Puzzle about the I-V characteristics of bilayer graphene compared with monolayer

[mldavidhuang]

I have done the calculation of bilayer gaphene and monolayer graphene, but I found that the current of bilayer graphene is larger than twice of monolayer graphene when the applied bias is low.(see the attachment)

This is strange because I think in any case the conductivity should be lower than parallel of two monolayer graphene because of interlayer scattering in bilayer system.

So I doubt the accuracy of my calculation, the script is attached, I beg help for checking anything wrong with my setting or is there any question with my assumption for I haven't seen any reference about such phenomenon.

[kstokbro]

You calculation seem technically correct.
The difference you observe must be related to a difference in the zero bias transmission spectrum, thus, I would investigate that in detail.

I think the bilayer graphene will have a different electronic structure compared to the single graphene, since there is an interaction between the two layers.
Thus, you must study and understand the electronic structure of the bilayer graphene

[mldavidhuang]

This is the zero bias transmision spectrum I get from my calculation, actually, I find it hard to understand the transmission spectrum of the bilayer from the band structure.

[kstokbro]

i think you forgot the attachment

[mldavidhuang]

Sorry for that！Here are the attachment

[kstokbro]

You see that the bilayer bandstructure is quite different from the single graphene bandstructure, this is reason for the different behaviour.

You need to include many more k points in transverse direction to get converged results for the transmission spectrum.

You might consider using user defined k-points around where the bands cross the fermi level.  I attach an example. Note this is just an example showing how it can be done, and you need to determine convergence you self.

[mldavidhuang]

Actually, there is something I don't quite understand in your code

Code

    k_min = 0.0
    k_max = 0.02
    k_n = 41

    k = numpy.array([(0,x,0) for x in numpy.linspace(k_min,k_max,k_n)])
    w = numpy.array([ 2 -(numpy.linalg.norm(i) == 0) for i  in k])

the k space you define are from (0,0,0) to (0,0.02,0) ,and what does w mean, I see it define as "kpoints_weights=w", this is what you mean by "user-define k-point around where the band cross the fermi level" ? because in my operation of ATK, I haven't met such settings. Could you explain a bit in detail to me ?

[kstokbro]

This is user specified k-points and corresponding weights. The purpose is to efficiently sample the region around the crossing of the fermi level. Thus, use a more efficient k-point sampling.

However,  you can also just increase the number of k-points in the MonkhorstPackGrid this will be equivalent, however, you will need more k-points.

[mldavidhuang]

Generally speaking, is more k-point the better the result? And how to test how much k-point is enough with the combination of accuracy and time-consuming ?

[kstokbro]

More k points is always better. You must increase the number of k-points until you results do not change any more.

[mldavidhuang]

Why the optimized interlayer distance of bi-layer Graphene is 3.08 Angstrom, but the value in other papers is around 3.34 Angstrom, is there anything wrong with my calculation ?

[amanpreet]

Hi ,
i have a quick qusetion for you.I am a new user of quantumwise.How to make bilayer or monolayer graphene ,is it done by starting from a graphene sheet(not ribbon) and repition in A direction two times. I want to study effect of graphene bilayer placed on different kind of substrates.

[Anders Blom]

You can build a larger sheet using the Custom Builder for nanoribbon but select "Sheet" instead of ribbon. This gives a monolayer; for bilayer (and perhaps also monolayer) it's better to start with graphite and repeat as needed in A and B, since there is a shift of coordinates (not just repeat) in the C direction.

[amanpreet]

Thanks for the reply.I am very much confused about how to decide the number of k points needed as they seemed to be the most important part of the calculation. I want to study effects of graphene layer placed on different kind of substrates(e.g SiC, GaAs, Si). How can we do such kind of epitaxial simulation in quantum wise.

[Anders Blom]

You need to test the k-points, but you need quite many, maybe 12x12 or 15x15 (in the plane) is a good starting point, then increase and see what happens.

Although it's in Japanese, Google translate can help you perhaps understand a bit of this case study of graphene on SiC: http://quantumwise.co.jp/example/fullerene/full-08.html