Complex band of graphene

[NH]

Dear,

In ATK, I suppose complex band calculation is done along C-axis. How do I define the unit cell to calculate the complex bandstructure of graphene (especially gated bilayer graphene with a gap) along the G-K direction?

Thanks a lot!

[Anders Blom]

To be a bit more specific, it's computed along the reciprocal C direction, yes.

Since the K point lies at (1/3,1/3,0) in the Brillouin zone, you should cleave the crystal with Miller indices 110 to get the C axis to point in the correct direction. This is easy to do in the Builder, you just insert graphene from the Database (possibly graphite, for bilayer) and then use "Builder>Surface (Cleaver)".

Now the complex band structure will be computed in a supercell where G-K lies on kC. The supercell is a bit bigger so actually K will be a point on "G-Z", not an end-point, but that doesn't matter.

A full scripts is attached for the calculation - I then took the scripts from the complex band structure tutorial to make nice 2D and 3D plots, also attached. The whole calculation takes about 30 seconds using a Slater-Koster sp3d5s* basis set and 5001 energy points in the complex band structure.

[NH]

Thanks for your help.
I will try it.