two-probe setup in new version of ATK(2015.1)

[zhangguangping]

Dear ATK supporters,

I recently read the manual of ATK-2015.1, and I found it seemed that there were a lot of difference between the new version and older versions (ATK-2008.10), of which I most interested was the setup for two-probe systems.
As is seen on page 23 of the manual of ATK-2015.1, figure 4.1 gives an illustration for a two-probe systems (also see the attachement Fig1).

As I know, the two probe system consists three parts: (1) the left electrode (in the left blue rectangle the ABC stacking in Fig1), (2) the central region (in the red rectangle in Fig1), and (3) the right electrode (in the right blue rectangle the ABC stacking in Fig1). The electron density for left and right electrodes are calcualted separately using periodic boudaries at three directions at the beginning of ATK two-probe calcualtion. And then, it will do a so called equivalent bulk calculation (left electrode + central region + right electrode) to get an initial electron density for the subsequent NEGF self-consistent calculation. Last, the NEGF self-consistent calculation. In this step, the electron density in the left and right electrodes is kept the same as in the separate bulk calculation. The electron density for the whole central region is self-consistent calculated. All the gold atoms in  the central region, we call screening atom layers.  And this is what is implemented in older version of ATK (say ATK 2008.10). Am I right?

However, in the new version (2015.1), why we call the left- and right-most three layers of gold atom in the central region the electrode extension? Must the left (right) electrode extension one copy of the left (right) electrode? As I see in the VNL-2015.1, one can only reduce the gold atom layers at eacb side of the central region to a copy of the left/right electrode as seen in Fig2 (if you use ABCABC in the electrode, one can only reduce this to 6 layers at each side). Why? How if I just want to use only 2 layers (suppose this can give a good screening.) of gold atom at each side of the central region for the screening effect while using a ABC stacking for both left and right electrode?

With best regards,

Guangping Zhang

[Anders Blom]

I could write a long reply, and will be happy to, but perhaps this older document answers almost all your queries already:
http://quantumwise.com/documents/tutorials/latest/UpgradeGuide/index.html/chap.upgrade.html#sect1.upgrade.twoprobe
Otherwise please feel free to ask more and more detailed questions

[zhangguangping]

Dear Anders,

Thanks for your reply. It greatly helps.

However, I have yet a question on the new setup in new versions of ATK (2010.8 and later).

As seen in Fig1 and Fig2 the old and new setups of the two probe configuration. The webpage given illustrates the changes between old and new setups in terms of periodic systems in XY directions, and the left and right electrode are the same material and surface direction.

The problem is that if the two electrodes are made of two different materials or although the same material but with different surface directions, e.g. (111) and (100), there should be same vacumm space in the leftmost or rightmost of the interaction region to aviod a direction interaction of the left electrode copy and the right electrode copy in the equivalent bulk calculation. This would give a better initial guess for the density matrix to the NEGF calculation from an equivalent bulk calculation. To be much better, some buffer layers may be used outside the electrode copy to simulate the electrodes to give faster convergence in the subsequent NEGF self-consistent. And the enssential different between old and new setups are whether the electrodes (or electrode copies) in the interaction region enter the self-consistent: (1) the system in the NEGF self-consistent cycles are both interaction regions (i.e., the same atom numbers); (2) the left and right electrodes in the interaction region for old setup in Fig1 do not update their quantities while the left and right electrode copies in the interaction region for new setup in Fig2 update, indeed we can consider this as a different boundary positions where the electrochemical potentials match with the bulk like electrode. If more screening layers used in the old setup in Fig 1, it will give the exactly result with that of the new setup, while bring an obviously increased compuational burden compared with the extra compuation in new setup in Fig2.

Therefore, back to the question, how to add a vacumm at the leftmost or rightmost in the interaction region, or even more, buffer layers in case of two different electrodes?
For the first attempt, is it enough to enlarge the z component of vector_c  for central_region_lattice? If so, is there problem for the matching between the interaction region and the electrodes?

With best regards,

Guangping Zhang

[Anders Blom]

The short answer is, that if you have a heterogeneous system (different left/right electrodes) you should simply avoid using the equivalent bulk (EB) step. The EB method is also quite bad for scaling in parallel, because it's a large bulk calculation, so often going for the two-probe solution immediately can be faster, even if it needs a bit more steps in the device calculation to converge, but it parallelizes a lot better.

Note however that the computational effort is exactly the same in the old and new approaches. In the old code, the electrodes were "secretly" added to the configuration just like you have the electrode copies explicitly in the central region configuration today.

[zhangguangping]

The short answer is, that if you have a heterogeneous system (different left/right electrodes) you should simply avoid using the equivalent bulk (EB) step. The EB method is also quite bad for scaling in parallel, because it's a large bulk calculation, so often going for the two-probe solution immediately can be faster, even if it needs a bit more steps in the device calculation to converge, but it parallelizes a lot better.

Note however that the computational effort is exactly the same in the old and new approaches. In the old code, the electrodes were "secretly" added to the configuration just like you have the electrode copies explicitly in the central region configuration today.

Dear Anders,

Thanks for your reply.

You mean if I use a heterogeneous system, the caculation should be conducted directly to the NEGF sefl-consistent after the calculations of the electrodes?

Thanks so much.

With best regards,

Guangping Zhang

[Anders Blom]

Right. You choose the NeutralAtoms option instead of the default EquivalentBulk in "Device algorithm parameters".

[zhangguangping]

Thanks a lot.

Guangping Zhang

[zhangguangping]

Dear Anders Blom,

As mentioned in the manual, there is control option for the density matrix in electrode copy in DeviceAlgorithmParameters class. That is, ElectrodeConstraint.Off or ElectrodeConstraint.DensityMatrix. If the ElectrodeConstraint.DensityMatrix option is used, one has to set an electrode_constraint_length, over which the atoms in the electrode copy within the central region will be initialized with a linear combination of the converged density matrix of the electrodes and the equivalent bulk density matrix. The weight of the electrode density matrix is 1 at the boundary and 0 at the distance electrode_constraint length from the boundary.

Here it use the word "initialized" NOT constrain. So the question is, since in new setup of device in new version of ATK as we discussed above, the quantities in the whole interaction region is fully self-consistent, the  density matrix in the electrode copy will also be fully self-consistent. Therefore, what is the differnece beweent ElectrodeConstraint.Off or ElectrodeConstraint.DensityMatrix to  the reuslts, except they give two different initial guesses for the density matrix at the begining of the NEGF self-consistent calcualtion?

With best regards,

Guangping Zhang

[Anders Blom]

Right, there is no direct influence on the results of this on the results, only indirect via the initial condition.

[zhangguangping]

Dear Anders Blom,

As seen in the attachment, the Green function G_M needs to be iterated self-consistent. In ATK 2015, the left electrode extension and right electrode extension both contribute to the screening. So, does the G_M now contains them? That is, the G_M now is for the central region not only the scattering region, am I right?

With best regards,

/Guangping Zhang

[Jess Wellendorff]

Yes, the Green's function is calculated and iterated for the full central region, not only the scattering region. The only difference between the scattering region and an electrode extension is that the former can be different from the electrodes (thereby providing electron scattering), while the latter must be periodic images of the neighboring electrode.

[zhangguangping]

Yes, the Green's function is calculated and iterated for the full central region, not only the scattering region. The only difference between the scattering region and an electrode extension is that the former can be different from the electrodes (thereby providing electron scattering), while the latter must be periodic images of the neighboring electrode.

Thanks for your kind reply.

With best regards,

/Guangping Zhang