Band Index of GNR

[GJK]

Hi,

After going through the tutorial http://quantumwise.com/documents/tutorials/latest/GrapheneBloch/index.html/chap.blochstates.html its crisp and clear to find the band index of valence and conduction band.But the band index is calculated for unit cell with even number of electrons.

So I am doubted with the following queries???

1.How to find the band index of valence and conduction band for a  GNR system containing odd number of electrons.(where special cases arise due to doping or adsorption).

2.From the various discussion  in  the forum its clear that band index and band structures are calculated for unit cell.But with special cases like adsorption (or) doping of GNR with various molecules (big or small) we can find the band structure for unit cell repeated(say 10 times along z direction).In that case (GNR with dopant or adsorbant)we get more number of electrons say for example 200,203 depending on cases.How to find the band index in these cases

If you say same procedure like as you have did for unit cell of ZGNR the band index for 200 electrons comes to be 100 for conduction band and 99 for valence band.Am I correct???But for the case of 203 electrons how to find the band index???

Waiting for the favorable suggestions after scrolling through the journals and forum???
 

[zh]

For a system with a gap and odd number of electron, one sometimes should perform the spin polarized calculations, rather than the non-spin polarization calculations.  In the spin polarized calculations for such system, the index for the valence (or conduction) bands can be easily counted:
1, 2, ...., (N_odd + 1)/2  for the valence bands of spin-up (or majority spin);
1, 2, ..., (N_odd - 1)/2 for the valence bands of spin-down (or minority spin)
(here the band index starts from 1)

In the non-spin polarized calculations  for such system:
1, 2, ...., (N_odd + 1)/2  for the valence bands


 

[GJK]

Thanks for the reply.
What about conduction band Mr.Zh
 For example if I have 201 electrons(for spin unpolarised calculation) in my system then my valence band  will be 101 and conduction band will be 102.Am I correct???

[zh]

Yes.

[Anders Blom]

For normal bulk materials, if you have an odd number of electrons your material will be metallic.

[GJK]

Ya absolutely Dr.Anders.Thanks for the comments.