In this tutorial you will build a range of graphene structures and study some of their properties. With VNL you can easily twist and stretch the structures using plug-in modules. You can then use ATK to calculate their electronic and vibrational properties. You will also learn to automate calculations on large structures using Python scripting.
In many VNL projects (depending on the study of course) you will need the appropriate plugins/AddOns, which can be installed via the AddOn Manager.
In this particular tutorial, you will need the TubeWrapper and CNTBuilder plugins. Please check that these are available, and install them if they are not.
You can open the AddOn Manager in two ways:
- The icon will pop up in the bottom-left corner of the VNL main window if updates to already installed plugins are available. Clicking this icon will open the AddOn Manager.
- You can also click in the top menu bar.
In any case, a long list of plugins will pop up, and you can perform various tasks for each plugin, e.g. update, install, uninstall, enable, and disable.
Build a graphene sheet¶
Open the VNL Builder . It is then easy to create a graphene sheet using a plugin; simply click . Leave the option for Chemical Properties at defaults. In the Geometry options, choose a chiral vector of (n,m)=(8,0), and click Build.
You now have a basic “building block” for the structure. Use theplugin to repeat it 10 times along the C-direction:
Build a CNT¶
You can now use the TubeWrapper plugin to wrap the nanosheet into a carbon nanotube (CNT). It is possible to turn the nanosheet into an open or a closed cylinder:
Transmission spectrum of a GNR¶
Let us calculate the electronic transmission spectrun of a graphene nanoribbon (GNR). First, build the ribbon using theplugin. Choose chiral indices (n,m)=(1,1) and repeat the structure 3 times the C-direction:
In order to correctly calculate the transmission spectrum for a bulk system, the bulk must qualify as a valid device electrode. This requires that the C-axis is perpendicular to the A,B plane, and that it is sufficiently long that the atoms in the unit cell only have Hamiltonian matrix elements with atoms in the nearest neighbour cells along C. This condition is usually fullfilled if the C-vector is longer than 7 Å.
- First, change the default output file to
- Then open the added calculator block to start editing the settings.
- Select the Extended Huckel calculator, and make sure the number of k-points is 1 for the A and B directions, and high for the C-direction, e.g. 100 k-points along C.
- In the Huckel basis set options, select Cerda.Carbon [graphite] for carbon and Cerda.Hydrogen [C2H4] for hydrogen.
- Finally, add a TransmissionSpectrum block to the script,
and save the Python script as
When the calculation is finished (it will run extremely fast), locate the output file ribbon11_twist0_nscf.nc in the VNL file browser window. Select the file and notice that the contents of the file are displayed in the VNL panel:
In this section you will learn how to twist a graphene nanoribbon using the VNL Twister plugin, and then compute the transmission spectrum.
Then open theplugin, and set a “Twist angle” of 72 degrees and a “Non-twisting zone” of 9 Å. Click Apply to perform the twisting operation.
Certain parts of the system to the left and right of the structure are not twisted; the length of the non-twisted part is specified by the value of “Non-twisting zone”. The rest of the structure is twisted by the sepcified angle.
You will now calculate the transmission spectrum of the twisted graphene nanoribbon. First, you need to convert the twisteds ribbon into a device – use thetool for this.
In the Scripter, add the following script blocks:
Open the New Calculator block and use the following settings:
- “ATK-SE: Extended Hückel (Device)” calculator;
- 1x1x100 k-point grid;
- “Cerda.Carbon [graphite]” basis set for C and “Cerda.Hydrogen[C2H4]” basis set for H.
Select the following settings in TransmissionSpectrum block:
- energy range of [-1,1] eV and 201 energy points;
- Krylov self-energy calculator;
- 1x1 k-point grid.
The NetCDF data file
GNR_twist.nc should now have appeared on the VNL LabFloor.
Select the TransmissionSpectrum item and use the Transmission Analyzer plugin
to visualize the computed transmission spectrum.
Note that the transmission peak has shifted down in energy as compared to the non-twisted ribbon. The twist represents a source of electron scattering, since it breaks the translational symmetry of the non-twisted ribbon electrodes along the transport direction.
Next, we are going to create a Möbius nanoribbon. Download the script
which is also reproduced below. The script loads a basic nanoribbon from the file
nanoribbon.nc, then performs the required operations of repeating,
twisting, and wrapping the ribbon, and finally saves the Möbius ribbon in
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from NL.Math.Utilities import rotationMatrix import math from NanoLanguage import * def twister_displacement(x, rotation_angle_per_z, rotation_axis, rotation_axis_center, z_start, z_end): """ Function for twisting a 1-d structure @param x : Coordinates of 1-d structure @param rotation_angle_per_z : size of twist in angle/length @param rotation_axis : axis to apply twist along @param rotation_axis_center : center of the rotation axis @param z_start : z value for starting the twist @param z_end : z value for ending the twist """ # do not twist for z > z_end z = x z = min(z,z_end) # do not twist for z < z_start z = z - z_start z = max (z,0.0) # find twist angle theta = z*rotation_angle_per_z # calculate the rotation matrix rotation_matrix = rotationMatrix(theta, *rotation_axis) # apply rotation return rotation_axis_center+numpy.dot(rotation_matrix, x-rotation_axis_center) def wrapping_displacement(x, width, wrapping_angle): """ Function for converting a nanosheet coordinate into a partly wrapped nanotube @param x : Coordinates of nanosheet atom @param width : Width of the nano-sheet @param wrapping_angle : maximum wrapping angle of the nanotube in radians """ # calculate the average radius of the incomplete wrapped tube radius = width/wrapping_angle # find the angle of the current atom angle = (x-width/2.)/radius # calculate the radius of the current atom atom_radius = radius+x # return atom position of the wrapped atom return numpy.array([x, atom_radius*math.cos(angle),atom_radius*math.sin(angle)]) def Moebius(ribbon, n, m, repetition): """ Function for generating a moebius molecule @param n : Chiral vector index @param m : Chiral vector index @param repetition : Repetition along z """ # build n,m ribbon #ribbon = NanoRibbon(n,m) ribbon = ribbon.repeat(1,1,repetition) # get properties of the ribbon lattice = ribbon.bravaisLattice() elements = ribbon.elements() cartesian_coordinates=ribbon.cartesianCoordinates().inUnitsOf(Angstrom) # calculate the length of the 1-d structure z_length = numpy.linalg.norm(lattice.primitiveVectors().inUnitsOf(Angstrom)) # calculate twist parameters rotation_angle_per_z = math.pi /z_length rotation_axis = numpy.array([0,0,1]) rotation_axis_center = numpy.sum(cartesian_coordinates,axis=0)/len(cartesian_coordinates) # define a function of one variable, f(c), for displacing the atoms f = lambda c : twister_displacement(c, rotation_angle_per_z, rotation_axis, rotation_axis_center, 0.,z_length) # apply the function to find new displaced coordinates cartesian_coordinates = numpy.apply_along_axis(f, 1, cartesian_coordinates) cartesian_center = numpy.sum(cartesian_coordinates,axis=0)/len(cartesian_coordinates) cartesian_coordinates = cartesian_coordinates - cartesian_center # define a function of one variable, f(c), for displacing the atoms f = lambda c : wrapping_displacement(c, z_length,2.0*math.pi) # apply the function to find new displaced coordinates cartesian_coordinates = numpy.apply_along_axis(f, 1, cartesian_coordinates) return MoleculeConfiguration( elements=elements, cartesian_coordinates=cartesian_coordinates * Angstrom ) ribbon = nlread('ribbon.nc', BulkConfiguration)[-1] moebius = Moebius(ribbon,1,1,100) nlsave('moebius.nc', moebius)
You first need to build a basic nanoribbon. Use the
Then make sure
Moebius.py is also located in the Prpject Folder, and execute it using
the Job Manager or from the command line. The output file
moebious.nc should appear in the Project Files list and the Möbius
configuration should appear on the LabFloor. Use the Viewer to visualize the
Buckling a graphene sheet¶
In this final section you will learn how to buckle a graphene sheet using the VNL Buckler plugin.
First, create a nanosheet as shown above in section Build a graphene sheet. This time, repeat the nanosheet 30 times in the C direction.
Then open theplugin, and set the “Buckling amplitude” to 2 Å and the “Non-buckling zone” to 9 Å. Select “NY = 1” and “NZ = 1” to enable buckling along the Y and Z axes.
Click Apply to perform the buckling operation.