# Indirect to direct band gap transition in SUPERCELLS?

My compound under investigation are cubic and construct corresponding 2x2x2 supercell. Properties like optical and mechanical seem to be correct as expected. However a problem arises in their electronic band structures where it changes from indirect band gap to direct band gap semiconductor. Is this even possible? Can anyone enlighten me with some literature where such findings occur in pristine supercells?

• Welcome to our forum! How the calculated optical properties are ok but the bands change behavior? Also, why a supercell?
– Camps
Sep 5, 2023 at 10:43
• Thank you sir for the comment. I am supposed to study the doping of certain compounds where supercells are required. So, for test calculation, I have performed bulk properties as well as in their supercells for consistency testing. However, I am currently unable to give proper reply to as to why this inconsistency occurs Sep 5, 2023 at 11:04

This is allowed, in fact you can almost always construct a supercell where this has to happen. Consider the band eigenvalue at k-point $$\vec{k}=(0,0,\frac{1}{p})$$ in a given unit cell; if I now make a $$1\times 1\times p$$ supercell, that k-point in my original cell maps to $$\vec{k}^\prime=(0,0,0)=\Gamma$$ in the supercell. This is true for any choice of $$p$$, and more generally all the k-points are remapped between the cells.
If I have a primitive cell with a VBM at $$\Gamma$$ and a CBM at any other rational k-point, I can always construct a supercell where that k-point would map to $$\Gamma$$ and the transition would appear to be direct. However, if you compute the direct transition probability in the supercell you will still discover that it is zero, because the states will still have the correct phase relation and there will be no overlap under the dipole operator. In other words, all the properties are correct, we just can't immediately tell from a bandstructure plot because the supercell k-point doesn't uniquely determine the phase any more.