Weird GNR I-V characteristic

[johnnie]

Hello,

I am new to ATK, I used Siesta before for atomic simulations and transport simulations.

I'm trying to obtain the ideal 2-port GNR I-V characteristics using the script attached (of course by changing the bias voltage from 0V to 0.5V). Since this is an ideal device, I expect to get linear I-V characteristics  with a resistance close to resistance quantum. However, I get an alternating I-V characteristics like

V (V)     I (A)

0           0
0.1V      36.4u
0.2V      42.6u
0.3V      38.7u
0.4V      34.8u
0.5V      37.5u

My question is: what's wrong with the attached script. And second question is: can you please give an example GNR ideal 2-port device script with a linear I-V characteristics?

Best regards

[Anders Blom]

In general, as commented on multiple times in this context, it doesn't make much sense to compute the transmission spectrum this way for a perfectly periodic structure at finite bias. See for instance http://quantumwise.com/forum/index.php?topic=1987.msg9714#msg9714.

If you want to extrapolate the zero bias transmission to get a linear response I-V curve, I suggest you have a look at http://quantumwise.com/publications/tutorials/mini-tutorials/167.

[johnnie]

Thanks Mr. Anders, I'll have a look at that.

[johnnie]

Hi again,

When I simulate the graphene ribbon structure, I get the aformentioned weird I-V characteristic but when I simulate the same structure as a graphene sheet, the I-V characteristics is normal I mean the ballistic resistance of 6.5k exists in the ideal graphene sheet device. Is this caused from the GNR itself or a computation problem?

Regards

[Anders Blom]

Maybe, but actually I don't understand the question. The basic point is that an ideal ballistic conductor is "uninteresting" and trivial to compute at finite bias.

[johnnie]

I understand that there's nothing new about an ideal device. But my question is: "An ideal device made of graphene sheet displays a quantum resistance of 6.5k as expected. However another ideal device made of GNR does not show this quantum resistance. Is this something about GNRs or is there a computation problem about GNRs in ATK?"

Thanks again.

[Anders Blom]

No, there is no problem with ATK. The problem is that you cannot apply a finite bias to a perfectly periodic structure because there is nowhere for the voltage to drop - there is no resistance. But you can still easily compute the conductance of the perfect GNR, by just computing the zero-bias transmission spectrum, either with a complete device setup (takes more time) or as a periodic structure (very fast, just the like the tutorial I referred to describes).

[johnnie]

Hi again and thanks for your reply.

You said that a finite bias cannot be applied to a perfectly periodic structure. However, when I apply finite bias to a perfect graphene sheet I get the resistance quantum of 6.5k using ATK as it should be. What's wrong with this?

Thanks again.

[Anders Blom]

I don't know exactly how you ran the simulation - I suppose it can work sometimes (and for 2d/3d systems generally better than for 1d). The problem is of course not that it's unphysical to apply a finite bias to a perfect system, but that the algorithms in ATK are designed for the non-perfect case, because there needs to be a place in the structure where the finite voltage can naturally drop. So, the most correct result you can hope to obtain is the linear response current based on the zero-bias transmission, which you might as well compute from the bulk system, rather than wasting time on the full device calculation.