Small G0W0 gap for BN nanotubes

[aramirezt]

Hello everyone, I am trying to calculate the GW correction to BN(5,0). I saw that the values reported for BNNTs with close diameter are within 7-8 eV (PRL. 126104 (2006) ). However I get a value of only 4.1 ev for GW-gap while in DFT-gap it is 2.13 in my calculations. I have converged the GW value respect to EXXRLvcs , QpntsRXp, NGsBlkXp. I have some doubts respect to about how many BndsRnXp and GbndRnge are enough, because if I increase this numbers the gap drecrease more, or what I am doing wrong. I attached my input and outputs. Thanks in advance.

[Daniele Varsano]

Dear Alfredo,
I'm not sure your results are wrong, as I'm not sure that the values indicated as continuum absorption onset in the paper you cited refers to the GW direct gap. Moreover a GW correction of 400% looks me quite strange.
In this paper: PHYSICAL REVIEW B68, 035427 2003 a rough estimation indicates a qp gap smaller than 4eV (even if it is just a rough estimation), moreover I can see here: PHYSICAL REVIEW B71, 165402 2005 that passing from (5,0) to (6,0) there is a difference of 0.5 eV at LDA level and it could reflect in a bigger difference at GW level.
Another issue about the onset, I can see here:
Appl. Phys. A 78, 1157–1167 (2004)
that for the (6,0) tube, the onset in absorption at RPA level is found around 4.eV to be compared with a DFT gap of around 2.68 (if that calculations agree with the PRB mentioned before), so it bring me to suspect that what is considered as onset in the PRL, is the absorption onset of an RPA calculations when the QP energies where plugged in the response function.
You can try to look for previous GW calculations on your system in order to compare your values, if any.
In any case, please note that the GW correction strongly depend on your supercell volume (highly increasing, and slowly converging with respect the vacuum size). This is also shown in the paper you mentioned. So a bias could be present, even if I've seen you used a cutoff in the coulomb potential and it helps for convergence.

This are just some quick speculations, that could be wrong, as I'm not familiar with this system.
Hope it helps,
Best,

Daniele

[aramirezt]

Thanks for your comments. I will check some literature and try bulk system or others tubes to compare.

[jmmorbec]

Hello everyone.

I am not working with BN nanotubes, but I have a doubt with respect to the convergence of BndsRnXp and GbndRnge. I noticed that the band gap of my system (bulk Ta3N5) decreases a lot when I increase GbndRnge (going below the experimental value). If I am considering 300 bands in scf/nscf calculations (I have 64 occupied bands), how should I decide about GbndRange?

I really appreciate any help.

[Daniele Varsano]

Dear Juliana,
the convergence of GW gap with respect unoccupied bands, in general, is very slow. In many case many unoccupied states are needed (it is a sum over state inserted to fulfill completeness). As it is a convergence variable, and in line of principle should be infinite, it has to be increased until the results does not change anymore in the range of accuracy you aim. So, if you calculated 300 bands and the using all the bands the gap still decrease considerably, you need to raise the unoccupied bands in your nscf calculations, and push the convergence in GW.. Direct comparison with the experimental value it is not the good criterium to stop. GW, especially in the G^0W^0 framework, even if in most cases does work very well, it is still an approximation, so it is not guaranteed that will match the experimental results. Anyway the source of the discrepancies could be several (ground state structure, inappropriate ground state electronic structure (xc funtional) etc. etc.).

Best regards,

Daniele

[jmmorbec]

Thank you, Daniele, for this clear explanation.