A tight biinding calcualtion of graphene like structure

[mohsen2002]

I plot the tight binding bandstructure of graphene. There is a very good aggrement with ab-inition calculation in the valence band. but there is a problem in the non-localized orbitals of conduction band especially in the Gama(0,0) point.
Any suggestion is appreciated.

 

[jpr0]

If you're comparing the results of a DFT calculation to a phenomenological nearest-neighbour tight-binding Hamiltonian then you should find that in the tight-binding band structure the conduction and valence bands are symmetric about the Dirac point (about the line E=0).

From a DFT calculation you should find that actually the two bands are not symmetric about this energy - the valence band appears to be flatter than the conduction band as far as I remember. I think this was due to the basis states not being mutually orthogonal (you should look in the Dresselhaus-Dresselhaus book on nanotubes).

If you want to reproduce the asymmetry between the two bands in the tight-binding Hamiltonian you can include a small next-nearest-neighbour coupling (say one tenth of the nearest-neighbour coupling).

If that doesn't help maybe you could just show us some plots and indicate what is wrong with them.

 

[mohsen2002]

Thanks for your reply,
The effect of next nearest neighbor on the band structure is very small. My question is:
Why the mail problem is around the Gama (Kx=Ky=0) point in FBZ?
Here is a sample fitting for hexagonal Boron Nitride. (black line are DFT result and red line as a tight binding calculation)