Bandstructure of 5 atom Germanene AC Nanoribbon

[agoldsto]

I'm doing research on the properties of Germanene nanoribbons and encountered a result that my advisor found questionable. For the four atom AC nanoribbon, the bandgap is roughly 0.8eV, and we're trying to shrink that. However when I increase the width by a single atom, it decreases to 0.08eV. My advisor says this is too small to be accurate, and mentioned using the quantum mechanical model in ATK. It's not a problem I've been able to solve by hand, so what options are available for a more comprehensive band structure analysis? Where can I find information on adding the quantum mechanical model to my calculation, and does this bandgap seem reasonable? Any help would be appreciated.

For my bandstructure calculator, in the new calculator box I used the Extended Huckel with no SCF iteration and dirichlet boundary conditions for the regions bounded by hydrogen. For the bandstructure I used the simple bandstructure box and 200 points per segment. I shared pictures of my results below. I used geometry optimization to obtain the buckling, and share pictures of both the 4 atom nanoribbon and 5 atom one, with bandstructures for both.

[Daniele Stradi]

Hi,

the Extended Huckel method might indeed give incorrect results if the target structure is very different from those used for the original derivation of the Huckel parameters. I would suggest instead to use DFT, either by using the LCAOCalculator or the PlaneWaveCalculator. DFT is more transferable and does not suffer the transferability problem of Extended Huckel, and as such it will give more physically correct trends.

Also, if you target is individual nanoribbons, I would suggest to modify the structure as follow:
1) Use periodic boundary conditions for the two unit cell planes normal to the B direction and increase the length of the B vector by a factor 2-3,  to ensure that the  periodic replicas of the ribbons are effectively decoupled. 
2) Make sure that the length of the A vector is at least 20 Angstrom, and use mixed (Dirichlet+Neumann) boundary conditions for the two unit cell planes normal to the A direction.

Best,
Daniele

[agoldsto]

I tried the simulations using both DFT and Extended Huckle. Using your recommendations, they now provide the same bandgap, but all the bands are flat. I assume this is because the single cell of the nanoribbon is decoupled from the neighboring iterations?

[Petr Khomyakov]

If z-axis is perpendicular to a nanoribbon plane, one should expect no band dispersion, as you say because of weak interaction between neighboring, periodic images of the nanoribbon monolayer.