Xd smearing effect on the hBN gap

[martinspenke]

Dear Daniele,

I tried to redo the tutorial in 2D hBN http://www.yambo-code.org/wiki/index.ph ... n_parallel
for the band gap with a small Xd damping range of 0.00001 eV, and ended up with a gap increase of about 1.8 eV(!) in comparison to 0.1 eV smearing.

My final indirect hBN G0W0 gap on a 16x16x1 grid with 15 angstrom layer distance, 200 bands and 0.00001 eV smearing is 8.1 eV.
By contrast for the same setup with 0.1 eV (default in YAMBO) I obtain 6.3 eV.

So, is this sizable increase of the band gap when sending damping to zero really physical ?
I checked it for a couple of other systems and observed in all systems a moderate to strong smearing effect on the band gaps.

Best wishes
Martin

[Daniele Varsano]

Dear Martin,
Thanks for reporting. A question: when reducing the screening you are also changing the number of frequencies? The two quantities are somehow related as finally it is an integration. Reducing the screening you will have sharper peaks in the dielectric function and you need more frequencies to sample it properly. Similarly as for smearing in occupation for metals and k point sampling.

Daniele

[martinspenke]

Dear Daniele,

many thanks for your quick response.

I checked the screening smearing 0.00001 eV for different number of frequencies, and obtained contradictory results regarding the indirect band gap.

For example : for 0.00001 eV and 30 frequencies the gap is about 8 eV.
for 0.00001 eV and 200 frequencies the gap is 7.254 eV (which seems to be reasonable but still by 1.0 eV larger than the set up 0.1 eV and 30 frequencies); however when I further increase the number of frequencies up to 400 frequencies, the gap becomes suddenly very small and about 2 eV (basically I get non-sense).

So I have some considerable oscillations in my results by increasing frequency sampling.

I further checked the effect of smearing and frequency sampling for the helium atom using the super-cell approach; and there I also observe a large impact of smearing but I do NOT have oscillations with respect to the number of frequencies.
For helium convergence is smooth and non-problematic; however for hBN convergence behavior with respect to number of frequencies is very very oscillating.

Best wishes,
Martin

[Daniele Varsano]

Dear Martin,
thanks for reporting.

I'm not convinced that reducing the smearing so much is the best way to proceed.
I try to explain, I can anyway be wrong:
In real axis integration, the GW calculation is indeed a convolution integral over frequencies. The W frequency dependency is given by the dielectric matrix eps_GG'(omega). In case it is a structured function (e.g. many localized peaks), considering a very small broadening you have a series of delta-like peaks which are not easy to integrate. In this case also considering many frequencies you can sample or not the peaks resulting in very oscillating behavior with respect to the number of frequencies.
In this sense a larger smearing (maybe not too large as you pointed out) it is just a way to make life easier and helps in performing correctly the convolution.

Please note that the values reported in the tutorial, I'm not sure they are the final converged results. They have been prepared for the school with the aim to be didactic and to be completed in a reasonable time, so no long heavy runs.

Best,

Daniele