Brillouin zone for Nanosheets

[marmotte]

I have a question about the BZ of nano-sheet when we perform a BS calculation. I saw that some points are automatically selected by ATK suc as G, X, Z. For a nanosheet or graphene monolayer, what is the best BZ ? is it depending on the structure of the bulk, for example what its the correct BZ for ZnO nanosheet (constructed from a hexagonal ZnO) ? I have the same question for the nanoribbons ?

I will appreciate much your help.

(Moderator edit: Corrected spelling of Brillouin to help searching)

[Anders Blom]

For structures represented only by a UnitCell, i.e. not a particular Bravais lattice class like FaceCenteredCube etc, there are not really any well-defined symmetry points, so ATK just offers XYZ which are dummy labels for the points (½,0,0), (0,½,0) and (0,0,½) in fractional reciprocal lattice coordinates.

For a nanoribbon, which is a 1D structure, normally only G-Z (provided the ribbon is oriented along Z) makes sense, since there is no dispersion in any other direction.

For a sheet it is a bit trickier since it's a supercell or a hexagonal structure (for ZnO and graphene at least), so in addition to the symmetry points being difficult, there will be zone folding. Therefore one should take care, and really think what the purpose of the calculation is. If you want the band structure, just calculate it for the primitive, hexagonal cell, before making a supercell.

[marmotte]

Dear Anders,

Thank you for your reply. I can accept that for Nanoribbons, we need only G-Z for the BZ. But let us imagine that I want to have the band structure of the nanosheet with a hole ( see the paper dx.doi.org/10.1021/jp2125069) how I can force the BS to consider the BZ of G-M-K-G ? I really need to get the BS for this BZ.
Best regards,

[Anders Blom]

In this case it's of course different, because you now have a new unit cell, which is large but still hexagonal. The trick here is to build the structure as hexagonal from the beginning, and after the repetition convert the lattice class back to hexagonal.

To do this for graphene is trivial, for ZnO you need to think just a little bit What I do is

• Insert graphene from the database
• Change the two atoms to Zn and O
• Change the lattice constant to 3.29 Å (1.90*sqrt(3), where 1.9 is the Zn-O bond length found in the paper you quoted)
• Repeat 6x6
• Open Bulk Tools>Lattice Parameters and switch the lattice class to hexagonal
• Modify as needed, e.g. make holes or add atoms
• If you now send to Script Generator you will see GMKA available as symmetry points, but note that they correspond to the lattice with a=b=19.74 Å

[marmotte]

Dear Anders,

Thank you very much. It is running now.

best