How to calculate the density of states (DOS) of isolated region in graphene?

[benhuzhou]

Hello
Everyone!
    I have a question about graphen, the two probe system is made of two electrodes and central molecule. The calculation of two probe system's DOS is very easy by using ATK. Howerer, I have read a lot of papers about calculation of DOS in isolated region, this is to say, no consider of two electrodes' affect. But I met a problem when I want to calculate the DOS of isolated region, when I drag the central molecule into VNL, I find that there is no DOS option in VNL, so, I want to know how to deal with this problem by using ATK?
Thanks!

[Anders Blom]

The question is a bit ambiguous. The concept of density of states applies to a system which is infinite and periodic in at least some directions. Therefore, there is no DOS for an isolated region... Or, well, you can of course say that a molecule has a spectrum of delta function-like spikes, which is like a DOS.

But perhaps you mean more something like the DOS for an infinite 2D sheet of graphene, or something like that?

[benhuzhou]

To Anders Blom
    Thank you very much for your answer! It is just like you said, I also think only the infinite system or periods systm have DOS. I got confused after I read a paper about grpahene (APL94-173110), if you have time, please read it,  and if you can not get this paper, I can sent it to you, please tell me your E-mail or QQ. There is a picture in this paper (Fig2(a)), I am sorry that  I do not know how to upload this picture.
Thank you again, Anders Blom.

[Anders Blom]

They don't explicitly write how they compute the "scattering region DOS" shown in the APL paper you mention (which is a very recent and nice application of ATK to graphene), but my guess is they perform a molecular calculation for the central region (more specifically, I think they use the MPSH functionality in ATK for this), and then plot the energy levels broadened by some Gaussian distribution. It doesn't really matter, they could just as well just have plotted the DOS as sharp molecular level, since the peaks are so narrow anyway.

[benhuzhou]

To Anders Blom:
    Thank you very much! According to your explanation, it means that  "scattering region DOS" just a broadened energy level. Therefor, if I want to calculate the  "scattering region DOS" , I only need drag the molecular( "scattering region" ) into VNL, then calculation its "Molecular energy spectrum". Is it right?  By the way, a similar problem which I have met, figure.2 showed the transmission a isolated CNT in the paper (CHIN.PHYS.LETT,Vol.25,No.9,3213(2008)), I do not know how to get this transmission of a isolated CNT by using VNL, since there are not transmission option when I just drag the scattering region molecular into VNL. I guess whether this result is obtained by the other soft or obtained by ATK script or not.
    Thanks again! ANders Blom.
    In addition, a question about bilayer graphene, if you have finished the design, please upload it, I want to design the bilayer graphene model according to your explanation.

[Anders Blom]

Yes and no

You approach will give the molecular energy levels of the isolated segment corresponding to the central region. This does not take into account the possible shifts of these levels induced by the coupling to the electrodes. Moreover, if you just take out a piece of graphene ribbon like that without considering the edge termination etc, you may get the wrong results. Also, the alignment of the level w.r.t. the Fermi level of the transmission spectrum will not be correct.

A more proper approach is to use the functionality in ATK called MPSH spectrum. Some details can be found in the manual, and you can also search the Forum for "MPSH". This way you get is the molecular spectrum taking into account the electrode coupling, normalized to a common Fermi level.

I have not made the bilayer structures, because as I said there it depends on how the edges should look like. If you have an idea about how you would like them, then I can look into the Python code to make it.

[benhuzhou]

To Anders Blom:
     Thank you very much! I will try to use the functionality in ATK.