GW for gated 2D structures

[DavidPolito93]

Dear Developers,

I am writing because I am trying to perform GW calculations for gated two-dimensional heterostructures.
In practice would start from QE calculations of two-dimensional heterostructures in field-effect configuration where it is also present a perpendicular electric field which charges my system. The concept and the QE implementation is that present in T. Sohier, Phys. Rev. B 96, 075448 (2017) [https://journals-aps-org.ezproxy.univer ... .96.075448].

My problem concerns the compatibility of such approach with a subsequent GW calculation with yambo. I am saying this because in this approach the key ingredient is a truncated Coulomb interaction in the direction perpendicular to the slab and the presence of the field which is screened by the system itself : the cutoff is on the coulomb kernel, and the potentials are a convolution of the charge densities (atomic or electronic) with this kernel and a "physical window" is defined within which we have our effective 2D system and outside we obtain a kind of mirror image of the physical (Fig. 3 in the paper I cited).

Do you think that a GW calculation is straightforward feasible (of course taking into account all precautions for a lowdimensional systems)? Or some problematics might arise?

Best,

Davide Romanin

[Daniele Varsano]

Dear Davide,

actually the GW calculation, on top of the gated 2D structure, could not be straightforward.
I need some time to think about the feasibility, actually that's an interesting question.

Best,
Daniele

[claudio]

Dear Davide

I think GW should not be compatible with the cutoff of QE.

The reason in my opinion is that the cutoff changes the Kohn-Sham potential and implicitly also Vxc.

Now Vxc is necessary for Yambo to calculate the GW correction

\epsilon_GW = \epsilon_KS + <\Sigma - V_xc>.

but Yambo is unable to recognise that the KS potential has been modified by the presence of a cutoff
and this would introduce an error, I do not know whether large or small.

At the end the solution will be to implement the same cutoff in Yambo, to calculate Vxc, Vhartree etc.. in the same way.

best
Claudio

[DavidPolito93]

Dear Daniele and Claudio,

Yes, indeed I was worried about that and wanted to check if it was feasible or not.

My other idea was to use a cutoff box with a size equal to the physical window but it sounded not so correct to me.

Anyway I’m interested in this feature so maybe if you want we could discuss it if it also interests you

Best,
Davide

[claudio]

Dear Davide

I think the implementation of their cutoff is not difficult,

then you have to check how to deal with charged systems, this is not completely clear to me

best
Claudio

[Daniele Varsano]

Dear Davide,

actually, I think there is a solution using an implementation we have just developed in Modena (not yet released) to enabling GW calculation on top of DFT+U, or any Vxc used in QE. Actually, Vxc is not anymore calculated by libxc but via a rebuilding of the bare Hamiltonian.

Code: Select all

V_nk^xc=eps_nk^ks-Ho_nk^0-Vh_nk

where eps is the KS eigenvalue, Ho is the bare Hamiltonian (kinetic +pseudo) and Vh is the Hartree potential.

In this way, Yambo is agnostic on the potential used in QE (local, DFT+U, hybrid or the modified potential you are using).
This has been implemented and we have started to validate and up to know results are consistent and encouraging.

If you are interested, we can arrange a call, involving also Fulvio Paleari and Andrea Ferretti who have been working on that.

Best,
Daniele

[claudio]

Dear Daniele

I had thought of that too, but the problem is that in Sohier et al. paper
they put the cutoff on all V_ks so even their V_hartree is different from our V_hartree

Claudio

[Daniele Varsano]

Dear Claudio,
you are right!! But, the Vh should be the easiest one to cut (Eq. 34) and it should be already implemented, while probably some care needs to be paid to the long range part of the pseudos (Eq.32). Anyway, I think this needs a (virtual) face to face discussion.

Daniele