Calculation the transport properties of graphene

[baizq]

Dear all,

is the anyone who has done calculation of the transport properties of bulk graphene using ATK? I have tried by using bulk graphene as electrode and bulk graphene(over 50 angstroms in the transport direction), but the properies look like nanoribbon, with quantized transmission spectrum. The IV curve is linear, which I think it is wrong. Is this because I use less kpoints or something wrong with setting?

help,help..............

[zh]

The gap of bulk graphene is zero. The linear behavior in the I-V curve may be reasonable.

[nori]

but the properies look like nanoribbon, with quantized transmission spectrum

I guess that your transmission spectrum is step-like but the values are not integer.
Is this right?
If so, your calculation is reasonable, graphene should have such a feature.

I think over 50 angstroms is too long and you can reduce the size along z direction to 7-10 angstroms.
(Maybe even the primitive cell size is OK, I'm not sure because I don't know the detailed algorithm though...)

[baizq]

but the properies look like nanoribbon, with quantized transmission spectrum

I guess that your transmission spectrum is step-like but the values are not integer.
Is this right?
If so, your calculation is reasonable, graphene should have such a feature.

I think over 50 angstroms is too long and you can reduce the size along z direction to 7-10 angstroms.
(Maybe even the primitive cell size is OK, I'm not sure because I don't know the detailed algorithm though...)

Hi nori,

Thanks for your reply...
Actually this question is posted by my labmate...Actually I even do not know what bulk graphene is.... Actually he has gone to Malaysia...Actually we can neglect this question...
Anyway...Thanks very much !!

baizq

[Anders Blom]

Just in case someone ends up here after searching

Converging the transmission spectrum of an infinite 2D graphene sheet is actually far from trivial. Although it may be sufficient with 9 or 15 in-plane k-points for the self-consistent loop (make sure to hit the K point), even with 200 points for the transmission spectrum the curve is rather jagged. So, such a system requires some careful considerations and patience, to ensure convergence of the results.

[yongjunwinwin]

I am a little confused about how to calculate the transmission spectrum of an infinite 2D graphene, what is the device model? In the origin calculation of transport properties the scattering region between two electrode is always finite. In fact I try to build the device model  from the bulk model shown in attachments but it doesn't work, so could you explain in more details about the model and the difference between the device model of graphene nanoribbon?

[zh]

The bulk graphene can also be described a supercell with orthogonal shape. The hexagonal one may be not suitable to build the device configuration of infinite system. Please  try the use of  orthogonal cell of graphene to build the device configuration.

[yongjunwinwin]

I construct the bulk graphene device from an orthogonal shape(seen in the attachment),is that right, I find the difference between bulk graphene device and graphene nanoribbon is that there is no vacuum space along Y axis, does it make any sense? Another question is that in the calculation of such model, is the center region treated as infinite or finite?

[zh]

I construct the bulk graphene device from an orthogonal shape(seen in the attachment),is that right, I find the difference between bulk graphene device and graphene nanoribbon is that there is no vacuum space along Y axis, does it make any sense? Another question is that in the calculation of such model, is the center region treated as infinite or finite?

It seems right. The configuration in your attachment makes sense.  Due to the periodic boundary along the y direction, the center region will be treated as infinite since no vacuum region along the y direction.

[yongjunwinwin]

Another question is how to set the k-sampling point for such system. I know for nanoribbon the reasonable k-sampling point is 1,1,100 for x,y,z for 1-D system, but when it comes to graphene, as the it is infinite along y, so the k-sampling point should be 1,9,9 or 1,9,100, is that sufficient? And the k-point sampling in transmission spectrum (1,1 for nA and nB) should also change? and how to change?

[zh]

The setup of k-grid along the y direction depends on the width of unit cell along the y direction.  Maybe the k-grid of 1x9x100 may be OK. The best way is to do the convergence of k-grid. Yes, the k-point sampling in the transmissions spectrum should be changed. You can refer to the example of Fe/MgO/Fe system the k-dependent transmission spectra.

[Anders Blom]

As pointed out in some other post on the Forum, infinite graphene is a bit trickier than a nanoribbon. While 9 k-points might be enough for the self-consistent loop, it should be checked (keep in mind the special nature of the K symmetry point, so a sampling of 10 or 9 or 11 points makes a big difference!) esp. when making a supercell. And then, for the transmission, be prepared to try 100, 200 or 400 points, otherwise the curves will be very jagged.

[mldavidhuang]

If a sampling of 9, 10, 11 will make a big difference, then according to which can we decide the right choice?
And I was a little confused with the k-point sampling in the basis set and the k-sampling in transmission spectrum, what is the difference between them, those two parameters have any relationship and why transmission spectrum don't need k in z axis, it seems we need more k-sampling for transmission spectrum and why? Just as mentioned by zh, in the example of Fe/MgO/Fe I found the k for calculatore is 6, 6,100 for x,y,z while in the transmission spectrum the k sampling is 30, 30 for kA and kB

[Anders Blom]

There is a physical reason why 9 k-points are better than 10, and also why 12 are better than 13 etc, which of course has to do with the point-like Fermi "surface" in graphene.

Indeed, the two k-point samplings are quite independent. In both cases the k-points are used to approximate an integral over the Brillouin zone, however the integrand is different, and depends differently on k. In the first case (the self-consistent loop) it's an expansion of the charge density, which rarely has any strong peaks or resonances as function of k, but may have a somewhat complicated functional form, and thus for some materials you only need 3x3 and for other 9x9 points. For the transmission spectrum, you may note in the FeMgO case that (in the parallel case) the majority transmission is well described with perhaps 11x11 points, but for the minority we may need 400x400 points. This is because the minority transmission has the character of resonant tunneling, with very sharp peaks which are hard to sample accurately.

In both situations, understanding the basic physics of the problem at hand is always essential.

[mldavidhuang]

Is that right that more k-point sampling in the self-consistent loop will be more time consuming,e.g. (9,9) will cost more time than (3,3) ?

And how to figure out what k-point sampling is better? Is it based on experience or is there any general rule that we can follow?