Band structure of cobalt adsorbed graphene

[saroj]

I have done the computations of band structure of cobalt adsorbed graphene. In 3x3 supercell of cobalt adsorbed (one cobalt atom) graphne, there is opening of band that is gap between conduction and valence band but there is no gap in 4x4 supercell of cobalt adsorbed graphene. I've done this in DFT implemented with quantum espresso. what is reason for the difference?

 

[Hypersphere]

Well, I'm not sure how sensitive DFT is to these things or how the specific material is supposed to behave, but in other simulations one often needs to pay attention to boundary conditions (you can check if you have an even-odd effect when changing cell size) and to finite size effects. For the latter, the finite size of the system may open up a gap which disappears at some point when taking the thermodynamic limit. The only way around this is to measure the gap for a number of system sizes and see if there's a trend or not (you may want more than two data points though), a practice called finite size scaling. Could it be either of these things?

 

[t!m]

These are also different physical systems, due to the implied periodicity of these calculations. The first has a density of one Co atom per 3x3 cell of graphene, versus one Co atom per 4x4 cell of graphene - so the second implies a lower density of Co ad-atoms, and therefore a reduced Co-Co interaction. Thus the answer to "which is correct" depends on the physical system you are interested in, i.e. what physical Co density. Other minor things like how you position the Co over the C atoms of graphene can also make a difference ...