About band structure calculation

[hokhani]

My question is more general but I explain it by a simple example i.e. graphene and tight binding method. I solved energy dispersion of graphene with tight binding by the two ways: First, I took graphene as a lattice with the two basis atoms A and B. In the second way, I took graphene as a lattice with four atoms, the two A and the two B atoms. In other words, I took the two unit cell as one and solve the problem. As expected, in the second way, I obtained a Brillouin zone half the first one but with larger number of bands. I don't know whether or not this approach is correct in treating the electronic properties of solids. Because for example using the second way in the insulators we may obtain the smaller gap for the insulator so that the material may no longer be an insulator! Could anyone please help me with that?

 

[Useful nucleus]

You will not get a smaller band gap, but certainly you will get more bands as you mentioned. There is nothing wrong in calculating the band structure for a supercell rather than the primitive cell.

In fact there are methods to unfold the band calculated using a supercell to retrieve the band structure of the primitive cell.

 

[hokhani]

You will not get a smaller band gap, but certainly you will get more bands as you mentioned. There is nothing wrong in calculating the band structure for a supercell rather than the primitive cell.

In fact there are methods to unfold the band calculated using a supercell to retrieve the band structure of the primitive cell.

Ok. Thanks. Bringing the states which are out of the smaller FBZ inside, results in new bands.