Graphene nanoribbon tutorial

[Anders Blom]

There is a new tutorial on the web site (http://quantumwise.com/publications/tutorials) on the topic of graphene nanoribbons that might be useful to some people

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I have several question due to graphene nanoribbon
1)Why there are hydrogen atoms,can we just delete it?
2)when we calculate energy bands for graphene nanoribbon then the paralel axes shows nothing
Should be gamma to K or how we know it?
3)How we can delete/replace atoms in "electrode" part?
4)Can u describe briefly what is transmission spectrum?I didnt find much from books.
There is no efficient data for x and y-axis .Y-axis says word "Transmission",x-axis says "E-Ef(Ev)"
Is there shown Fermi level?

[Anders Blom]

I have several question due to graphene nanoribbon
1)Why there are hydrogen atoms,can we just delete it?

You can delete them, but you would change the physics. They are used to saturate the dangling carbon bonds. All other carbon atoms in the graphene sheet have 3 nearest neighbors (carbon), but the edge atoms only 2. So to get all bonds saturated, you add hydrogen. This is a normal technique, and even if you don't see the hydrogen atoms in some plots in publications, that's often because they are just not shown.

2)when we calculate energy bands for graphene nanoribbon then the paralel axes shows nothing
Should be gamma to K or how we know it?

The default route for a periodic atom configuration (which the ribbons are) is k=(0,0,0) to k=(0,0,pi/a) where a is the period length in the Z direction. So it's not the K point for graphene, it's rather the Z point = (0,0,1) in fractional coordinates.

3)How we can delete/replace atoms in "electrode" part?

You basically have to do this by hand for the ribbons, either you want to change the existing structure or build some new structure from scratch. What exactly do you want to change?

4)Can u describe briefly what is transmission spectrum?I didnt find much from books.
There is no efficient data for x and y-axis .Y-axis says word "Transmission",x-axis says "E-Ef(Ev)"
Is there shown Fermi level?

A very good book on the subject (although the presentation is a bit broader than what ATK covers) is by S. Datta, Electronic Transport in Mesoscopic Systems.

The transmission spectrum T(E) measures the accumulated probability that the electrons will be transferred from incoming states on the left electrode to outgoing states on the right electrode. This "probability" can at any energy E be larger than 1 since it's a sum of contributions from all possible modes (essentially all different bands crossing the particular energy). Each mode can however only have probability 0<T<1; these are the transmission eigenvalues that you can compute with the function calculateTransmissionEigenvalues().

T has no unit (it's just a number), so therefore it's just written transmission. On the other axis, you have the energy. Since absolute energies have no meaning, the energy used in the evaluation is always taken relative the average Fermi energies Ef of the two electrodes. Please see this thread (the later posts) for a longer discussion on this topic.

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Thx for replies.

You basically have to do this by hand for the ribbons, either you want to change the existing structure or build some new structure from scratch. What exactly do you want to change?

I want to do some simple operation
graphene sheet with width=6 and rep=2
I want to replace some C atoms to B and N atoms.I dont want to change structure just simple atom replacement.Or another words i would like to see graphene sheet which is made in Boron or Nitrogen

If i go to the atomic manipulator i cant change nothing
Second chance i went to the Molecular Builder and did some replacements and back to the Manipulator and all seemed ok.But when i dragged it to the Nanolanguage scripter i didnt see quantities availability "ENERGY BANDS" for calculating.Instead of "Energy bands" i see "Energy Spectrum Molecular Energy spectrum"

Is there some theoretical  reason for that?


Second question about Energy density.In some cases it shows beatiful DOS diagramm,other cases it shows only preview for nanoscope?

[Anders Blom]

I want to do some simple operation
graphene sheet with width=6 and rep=2
I want to replace some C atoms to B and N atoms.I dont want to change structure just simple atom replacement.Or another words i would like to see graphene sheet which is made in Boron or Nitrogen

I recently realized myself that this could be interesting, so I made an updated script that support boron-nitride or any other two-atom basis hexagonal nanoribbon. I have attached it to this post; use it like the old script, there are just some extra parameters at the top. There is even now a switch to turn on/off the hydrogen edge termination

If i go to the atomic manipulator i cant change nothing
Second chance i went to the Molecular Builder and did some replacements and back to the Manipulator and all seemed ok.But when i dragged it to the Nanolanguage scripter i didnt see quantities availability "ENERGY BANDS" for calculating.Instead of "Energy bands" i see "Energy Spectrum Molecular Energy spectrum"

You should not edit a periodic structure in the Molecular Builder (MB), but in the Bulk Builder. The MB produces molecules, and you cannot compute the band structure of a molecule. Better stick to PeriodicAtomConfigurations all the time, otherwise you lose the unit cell, and it's gets messy to figure out the alignment.

Second question about Energy density.In some cases it shows beatiful DOS diagramm,other cases it shows only preview for nanoscope?

I must admit I don't understand the question. Energy density?

I hope the new script will help you out a lot, so that you don't actually have to go via the manipulators. If, however, you still need to do simple modifications, use the Bulk Builder on the PeriodicAtomConfigurations. If you only want to change some specific atoms to B/N, then I can suggest a suitable approach, if you give me some more details.

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armchair = False   # False -> zigzag
width = 14          # ribbon width across, number of layers (must be even for zigzag)
repetitions = 1    # repetitions of the minimal unit along the ribbon
PAC = True         # False -> molecule

# The two atoms in the "graphene" basis
atom1 = Boron
atom2 = Nitrogen

# Set to false to remove the edge hydrogen termination
include_H = True

Thx ,that script seems perfect.
Altough, is  that script only for armchair(x,x) and zigzag(x,0) structures
what about chiral ?

[Anders Blom]

Actually for graphene nanoribbons there are only 2 types, armchair and zigzag.

But the notation used in the literature is not entirely consistent. What I mean by these terms is the edge type, while sometimes one encounters a notation related to the "corresponding unrolled nanotube". Highly confusingly, this results in the opposite labeling (i.e. a zigzag edge ribbon is made from unrolling an armchair nanotube).

But at any rate, there are only 2 different types; chiral tubes cannot be unrolled unto something that looks like a ribbon (as far as I know). Well, you can of  course always unroll it, but it will not have straight edges.