self-energy probelm

[Jenny]

Hi, all.

I used ATk-13.8.1 to do a calculation of a molecular with two electrodes device. And I found that NEGF was applied here which the self-energy would be chosen to calculation the transmission property of the system.

Would you please explain to me the different matrix of the three self-energy used here?
Recursion
Krylov
Direct

And under what condition, should we use the different self-energy?

Jenny

[Anders Blom]

Krylov is often faster but uses some approximations that sometimes (but far from always) can lead to some problems with negative transmission (which is unphysical). Recursion is a standard workhorse which always works, Direct basically gives always the same results but is a bit slower (mostly still included in ATK for historical reasons).

Ideally all give the same result, but they differ somewhat numerically, and how they perform, and to some extent also how they scale in parallel.

[Jenny]

Krylov is often faster but uses some approximations that sometimes (but far from always) can lead to some problems with negative transmission (which is unphysical). Recursion is a standard workhorse which always works, Direct basically gives always the same results but is a bit slower (mostly still included in ATK for historical reasons).

Ideally all give the same result, but they differ somewhat numerically, and how they perform, and to some extent also how they scale in parallel.

Dr. Anders Blom,

Thank you for your reply. But I got different results with Recursion or with Krylov self energy. And with Direct self-energy, I got the result which is same as Krylov. In this case, how should I choose?

BTW, can you introduce some paper or books which talks about the self energy calculation methods which are used in Quantumwise?

Thanks a lot.

Jenny

[Anders Blom]

How different? Just numerically different, or really different? What version of ATK? What system...?

[Umberto Martinez]

BTW, can you introduce some paper or books which talks about the self energy calculation methods which are used in Quantumwise?

Start from the ATK Reference Manual where usage examples and notes, with references, are reported.
http://www.quantumwise.com/documents/manuals/latest/ReferenceManual

check the SelfEnergyCalculators entries.

[Jenny]

How different? Just numerically different, or really different? What version of ATK? What system...?

Dr. Anders Blom,

Please find my system as attached. And I got the T=6.99971 for Recursion, and T=6 for the other two methods. I guess this is not a numerical different. And also, Atk 13.8.1 is what I'm using.

Thank you very much.

Jenny

[Umberto Martinez]

I am not sure how you get T but your structure looks wrong (H atoms not bonded to the CNT).
Is this what you actually want to simulate?

[Jenny]

I am not sure how you get T but your structure looks wrong (H atoms not bonded to the CNT).
Is this what you actually want to simulate?

Dear Dr. Umberto Martinez,

This configuration is carbon with aluminum (not H) system which is optimized with a unit cell to max force 0.05eV/A. And yes, I guess the bonding may be weak or not exist.
And I actually do want to simulate the system of CNT with Al, would you please give me some suggestion?

Thanks a lot.

Jenny

[Anders Blom]

I think it would help to assess your question if you post the results also, not just a number but the full transmission spectrum plot. The other crucial question is, where is your scattering? This looks like a perfect periodic structure, which is kind of confirmed by the fact that you get perfect integer transmission. So, it's a fairly uninteresting system, from a device perspective, and in fact you could compute the transmission just from the single unit cell.

[Jenny]

I think it would help to assess your question if you post the results also, not just a number but the full transmission spectrum plot. The other crucial question is, where is your scattering? This looks like a perfect periodic structure, which is kind of confirmed by the fact that you get perfect integer transmission. So, it's a fairly uninteresting system, from a device perspective, and in fact you could compute the transmission just from the single unit cell.

Dear Dr. Anders Blom,

Thank you for your reply. Yes, the device is perfect as you mentioned. And here I attached the transmission spectrum plot with three different self-energy.

Jenny

[Anders Blom]

You can try to lower the infinitesimal. This problem is, probably, restricted to cases where there is no scattering, i.e. for a perfectly periodic device - which is a bad idea anyway.

[Jenny]

You can try to lower the infinitesimal. This problem is, probably, restricted to cases where there is no scattering, i.e. for a perfectly periodic device - which is a bad idea anyway.

Dear Dr. Blom,

I'm a little bit confused. Why you say that it's a bad idea to look into a perfect system without scattering? Do you mean that the perfect system is unreal in reality so it's useless to discuss about it?

Thanks a lot.

Jenny

[Anders Blom]

I mean two things.

1) A perfectly periodic structure is not a device, it's a material. You can't use it for anything electronically, it's not a transistor or a diode or a sensor, you can't turn it on or off.
2) Computing the coherent, elastic transmission at finite bias of a perfectly periodic structure is ill-defined. There is no scattering and therefore no natural place for the voltage to drop. To have any finite current the electrodes much be metallic (or highly doped semiconductors) and since it's periodic, so is now your central region. But it doesn't scatter, so the current will be very high. While it may work, it can also be hard to converge and there may be numerical instabilities. In any case, the algorithms in ATK are not designed for this case.

Also, related to 2, you don't need to set up a device to get the zero-bias transmission, you can get it directly from the minimal unit cell, as described in a tutorial.