Different bandstructures for unit cell and supercell

[Inaoton]

Hello,
             I have done band structure calculation of a crystal unit cell and further create a super cell of the the unit cell and then  calculated its corresponding band structure. I found that the  band gap was found at R-point in unit cell and G-point in super  cell. Can someone explain this?

[Petr Khomyakov]

I suppose it is due to band folding, as the Brillouin zone of the supercell is smaller than that of the corresponding unit cell. You may search for band folding "effect" in the web, or have a look at any textbook on Solid State Physics.

[Inaoton]

Thank for your help.
Another question is that does  supercell gives lesser band gap than its corresponding primitive cell?
I got a band gap of 1.36 eV in supercell while for primitive I got 2.24.
I used the same calculator settings except the k-points.

[Petr Khomyakov]

The band gap should not change, provided that you have converged your calculation with respect to the k-point grid density, or at least have used consistent k-grids in the unit and supercell calculations.

[Inaoton]

Sir
          I have set up the calculations after converging all the parameters separately for unit cell and super cell. The super cell is a 2x2x2 repetition of the unit cell. After performing geometry optimizations,  I am not able to get the band gaps equal(unit cell with direct band gap 2.22eV and super cell with indirect band gap 1.53eV). Could you please give me me some clues that is causing it?
The scripts and band structures  are attached.

[Petr Khomyakov]

This may happen because the relaxed supercell structure does not need to be the same as that for the corresponding relaxed unit cell structure. An illustrative example would be a surface reconstruction when using a large supercell structure allows one to find a lower energy surface, compared to the energy of the surface modeled with a primitive cell.

[Inaoton]

Sir
            Both are relaxed structures, one is a super cell of the other. But the band gap should be around the same for both , right?
Even when I calculated the dielectric function for both the structures separately, I observed that the imaginary part was following the same pattern as that of the primitive cell with absorption edges around  1.5 eV.  But the only difference was in the value of dielectric constant of the real part, the value smaller in the super cell.
           Are calculation settings the only one which alter the result in super cell calculations?

          I have created the super cell to dope with other atoms. Should I try VCA method?

[Petr Khomyakov]

As I said, it depends if the relaxed supercell structure can be built by just repeating the relaxed primitive cell structure. If so, the gap should be the same.

Otherwise, you have an additional reconstruction upon optimizing the supercell structure, and the band gap does not need to be the same for the two systems.

[Inaoton]

Thanks for clarification. I did this one also. I am still not  getting the solution.
        Let me sum up for once .
1.     I took a unit cell and calculated the  band gap ( 12 x 12 x 12 k point sampling and cut off  440 Hartree )  to be 2.24 eV.
2.     Next I did ion relaxation of the above structure at the above settings, I got band gap 2.22 eV.
3.    Then  I make a 2 x 2 x 2 super cell from the unrelaxed unit cell  and found the band gap (6  x 6 x 6 k point and 400 Hartree) to be
         1.36  eV.
4.     The above  super cell was relaxed to give a band gap of 1.53 eV.
5.      Now the relaxed unit cell was repeated to make a super cell which gives a band gap of 1.61 eV  before and after ion relaxation (with both settings  440 Hartree calculated with  6  x 6 x 6 k and 12 x 12 x 12 k point  separately ).
So even the supercell  constructed using the relaxed unit cell does not give same band gap as that of the corresponding unit cell.
             

[Inaoton]

Otherwise, you have an additional reconstruction upon optimizing the supercell structure, and the band gap does not need to be the same for the two systems.

So which band structure should I consider?
1. The supercell which is a just a repetition of optimized unit cell
                 OR
2. The optimized structure of super cell in 1.

[Petr Khomyakov]

I would say that you have to consider using the optimized supercell, provided that there is a reconstruction indeed.