about calculate bandstructure of the graphene nanoribbon

[yongjunwinwin]

In using the ATK, I found that the bandstructure of GNR depends on the lengh of the ribbon, when using the example in the tutorials, I got the same bandstructure in the example, but when I increase the length with the same settings, I got a totally different result. Is that right? or I have to change the settings like the k points sampling?

[Anders Blom]

I assume you increase the length by repeating the unit cell along Z. In that case your Brillouin zone changes as well, and you get what is know as zone folding.

There is no point in computing the band structure for a repeated unit cell, it just takes longer time and the results become confusing because of the zone folding.

[yongjunwinwin]

Yes！I did repeat the unite cell along Z to increase the length of the ribbon, thanks for your answer!
But a question raises that because I want to stimulate the model of a molecule absorbed on the surface of the ribbon,but just using the unit cell of the ribbon cannot include the whole molecule. If increase the length of the ribbon may distort the bandstructure, then what should I do to get the accurate bandstructure of the model I mentioned?

[Anders Blom]

The band structure is not the relevant quantity to compute in that situation.

[yongjunwinwin]

Then what can I do to analysis the band gap or doping effect?And to note, I have see many papers features the electronic properties like band structructure of such model,  how can they manage that? is the bandstructure is not calculated through the model?

[Anders Blom]

Well, of course if you want to study specifically the band gap and some impurity levels, then it's fine to use the approach you mentioned. The molecule also breaks the periodicity, so you get a new Brillouin zone, if you wish. In this case the zone folding just means you get more bands, but it doesn't affect the gap.

You just have to be aware that you cannot directly compare the bands to those of the single unit cell of the ribbon. However, in any case you had better look at the density of states more, perhaps, than the band structure.

[mldavidhuang]

Thanks for your reply! That is really instructive!

[yongjunwinwin]

Thank you very much!