questions about surface layers

[beark]

Hello, I've just start to learn ATK recently and I found the manipulation of "surface layers" confusing. In the "atomic manipulator" module of the VNL program, one can set the number of either left or right surface layers. One could then drag the two-probe configuration to the "nanolanguage scripter" module to get a .py file. Actually, the .py file is the only need file for the atk program. But I found that there is only scattering elements which are the combination of surface layers and scattering region such as a molecular. Does it means we don't treat "surface layers" explicitly and separately, we treat the central region which contains the "surface layers" as a whole?

BTW:I have learned in some articles that the surface layers act as the screening layers to protect the electrode from influenced by the scattering region. Then how can I test whether the screening is enough? Do I need to inscrease the number of surface layer until my interest current or transmission spectrum converged?

Many thanks

[Anders Blom]

Welcome to the Forum, beark!

This is certainly one of the trickier concepts in ATK. From your well formulated question I can see that you are on your way to understanding it, however

From the setup perspective, yes, there are only 3 components: left electrode, central regions, and right electrode. The Atomic Manipulator treats the surface layers internally a bit different, in order to make it easier for the user to add and remove layers.

The physical relevance of the surface layers is however distinctly different from the rest of the scattering region. As you state yourself, their role is to screen the influence of the real scattering part (the molecule, nanotube, interface layers, whatever constitutes the real middle part of the device) such that the fundamental approximation (that the electrodes are bulk-like) holds.

In principle yes, you need to converge the results in the number of layers, but this is quite expensive. In practice, you will hopefully get a feeling for your own types of systems and how efficient they are at screening. Some quantities that will help you assess the quality of the screening is to compute the voltage drop (search the Forum for several good discussions on this) or the effective potential, and check if it is smooth across the boundaries between the electrodes and the scattering region.

Large bias requires more screening. 1D or quasi-1D systems screen less efficiently than whole metal surface, but fortunately it's less expensive to increase the number of screening layers for chains and nanotubes etc.

Hope this answers your questions, but just keep asking if something is still unclear!

Good luck with ATK, I hope you will enjoy the program!

[beark]

Thank you very much! 
Now I may express my understanding that in the basic approximation, the left(right ) electrode is exactly bulk-like (the charge and the spin distributions are just as they are in the periodic bulk),  and physically, if we investigate the physics quantities (effective potential, charge ,spin .etc) of surface layers, they will gradually (smoothly )change to their bulk values when they get more and more closer to the corresponding electrode part.  Thus if the screening is not enough, a sharp voltage drop across the boundary will appear. However, I wonder in some conditions like calculation about spin transport, is it necessary to  check the smoothness of other quantities like the spin distribution?
In addition, several days ago, I did a spin polarized calculation of graphene ribbon. While the surface layers and the middle part are the same (homogeneous) ， how to distinguish between them? and I don't know if I want to calculate the MPSH, while part should I contain, maybe all the central region?
Furthmore, The initial spin of the electrode is zero and it kept zero after electrode calculation. The initial spin of surface layers  is also set zero and the middle part is set to be ferromagnetic. However, after I finished the self-consistent calculation at 0.0eV(bias), the surface layer also becomes ferromagnetic and the spin polarization intensity is the same as the middle part. Therefore a sharp spin distribution change appears between the surface layers and electrode. Is it because the number of surface layers is too small? But I think even if I increase the number of surface layers, they will still be polarized and the polarization intensity will be the same as the middle part. Or it is a wrong model?

[Nordland]

Hey Beark.

I think you are on the right track, however you should never use the initial spin zero for a spin calculation as it is a saddle point, and hence it will remain so for any bulk calculation, therefore you should always introduced some spin-polarization into the system by using perhaps a small value 0.005 or similar.

[beark]

Thank you! Nordland.
I will try to set the spin-polarization to a small value and see the result.

En, in my opinion, saddle point means it isn't a real local minimal. The energy will decrease if the variables change along certain path. Why did you say the spin will remain so for any bulk calculation? Is it due to the algorithm that the program adopt?

[Nordland]

In order to introduce any spin-polarization in DFT calculation, the potential must be a slightly difference for up and down electrons. Since the potential is sum of the the hartree potential (always unpolarized) and the exchange correlation potential, then exchange correlation must be polarized, however the exchange correlation potential is determined by the density solely.

However all the exchange correlation potential is constructed in such a way, that in the limit that if the system is unpolarized, then exchange correlation potential will also be unpolarized.

Therefore it goes like this, you set up a initial density, that has spin-components, but the polarization ( the spin up density minus the spin down density) is zero in all regions of space. Therefore the exchange correlation potential will become unpolarized, and hence the hamiltonian will in effect be unpolarized as up and down electrons feels the same potential, hence when you solve the schrodinger equation, you will end up with a density matrix that is in effect unpolarized, and hence you will get a new density that is unpolarized, and then your exchange correlation will again become unpolarized, and then it contiunes repeating the exact same pattern.

Perhaps saddle point is not the most correct word to use, but in a sense it gives the correct picture. If we converged the calculation with initial spin-polarization set to zero, we will end up with a minimum energy, however it is not the true minimum,
as we have not searched in all paths, but only in a certain path.

Perhaps the correct word could be that the zero spin-polarization density is a sub-space, and hence all transformations will still make the density living in this sub-space, and therefore in terms of total spin-polarization it becomes a fix-point.

I hope you can understand my ramblings

[beark]

Oh, I see. Start from spin-unpolarized, end to spin-unpolarized. The spin polarization just cann't go out the circle. What a pity。。。

Thanks again
 

[Nordland]

Well fear not - It is only a technical thing in the construction of the Kohn-Sham ExchangeCorrelation, and hence we are allowed
to cheat without comprising the results. Simple add a very small spin-polarization to a single atom, if the systems minimum is unpolarized, it will quickly remove this small pertubation, if the system is true nature spin-polarized, it will quickly spread to the entire system.

[beark]

Yes. In my last post, I just want to say that due to technique considersation, we will get a spin unpolarized result if we initial it as spin unploarized.