In this tutorial, you will learn how to calculate the transport properties of a graphene nanoribbon with a distortion. The focus is, as for the silicon band structure tutorial, on showing the basic work flow in VNL, this time for a device. Thus, there will not be many discussions about the physics involved, neither of the system geometry nor the results.

A device geometry in ATK consists of two semi-infinite, periodic electrodes (the left/right electrode extends to infinity in the negative/positive Z direction, the transport direction), and a finite scattering region between them. The electrodes may be different, but should be periodic, and must have a common unit cell in the X/Y plane. The scattering region plus an extension copy of the two electrodes forms the central region, as depicted in the figure below.

The scattering region is the part of the central region which is different from the electrodes. In the picture above it's obvious that the molecule forms is most important ingredient of the scattering region. However, also the two outermost layers of the metal surfaces are in the scattering region, and are allowed to undergo reconstruction. Conversely, the three layers closest to the electrode (the electrode extensions) must remain bulk-like in terms of the their atomic positions. The electron density and effective potential is however self-consistently computed in the entire central region, and in the case of a finite-bias calculation, the bias is applied across the whole central region.

The easiest way to build a device is usually to define the central region as a periodic extension of the intended electrode materials, then modify the scattering region (possibly inserting additional atoms, molecules, layers, etc), and finally extract the electrodes. The device geometry can then be optimized. You will practice this procedure in this tutorial.

In this section you will first build a perfect graphene nanoribbon, and then make some changes to it in the Builder.

Open the Builder by clicking the icon on the main toolbar (when opening the Builder the first time in a session it can take a bit longer since it must initialize all addons).

When the Builder opens, click the Add button to the left of the stash area. From the menu that appears, choose Add Custom>Nanoribbon.

To make the calculations of this tutorial run as fast as possible, select a very narrow ribbon with chiral indices (2,2), corresponding to a zigzag graphene nanoribbon, 8 carbon atoms wide. Leave the other parameters are they are. You can click Preview to see how the ribbon will look, then click Build to add it to the stash.

In order to have a long enough ribbon to form the central region, you need to repeat the nanoribbon unit cell in the Z direction. To do this:

To make things more interesting, you will now make a Stone−Wales defect by rotating a bond 90 degrees.

The scattering region is now defined. To convert the system to a device, open Device From Bulk... under Device Tools.

The Builder will automatically try to detect the periodicity of the region closest to the edges of the central region, and suggest possible electrodes. In order for this to work, there should be at least one full period plus one additional layer of the electrode present in the central region.

The suggestion 7.38 Å generates a reasonable electrode for this system (3 periods of the nanoribbon cell), so click OK to create the device geometry.

Although the geometry at this point resembles the desired structure, the Stone−Wales defect was just created by rotating the bond. In reality, the bond length also changes, to accommodate the new double-pair of pentagons and heptagons which are formed when the bond is rotated.

For carbohydrates (and a few other systems), a very fast method to optimize the geometry is to use the Brenner potential which is part of the set of built-in classical calculators in ATK. This calculator is in fact accessible directly in the Builder.

Open the Coordinate Tools>Quick Optimizer plugins. Run 10 optimization steps by pressing the Run button.

After about 10 seconds the geometry will be updated. The forces are still quite large, but you can in principle press the button a few more times to get to a converged state (or, increase the maximum number of steps to 100 and then press Run).

It is however instructional to also consider a more general approach for optimizing device geometries, which also can be applied to other force calculation methods than the Brenner potential. Therefore, leave the system as it is, for now.

The final geometry optimization and further computation of the transmission spectrum will be set up in the Script Generator. Therefore, send the graphene ribbon to the Script Generator via the "Send To" button .

The calculation you will set up in this section is the following:

You will use the Brenner potential for the optimization also here, since it is pretty accurate for this system, and very fast. Then, you will use the semi-empirical extended Hückel model for the transport calculation, also to save some time. The work flow as such is however generic, and if you want you can replace either method, or both, by ATK-DFT.

This work flow, which thus combines two different calculation methods, can be realized in one single script in ATK. You will now set this up by following the instructions below.

Now you need to make sure that each script block is set up properly.

The script is now ready to be run, but first make sure to save it!

Run the calculation as you learned in the previous chapter, by dropping the script on the Job Manager (or send it to there from the Script Generator). It should take just a few minutes to finish.

When it finishes, locate the NetCDF file in the file browser. Note that in addition to the analysis quantities, there are three configurations stored in the file; the first one is the original geometry calculated with the Brenner potential, the second one is the optimized geometry, also calculated with the Brenner potential, and the third one is the converged Hückel transport calculation.

To view the transmission spectrum, select it and click the Plot button. For a perfect zigzag graphene nanoribbon, i.e. if you had not introduced the defect, you would see perfect, integer transmission at all energies. But in the system with the Stone−Wales defect the transmission is suppressed quite a lot, indicating strong scattering from the defect.

Specifically, there is a very noticeable dip in the spectrum at about 0.15 eV above the Fermi level, where the transmission is almost completely blocked. That is why this energy was selected for the second transmission pathway; it will now be interesting to see how the electron propagates at this energy.

Next view the transmission pathways. In the same way as other quantities, select it in the Result Browser and press Plot in the Result Viewer to plot it. It takes some time to render the plot, but when it is ready the volume of each arrow indicates the magnitude of the local transmission between each pair of atoms, the arrow and the color designates the direction of the electron flow.

The positions of the atoms are quite obviously deducible, but you can also add them explicitly by dropping the DeviceConfiguration with id gID002 onto the plot. The bonds hide the arrows, however, so the best option is to plot them as lines (right-click the plot and choose Properties to open the dialog).

Next open transmission pathway entry in the properties menu and change the color mode to Magnitude. This will change the coloring scheme to select the color based on the magnitude of the local transmission.

The final rendering of the transmission pathways at the two energies, zoomed in around the defect, will look as below:

As an exercise, it is recommended to redo the calculation above, but without the defect. The resulting transmission spectrum and transmission pathways are shown below, and can readily be compared to the results with the defect present.