the I-V characteristics of graphene: zigzag vs armchair?

[fee]

I wanna calculate the transport properties of graphene using atk 2008.10. Two kinds of unit cell were used to set up the two-probe system, which the z-direction of one was along with zigzag edges and that of the other one along with armchair edges. The structure of both two were infinite graphene.However, the I-V characteristics were totally different. I don't know why. Can anybody tell me the reason? Thank you.

[kstokbro]

If you use a lot of k-points in the direction perpendicular to the transport direction, the transmission spectrum at zero bias of the two structures should be similar.
see also other post on the forum.
Note that ATK2008.10 is no longer supported, and we recommend upgrading.

[fee]

yes, the transmission spectrum is similar, but why are the I-V characteristics are so different? The current of unit cell along zigzag edges is nineteen orders higher than that of unit cell along armchair edges. It's incredible.

If you use a lot of k-points in the direction perpendicular to the transport direction, the transmission spectrum at zero bias of the two structures should be similar.
see also other post on the forum.
Note that ATK2008.10 is no longer supported, and we recommend upgrading.

[Anders Blom]

There is not enough information in your post to answer the question. For instance, what is the k-point sampling for transmission and the self-consistent calculation? If the transmission spectra are the same then the current will be the same.

[fee]

The k point is different in the scf process and transmission calculation. In the process of self consistence, the k point is set to be (27, 1, 9).The higher point (27,1,15) was also tested to get the same results of I-V characteristics in both units. So I can't understand why the I-V characteristics are so different for the two kinds of unit cell even the k-point has been proved to be enough.
For transmission calculation, the kpoint is set to be (10,10), which usually is not enough, but the  transmission  calculation of higher k-point was not convergence. However, the the transmission spectra ( (10,10) k point) show similar step-like spectra, like the picture.

There is not enough information in your post to answer the question. For instance, what is the k-point sampling for transmission and the self-consistent calculation? If the transmission spectra are the same then the current will be the same.

[Anders Blom]

27 k-points should indeed be enough for the scf loop, however you need perhaps 200 points for the transmission. Note that you don't need 200x200, there is no dispersion in Y, you should do (200x1).

[fee]

Thank you! I will try to recalculate the transmission.
But if the scf calculation is right, how can I get such different results of I-V characteristics of graphene for just different unit cells? I can't understand it from physics. And I notice many other people in the forum are trying to calculate the transport properties of graphene, interestingly most of them set up graphene models using the zigzag unit cell. Should the I-V characteristics dependent on the unit cell?

27 k-points should indeed be enough for the scf loop, however you need perhaps 200 points for the transmission. Note that you don't need 200x200, there is no dispersion in Y, you should do (200x1).

[Anders Blom]

Your transmission spectrum with 10 kpoints is just not correct, that's why. It has a gap around the Fermi level which is not physical, we know for a fact that graphene is metallic, hence immediately you can see something is wrong there, and it's because your k-point sampling doesn't capture the K point where all the low-energy transmission occurs.

I'm not sure how you got the linear I-V curve for the Z "edge", if the current is evaluated from the transmission spectrum you showed in the later post you should have zero current at least up to 0.7 V bias or so. You must have used different k-points for the current and transmission?

[fee]

yes, the k-point for the current and transmission is different. So I changed the k-point to (51,1,9) for scf and (51,1) for transmission then. The current keep the same as before : graphene with zigzag unit cell has a much higher current compared to graphene with armchair unit cell. But the transmisson spectra changed a lot, see below.

The k-point of transmission spectra and current need to be equivalent,is that right?

Your transmission spectrum with 10 kpoints is just not correct, that's why. It has a gap around the Fermi level which is not physical, we know for a fact that graphene is metallic, hence immediately you can see something is wrong there, and it's because your k-point sampling doesn't capture the K point where all the low-energy transmission occurs.

I'm not sure how you got the linear I-V curve for the Z "edge", if the current is evaluated from the transmission spectrum you showed in the later post you should have zero current at least up to 0.7 V bias or so. You must have used different k-points for the current and transmission?

[kstokbro]

In ATK2008.10 there is a command called current, it makes a separate transmission spectrum calculation which is used to calculate the current.
For a finite temperature the current depends on exactly how much of the transmission spectrum is used, in particular for systems with a gap like graphene this method is not accurate enough.

In ATK11.2 the currents is calculated directly from the transmission spectrum, thus, you dont need an extra transmission spectrum calculation, you have control over which transmission spectrum is used for the current calculation and you can calculate it for different temperatures without any overhead.
Thus, it would be best for you to upgrade to ATK11.2 to perform the calculation, and you need more k-points, the transmission spectrum should look like a wedge, i.e. rise linearly from the fermi level.

[nori]

The k-point of transmission spectra and current need to be equivalent,is that right?

Exactly.

You should be more careful about the k-point sampling for the armchair because Dirac point is not located at Gamma point.
(On the other hand, You can easily include gamma point in the case of the zigzag by using odd k points)
That's why you should analyse the k-resolved transmission coefficient at the fermi level in order to check that Dirac point indeed is included.