Regarding Graphene Device Tutorial (zigzag-armchair-zigzag)

[praanshu]

Hi,

In the tutorial of the graphene nanoribbon device with zigzag contacts and armchair graphene as the centre, I want to plot electronDifferencePotential through the middle of the device however the 1D projector can only plot along axes or provide and avarage across 2 axes. To be able to plot the quantities in the device region of the structure however I would need to understand how the Potential is stored. For instance since my device is in the centre of the box I only need the values at a = 5 A (or 0.5 fractional coordinates). Next I'd need to know the potential across a straight line in the B-C plane with slope 30 degrees. Can you please guide me as to how this can be done.

Thanks and regards,
Praanshu

[Jess Wellendorff]

Did you consider using
a) the "through point" projection option in the 1D Projector.
b) the cutplane representation of your grid in the Viewer, where you can select both position and angle of the cutplane plot (see attached PNG).

[praanshu]

Dear sir,

Thank you for the reply, though my predicament is a bit different. To explain the same consider the following (attached) figure.  I want to obtain the 1D projection of the Potential along the lines as shown in the attached figure in white.

[Jess Wellendorff]

Very interesting idea. Working on an example of how to do it...

[Jess Wellendorff]

Attached is a script that plots the ElectronDifferenceDensity along a path which is specified in cartesian coordinates (nc file produced by nanoribbon_device.py is input). The end points of the path is given by the central region edges and cartesian coordinates of selected atoms (indices 35 and 83). The "evaluate()" method is used to evaluate (rellay: interpolate ) the GridValues data in any cartesian point. Note that this is a strictly 1D evaluation of the electron difference density, so no averaging in any directions. Black dots indicate where the 1D path shifts direction. See the PNG. Note that the x-axis in the plot is currently the C-coordinate of the path, and not the actual distance along the path. Changing this should be fairly simple.

Hope this is useful. See also the reference manual http://www.quantumwise.com/documents/manuals/latest/ReferenceManual/index.html/ref.electrondifferencedensity.html

[praanshu]

Thanks Jess,

This works perfectly. I just wanted to know is there some kind of linear interpolation being done to evaluate the density at the points specified in the script (xyz format)? Since it is not necessary that points on the paths be grid points (as suggested by the script itself) the output curve has some unexpected noise, is this due to some hard matching rules like evaluating density at the closest grid point for each point specified in the file.

[Jess Wellendorff]

I am not sure what noise you are referring to, but perhaps the plot improves if you decrease the distance between the sampled points ("dc" parameter in the plotting script). I am not sure if the GridValues interpolation is linear or to higher order, but I am confident that it does not simply return the value from the closest grid point. Some sophisticated interpolation is most certainly used. We use the same functionality for plotting isosurfaces etc, where efficient interpolation is crucial...

[kanna]

Hi Jess,
Just a clarification.
From what I understand the ElectronDifferenceDensity refers to the distribution of density along the C direction, and since we find that there is a finite spacing between the atoms we find an oscillatory behavior in the middle part of the plot. But on a more fundamental level is this oscillatory behavior due to difference between the self consistent value which is the output of the NEGF converged solution and the superposition of atomic valence densities which are decaying exponentially (so the charge is zero away from the ion centre while the Density from NEGF is not necessarily zero since it dies down slower)?
Also on another note: to study the effect of bias on a device (say 1V) : we need ElectrostaticDifferencePotential(at 2V) - ElectrostaticDifferencePotential(at 1V). Am I correct in my understanding ?

Thanks
Kanna

[Jess Wellendorff]

The ElectronDifferenceDensity is not restricted to the C-direction. It is a 3D grid covering all of your simulation cell, but you can project the 3D grid onto different planes and lines in space.  More precisely, it is the difference between the self-consistent valence charge density and the superposition of atomic valence densities. As such, it tells about charge rearrangements due to interactions between the atoms. So yes, the oscillations in the middle parts of the device shows that something is "going on" there

The ElectrostaticDifferencePotential is simply the Hartree potential corresponding to the ElectronDifferencePotential. It should differ at different biases, particularly near the electrodes.

[kanna]

Thanks Jess.