ABINIT Discussion Forums

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

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

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

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

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

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