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Fun with graphene

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Dear Sir,
         In case of repeated cells (at least 4-5 times) it is possible to get a sine kind wave and then we can say that it is the amplitude of wave but for smaller system, like unit cell ( no repetition or 2 repetition) I am not getting proper sinus-shape wave, then what should be the interpretation of that amplitude? Please help me.


Anders Blom:
The fundamental requirement for a sensible bandstructure calculation is that the structure is completely periodic. So any number of repetitions will be fine. The "buckler" plugin always maintains the periodicity of the system, so any number of periods you choose is also fine. Beyond that, it's really just a matter of what geometry you want to study.

It's difficult to imagine that the period of the ripples in graphene would be of a similar magnitude as the unit cell itself. It that were the case, we would probably not be speaking as much about graphene today as we do. For the most part, graphene stays very flat on length scales up to many repetitions of the unit cell. The amplitude of the ripples depicted in various "artists representations" of buckled graphene is also most likely grossly exaggerated. So if you really want to look at realistically rippled graphene, I would first of all look for real experimental results, and if my suspicion holds (I haven't checked myself, I must admit), the structure to build is 10-10 repetitions with a wave period of 1-4, and an amplitude significantly smaller than 1 Å.

Finally, I would also expect that the ripples have a small effect on many properties (not all, of course). Look for instance at our tutorial (http://quantumwise.com/documents/tutorials/latest/GrapheneExplorer/index.html/chap.twister.html#sect1.twister.conductance) where we show the conductance as function of the twist angle of a graphene nanoribbon - the twist at most affects the Fermi-level transmission by 10%. To me, this indicates that the properties of graphene are not crucially dependent on minor details but rather the overall shape of the graphene, a fact supported also by the ability of simple nearest-neighbor tight-binding models to give very similar results as DFT. I assume that the whole "point" of graphene is the sp2 bonding, and that picture is not really broken when you bend, ripple, maime or otherwise abuse the material. Of course, this only holds to a certain point (once you have bent the graphene into a nanotube, clearly things change) and needs to be studied carefully, but this also means that one has to be careful to set up realistic calculations, else the results become meaningless.

Dear Anders,

I have downloaded the plugin but I couldn't find them in the Builder/Add Custom ! could you please tell me where it is installed ?

Many thanks

Anders Blom:
Downloading is not enough, you also have to install them in VNL, and then restart VNL. See the instructions in my original post. However, the plugins will not appear in the "Add" menu, they will be under "Coordinate Tools".

Dear Anders,

Could you please provide some references of the mathematical formulas that you used for buckling, twisting and also tube wrapper. I'd like to have an estimation of the effect of the parameters such as angles.



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