Effect of supersize unit cell on band structure results

[Quantamania]

This is Quantamania with a new question.  I have been finishing up my dissertation work, and we are putting together results that were obtained using the graphene and h-BN layers in unit cells that are big enough to include 2x2 or more repetitions of atoms along the layers.  A 1x1 unit cell of these layers has 2 atoms and initial lattice dimensions, while a 2x2 unit cell has 8 atoms and double the lattice parameter length along the a-axis.

Here is my question: what are the effects of a 2x2 or larger unit cell on calculations of the resultant band structure originally computed for a 1x1 unit cell? 

So far, I have observed some significant changes compared to a 1x1 unit cell (the smallest cell needed for the models), even when using a 5x5x5 integration grid.  This will help me understand my new work and make connections between solid-state physics and quantum chemistry.

[Anders Blom]

The effect of using a larger unit cell than the primitive one is so-called zone folding. I'm not sure I can explain it in a simple way in a small forum post, but you'll certainly find information about it in standard textbooks on solid state physics.

[Quantamania]

Thanks, Anders Blom.

I had discussed folding with my mentor when we were comparing the 1x1 unit cell with the 3x3 unit cell, which has the Dirac cone point at a different place.  I might bring in some pictures to show you the results for graphene done in both cells.  We had been using the 2x2 cells to examine the eigenstates found in the 1x1 cell models, so we decided to do a small set of models in this format.

In the pictures I provided, all graphene layers have been computed with Gamma-K-M-Gamma for the band structure pathway and good quality integration grids.  Each model has the original graphene unit cell repeated to create larger cells.  The band structures are for 1x1, 2x2, and 3x3.  You can clearly see where the Dirac cone is, by looking for the X-shape intersecting the Fermi energy level at zero energy.  Does zone folding explain why the Dirac cone shifts crystal momentum in the 3x3 cell?

[Anders Blom]

yes