Table of Contents. Table of Contents Exploring graphene. Build a graphene sheet Build a CNT Transmission spectrum of a GNR Twisted nanoribbon
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1 Table of Contents Table of Contents Exploring graphene Build a graphene sheet Build a CNT Transmission spectrum of a GNR Twisted nanoribbon Transmission spectrum Möbius nanoribbon Buckling a graphene sheet
2 QuantumATK Try it! QuantumATK Contact Docs» Tutorials» Tubes, ribbons and other 1D nanostructures» Exploring graphene Exploring graphene Downloads & Links PDF Basic QuantumATK Tutorial ATK Reference Manual Moebius.py In this tutorial you will build a range of graphene structures and study some of their properties. With QuantumATK you can easily twist and stretch the structures using plug-in modules. You can then use QuantumATK to calculate their electronic and vibrational properties. You will also learn to automate calculations on large structures using Python scripting. Hint In many QuantumATK 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 QuantumATK main window if updates to already installed plugins are available. Clicking this icon will open the AddOn Manager. You can also click Help AddOn Manager 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.
3 Build a graphene sheet Open the QuantumATK Builder. It is then easy to create a graphene sheet using a plugin; simply click Add From Plugin Nanosheet. 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 the Bulk Tools Repeat plugin to repeat it 10 times along the C-direction:
4 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 the Add From Plugin Nanoribbon plugin. Choose chiral indices (n,m)=(1,1) and repeat the structure 3 times the C-direction:
5 Note 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. Next, transfer the structure to the Script Generator using the botton, and double-click the New Calculator icon to add a calculator block to the script. First, change the default output file to ribbon11_bulk.nc. 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 ribbon11_bulk.py. TransmissionSpectrum block to the script, and save the Python script as
6 Send the script to the Job Manager in order to execute it. The job starts when you click the icon.
7 When the calculation is finished (it will run extremely fast), locate the output file ribbon11_twist0_nscf.nc in the QuantumATK file browser window. Select the file and notice that the contents of the file are displayed in the QuantumATK panel: You can now select the TransmissionSpectrum object, which has this icon:
8 and use the 2D Plot or Transmission Analyzer plugins to plot the electronic transmission spectrum. Twisted nanoribbon In this section you will learn how to twist a graphene nanoribbon using the QuantumATK Twister plugin, and then compute the transmission spectrum. Open the Builder, and select the nanoribbon created in the previous section. Then use the Bulk Tools Repeat tool to repeat the configuration 7 times in the C direction: Then open the Coordinate Tools Twister plugin, and set a Twist angle of 72 degrees and a Nontwisting zone of 9 Å. Click Apply to perform the twisting operation.
9 Certain parts of the system to the left and right of the structure are not twisted; the length of the nontwisted part is specified by the value of Non-twisting zone. The rest of the structure is twisted by the sepcified angle. Transmission spectrum You will now calculate the transmission spectrum of the twisted graphene nanoribbon. First, you need to convert the twisteds ribbon into a device use the Device Tools Device from Bulk tool for this. Then rename the device configuration as GNR_twist and send it to the required ATK Python script. Script Generator to create the
10 In the Scripter, add the following script blocks: New Calculator Transmission Spectrum 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. Then save the script as GNR_twist.py and execute it using the just a few minutes. Job Manager. This calculation will take The NetCDF data file GNR_twist.nc should now have appeared on the QuantumATK LabFloor. Select the TransmissionSpectrum item and use the Transmission Analyzer plugin to visualize the computed transmission spectrum.
11 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 nontwisted ribbon electrodes along the transport direction. Möbius nanoribbon Next, we are going to create a Möbius nanoribbon. Download the script Moebius.py, 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 moebius.nc from NL.Math.Utilities import rotationmatrix import math from QuantumATK import * def twister_displacement(x, rotation_angle_per_z, rotation_axis, rotation_axis_center, z_start, z_end): """ Function for twisting a 1-d x : Coordinates of 1-d rotation_angle_per_z : size of twist in rotation_axis : axis to apply twist rotation_axis_center : center of the rotation z_start : z value for starting the z_end : z value for ending the twist """ # do not twist for z > z_end z = x[2] 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)
12 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 x : Coordinates of nanosheet width : Width of the 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[2]-width/2.)/radius # calculate the radius of the current atom atom_radius = radius+x[1] # return atom position of the wrapped atom return numpy.array([x[0], atom_radius*math.cos(angle),atom_radius*math.sin(angle)]) def Moebius(ribbon, n, m, repetition): """ Function for generating a moebius n : Chiral vector m : Chiral vector 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()[2].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_coordina # 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)
13 You first need to build a basic nanoribbon. Use the Add From Plugin Nanoribbon plugin and select, for example, the chiral vector (n,m)=(6,6). Save the created ribbon in the Project Folder as ribbon.nc. 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 structure.
14 Buckling a graphene sheet In this final section you will learn how to buckle a graphene sheet using the QuantumATK 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 the Coordinate Tools Buckler plugin, and set the Buckling amplitude to 2 Å and the Nonbuckling 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.
15 Copyright 2018, Synopsys Denmark.
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