 (2020). So I wonder how to get a meaningful and correct 2D polarizability alpha_2D using Yambo, because I knew that Yambo can calculate that parameter. Here are my questions:
(1) I noticed that the output file o.alpha_q1_diago_bse obtained using the truncated coulomb potential in a BSE calculation contained two types of alpha_2D (alpha and alpha_o) which were very different in value. Is the value of alpha the result of the BSE calculation, and alpha_o the result of the GW calculation? Or are they should be the same?
(2) In theoretical calculations, just like paper Nature Nanotechnology volume 15, 367–372 (2020), which value should we use, the BSE result, the GW result, or the result which we should calculate in RPA? I tried both BSE and RPA calculation in yambo, but the RPA result o.alpha_q1_inv_rpa_dyson also contains two types of alpha_2D (alpha and alpha_o) and those results are different from the BSE result. What's worse is that the Re(alpha) in the RPA result are negative, is this reasonable? There are so many alpha_2D, so I'm not sure which one should i choose...
(3) As we can seen, the two-dimensional polarizability alpha_2D is energy-dependent, should we choose the alpha_2D at zero energy to use?
The input and output files are attached.

Best wishes,
Haozhe

yambo.zip

[Daniele Varsano]

Dear HaozheLi ,

1) The first column are the BSE results, the following one (alpha_0) are -the non interacting alpha (Independent Particle). If you have taken into account GW corrections the energy difference entering in the IP response are the GW ones.

2) They are different because they are calculated at different level of theory. Which one to use it really depends on what you need it for. In the paper you mentioned, the screened interaction calculated at RPA level was fitted with the 2D expression of the screened interaction potential to extract the alpha_2d.
The purpose was to build a screened interaction potential to be used in a model Hamiltonian, and for consistency, the RPA screened potential is the one entering in the BSE equation.

3) Usually the BSE is solved considering a static interaction (omega=0), this is the standard way, but of course dynamical effects can play a role.

Your RPA output is indeed very strange, all the imaginary. part is negative which is not physical, something weird has happened, but I do not have enough information to understand what went wrong. Please note, you are using hybrid functional as starting point, depending on how you are calculating the dipoles, in the default algorithm use by Yambo the non local commutator with the non-local part of the xc potential is neglected. I cannot say if this is important or not.

A check you can do anyway is to calculate the RPA response in the transition space, this is done as a BSE calculation setting BSKmod= "HARTEE", and BSEmod='coupling'.

Best,
Daniele

[HaozheLi]

Dear Daniele,

Thanks for your helpful answer.

Your RPA output is indeed very strange, all the imaginary. part is negative which is not physical, something weird has happened.

Yes, I noticed that the RPA results are very weird .Actually, I have calculated RPA result on top of PBE functional for another 2D material, but i also found that both of Im(alpha) and Re(alpha) are negative. It seems that there are something wrong in my calculation?
My workflow is:
(1) use QE to calculate single-particle ground states and use p2y to convert the wavefunctions and then use yambo to initialize;
(2) use command yambo -o c -k hartree -F RPA.in following the tutorial in the official website to generate the input file RPA.in.
Did I miss or get anything wrong?
The input and output files are attached.

Best wishes,
Haozhe

alpha_pbe.zip

[Daniele Varsano]

Dear HaozheLi,

can you please post also the report file?
Can you also repeat the calculation from scratch setting RandQpts=0?

Best,
Daniele

[HaozheLi]

Dear Daniele,

The report files of two different calculations (one for GAUPBE and one for PBE) are attached.

Best wishes,
Haozhe

report.zip

[Daniele Varsano]

Dear HaozheLi,

Can you also repeat one calculation from scratch setting RandQpts=0?

Best,
Daniele

[HaozheLi]

Dear Daniele,

Do you mean using the command `yambo -o c -k hartree -r -F RPA.in` as before but only setting RandQpts to 0 and not changing anything else (including RandGvec) in both hybrid functional and PBE?

Best wishes,
Haozhe

[Daniele Varsano]

Dear Haozhe,

PBE only is enough. You can also lower the parameters (bands and NGsBlkXd) to speed up the calculation.
You can use the same input file you are using changing RandQpts to 0 and run after having removed the ndb.RIM from your directory.

Best,
Daniele

[HaozheLi]

Dear Daniele,

It seems that the results didn't change significantly.

Best wishes,
Haozhe

RandQpts=0.zip

[Daniele Varsano]

Dear Haozhe,
ok thanks for the test, it was just to exclude this possibility.
At this point we need to reproduce the problem. In order to do that, can you produce a minimal tests (minimal parameter of bands, NGsBlkXd, k points) reproducing the problem? Something that runs in few minutes as I do not think it depends on the convergence parameters. Then you can post the scf/nscf input and pseudopotentials.

Best,
Daniele