Hello,
I calculated CsSnBr3 electronic band gap for unit cell and supercell. While the band gap was at R point for unit cell, at Gama point for supercell. The band gap are at different point for each other. Is it possible?
Thanks
Yes, it is possible for the band gap to occur at different points in the Brillouin zone (BZ) for the unit cell and supercell calculations. The position of the band gap in the BZ is determined by the symmetry of the crystal structure and the electronic states within it.
In your specific example, CsSnBr3, the unit cell calculation resulted in a band gap at the R point, while the supercell calculation yielded a band gap at the Gamma (Γ) point. This discrepancy can arise due to the different symmetries exhibited by the unit cell and supercell structures.
When the supercell is created by replicating the unit cell, it can introduce additional periodicity or alter the symmetry of the crystal structure. This modification can lead to a change in the electronic states and, consequently, the location of the band gap in the Brillouin zone.
Yes, this is actually expected and it's called Brillouin zone folding. In your case, R point should be (0.5,0.5,0.5) in your unit cell. If you construct a 2x2x2 supercell your R point will be folded into the Gamma point. It's very important to note that electronic and structurally speaking your system is IDENTICAL, the band are just folded. Your band gap should be the same as well. There are procedures to unfold band structures back to the unit cell, which makes the comparison between unit cell and supercell much more clear. After unfolding what you will obtain are spectral functions. You may take a look at Figure 3a of M. Zacharias et al., Physical Review B 102, 045126 (2020) for an example of how an unfolded band structure compares to the unit cell.
Most of the big codes such as Quantum-Espresso and VASP have built-in ways to do it. You shall take a look in some tutorials.
Cheers.
Just to avoid a possible confusion with my previous reply. The unit and supercell will only be electronically identical if one is just perfectly doubled, tripled and etc. That means that in this situation, after the unfolding your supercell bands are going to essentially overlap the unit cell one.
If there are structural differences on the supercell due to tilting, distortions or something else, after the unfolding there will be changes in relation to the unit cell.
This can be important in your context, since the unit cell of a perovskite system without tilting will be smaller than one with tilting, for example. So if you want to compare the two systems you'll have to unfold the tilted one(supercell).
Cheers.
Bruno Cucco Thank you for your comment. Actually, can you information about that how can i do this problem in files ? ı used VASP code. Should i do this anyone in KPOINTS file or any ? This material is the cubic phase
I think the best i can do it's share a link with some tutorials on how to do it, because there is a procedure behind it with a couple steps.
In this GitHub link you'll find some information on how to do it with VASP using some scripts: https://github.com/QijingZheng/VaspBandUnfolding
If you want to have a proper look into the theory behind it and what is band folding I strongly recommend you this paper:
V. Popescu and A. Zunger, “Extracting E versus K effective band structure from supercell calculations on alloys and impurities”, Phys. Rev. B 85, 085201 (2012)
Good luck!
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