gw calculation is always more accurate than LDA?

[jiangx3]

Dear All,

I want to calculate the band gap of graphene. For graphene, k=-1/3 1/3 0.0 is the band gap=0 point. After the GW calculation, I found that the LDA gap is almost zero but the gw band gap is much larger which conflicts the true value(graphene should be closed gap in this k point).



k = -0.333 0.333 0.000
Band E0 <VxcLDA> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E
4 -2.493 -13.594 -12.723 -0.379 0.771 -0.297 -13.214 0.380 -2.113
5 -2.489 -13.565 -11.042 -1.705 0.771 -0.297 -12.934 0.631 -1.858

E^0_gap 0.004
E^GW_gap 0.255
DeltaE^GW_gap 0.251

Thanks in advance for your reply!

Best regards,
XUeping Jiang

[Robin]

Dear Jiang,

I guess the problem is on your side. Actually, one paper in PRL calculated the GW band structure of Graphene, and a metal was obtained there.

See: Ab Initio GW Many-body Effects in Graphene, PRL 101, 226405 (2008) or http://prl.aps.org/pdf/PRL/v101/i22/e226405

The coordinates of the K point you mentioned is different from the usual one, (-0.333, 0.667, 0.000).

Sincerely,
Guangfu Luo

[jiangx3]

Dear Guangfu,
Thanks so much for your reply!

The k point which contributes 0 band gap should be the point (2/3,1/3,0.0), but I find gw would not give this point directly and I find if I take ngkpt=12 12 1 then I can find a k point (-1/3 1/3 0.0) which is equal to the point (2/3,1/3,0.0). Also I see that the LDA band gap there is almost zero.

I don't understand why the k point (-0.333, 0.667, 0.000) would lead to zero band gap, and can you should me this point in the reciprocal cell of graphene? Also how can we cut the reciprocal cell to get this k point? I mean what 'ngkpt' and shiftk should we take?

Thanks and Best regards,
Xueping jiang

[mverstra]

your k-point is correct, but you probably need to converge everything much more tightly (unit cell size as well, numbre of bands...). Check the details of the PRL calculation - it's not easy to do GW on graphene.

matthieu

[jiangx3]

Dear Matthieu,

I have the following questions for the convergence study:

1. for the geometry optimization, is it from the LDA calculation?
2. for the convergence study, can we do it as the tutorial did? I mean save the result of the first calculation and use it in the following convergence study? Is it the normal way?

Thanks and Best regards,
XUeping Jiang

[Hantarto]

Dear Abinit GW team,
I also encounter band gap opening in calculating graphene wih GW. At k=0.333 0.333 0, E^0_gap & E^GW_gap information are missing, but certainly it opens the band gap. What does it mean ?
Thank you & best regards,
Hantarto

Here is part of the output text :

Perturbative Calculation

k = 0.000 0.000 0.000
Band E0 <VxcLDA> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E
4 -6.359 -17.258 -21.116 3.194 0.818 -0.223 -17.801 -0.543 -6.902
5 0.059 -3.105 -0.913 -1.560 0.915 -0.093 -2.527 0.578 0.637

E^0_gap 6.418
E^GW_gap 7.540
DeltaE^GW_gap 1.121

k = 0.333 0.333 0.000
Band E0 <VxcLDA> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E
4 -3.343 -13.935 -14.400 0.163 0.816 -0.226 -14.182 -0.246 -3.590
5 -3.343 -13.935 -10.382 -0.780 0.816 -0.225 -11.672 2.263 -1.080

k = 0.333 0.667 0.000
Band E0 <VxcLDA> SigX SigC(E0) Z dSigC/dE Sig(E) E-E0 E
4 -7.938 -13.164 -16.825 2.622 0.791 -0.265 -13.985 -0.821 -8.759
5 1.539 -13.978 -7.496 -3.164 0.799 -0.252 -11.328 2.650 4.188

E^0_gap 9.477
E^GW_gap 12.947
DeltaE^GW_gap 3.470