bandgap underestimation in h-BN monolayer by G0W0 in Yambo?

[Dean]

Dear all,
I find an obvious bandgap underestimation in h-BN monolayer by G0W0 in Yambo, as shown in the following figure.
After many testes with same parameters, the G0W0 gap at K point is calculated to be 7.40 eV, which is 0.37 eV smaller than that (7.77 eV) from BerkelyGW code in Table SI in Ref. (Phys. Rev. Lett. 128, 047402)(https://journals.aps.org/prl/abstract/1 ... 128.047402)
Another problem is that small QP gap at K will lead to small optical gap from BSE calculations, as shown in Table SII in Ref. (Phys. Rev. Lett. 128, 047402). The first exciton energy is calculated to be 5.4-5.5 eV, obviously smaller than experimental results (5.9-6.0 eV).
So, my question how to improve my calculations to get correct QP gap and exciton energy consistent with experimental results in BN monolayer?
Thanks a lot.

[palful]

Dear Dean,

Yeah, it is not easy to obtain results exactly on top of experiments, especially for large band gap materials.

First of all, let me point out that in the table SI of the reference you cite, they get a similar result to yambo (7.40 eV) when they use the full-frequency approach for the dynamical screening, which is a more exact treatment (integrating explicitly over the frequency range) than the plasmon-pole approximation (PPA) employed to get the larger value of 7.77 eV.
I assume that you are using the plasmon pole approximation in Yambo: the reason why the two PPAs give different result may be that the codes implement two different schemes: Hybertsen-Louie PPA for BerkeleyGW and Godby-Needs PPA for Yambo. In a different system, it has been shown that HL-PPA may tend to overestimate results [Phys. Rev. B 84, 241201(R), 2011].

Second: when you talk about agreement with experiment, consider also that in monolayer hBN the gap renormalization effects due to electron-phonon interactions are very strong (reduction of ~0.5 eV). Considering that the luminescence emission peak is at ~6 eV and the (static) exciton binding energy is ~2 eV, we may estimate the "true" quasiparticle band gap only due to electronic correlations to be above 8 and below 8.5 eV. In the table SI, this is achieved only by the eigenvalue-self-consistent G0W0 approach of their Ref. [34], obtained with the code GPAW.

My suggestion, if you want to obtain reasonable results including the cancellation effects due to electron-phonon corrections that you are not explicitly computing, would be to try an eigenvalue-self-consistent G0W0 calculation in Yambo using the GN-PPA (or full frequency).

Cheers,
Fulvio

[Dean]

Dear palfyl,
Thanks for yiur reoly.
1.As you said, "electron-phonon interactions are very strong (reduction of ~0.5 eV).", is there any reference?
2. I have perform some limited eigenvalue-self-consistent GW calculations, which will increase QP gap by 0.3-0.4 eV. Then QP gap at K is still smaller than 8-8.5 eV.
3.Is there any tutorial using the full frequency in Yambo?
Thanks in advance.