Dear Marcos, Consider a 1D system. Imagine that we have the dispersion plot for a primitive cell for k from 0 to kmax. For a 2x supercell, we have all the same bands, but now we need to squeeze them into a reciprocal cell (not the IBZ, but simply the complete 1st Brillouin zone) half the original size. On the other hand, vectors k and k+kmax/2 are now equivalent (for the supercell case). So, if we just take the k>kmax/2 part of the plot for the unit cell and shift it left by kmax/2, we should get the picture for the supercell's 1st BZ. It would now be twice as small & contain twice as many bands.
So your extra band crossing is actually the same one, but these bands belong to the other unit cell in your supercell. It all looks more clear when applied to some simple system like the pi band of polyacetylene. Hope this helps! 2008/6/17 Marcos Verissimo Alves <[EMAIL PROTECTED]>: > Hi all, > > I have a question on band plotting within supercells. Could be stupid, but > I am a bit confused by some results I am obtaining. > > Let's take a unit cell of graphene. When I plot the band structure, I get > the usual band structure. > > Now, let's take a 2x2 supercell of graphene. The supercell vectors in > reciprocal space are halved with respect to those of the unit cell, as > they should (I checked it by adding them to the the siesta output), so the > coordinates of the K-points and M-points (the points of high symmetry of > the BZ) should also be halved, shouldn't they? But it seems that they are > not - I have to specify points whose coordinates are doubled respect to > those of the unit cell, no matter if I choose the scaling of the > coordinates to be pi/a or to be given fractionally in terms of the > reciprocal lattice vectors (just like we specify fractional coordinates > for the C atoms as (0,0,0) and > (1/3, 1/3, 0) for graphene). > > Another thing that is funny is the fact that, for the 2x2 supercell, I get > a band crossing between K and Gamma that shouldn't be there. That I should > get more bands for the supercell, I understand. However, I am not sure I > should get these extra band crossing, which could lead me to a wrong > conclusion about the nature of the material (metallic instead of > semimetallic, if I were to judge only from the band structure). > > Am I doing some really stupid conceptual error? I am attaching the input > files and a graph of the band structure in eps format. The bands for the > 2x2 > supercell have been displaced by +0.1 eV to make visualization a bit > easier. The flags for band lines are in the bottom of the fdf files. > Calculations were done with SZP to save time, but of course this would not > influence the problem at all. > > > Cheers, > > Marcos > > > -- > Dr. Marcos Verissimo Alves > Post-Doctoral Fellow > Unité de Physico-Chimie et de Physique des Matériaux (PCPM) > Université Catholique de Louvain > 1 Place Croix du Sud, B-1348 > Louvain-la-Neuve > Belgique > > ------ > > Gort, Klaatu barada nikto. Klaatu barada nikto. Klaatu barada nikto.
