K-point in calculating graphene energy band gap

[syakirah]

Is there any specific  explanation on k-point value when calculating band gap of graphene using DFT? Why need to use na =3, nb = 3, nc =1 and na=9, nb=9, nc=1? And why on the Brillouin zone need to use G,M,K,G?
I really need help on this. Thank you.

[Jess Wellendorff]

The graphene Dirac cone is supposed to be located at the K-point, but you can of course choose to map out any k-point path in the Brillouin Zone that you like. The k-points used in the calculator should be sufficient to accurately sample the graphene electronic structure, so 9x9x1 is usually a good choice, but in general, the more k-points the better.

[syakirah]

Thank you Mr Wellendroff, to spend your time to answer my confusion. There's one more thing that confuses me. I'm sorry if I ask too much. When i run the simulation for 4 layers graphene using k-point 9x9x1 the result is quite strange. So, I run the simulation for 4 layers graphene using k-point 3x3x1 and the result came out better. Since you said that the higher k-point value the better, why it happen to be that the result of 3x3x1 is better than 9x9x1? Thank you.

[Jess Wellendorff]

I am not sure what you should expect for multi-layer graphene, but it looks like the BZ paths are not the same in the two images.

[syakirah]

okay, thank you.