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#13 Finding the Electronic Structure of a Material Using a Band Structure (2)

Viewed : 843 times,  2019-08-13 13:55:07

Previously, weekly tip #12 covered band structures. This week’s tip looks into calculating a band structure using Materials Square.


1. How to calculate a band structure

The following 4 steps should be taken to obtain a band structure by using DFT (Quantum Espresso).

  1. DFT calculation (pw.x)
  2. Run k-points re-ordering calculation (pw.x, calculation='bands')
  3. Run Band-related properties calculation (bands.x)
  4. Band structure Plot & Analysis


Through Materials Square, you should add two Quantum Espresso modules to obtain a band structure by following the above 4 steps. Follow the workflow guide:

  1. Build Structure at the 'Structure Builder' module
  2. Add a 'Quantum Espresso' module and connect that with the structure builder module
  3. Set the input script for scf or optimization calculation
  4. Submit the job
  5. Add a new 'Quantum Espresso' module and connect that with the Quantum Espresso module to perform the restart calculation
  6. Set the input script for band structure. For example, change the calculation type as bands and set the high symmetry points.
  7. Submit the job
  8. Add a 'Band Sturucture' module and connect that with the second Quantum Espresso module


In first, you should create a calculation model to obtain a band structure. You can create this model in various ways. For example, filling in information through the 'Crystal Builder' menu, importing a structure file, or pasting coordinate data in the 'Edit' menu. 

Upon completion, Add a Quantum Espresso module. Connect that with the structure builder module to activate the first Quantum Espresso module. 
And next, set the input script for the basic DFT calculation in the first Quantum Espresso module. If the 'Scripting option: Template', you can easily set the input script. Select 'Data to get: Energy & Structure' to perform the basic DFT calculation.

Once the calculation is completed, add a new Quantum Espresso module. And then, connect with that to the first Quantum Espresso module, to activate the second QE module. If the 'Scripting option: Template', you can easily set the input script for band structure calculation, also. Select 'Data to get: Band Structure'. Then the input script will be set as automatically 'calculation type: bands' and the 'k-point sampling: High symmetry points'. The input script will be copied from the connected first Quantum Espresso module. Set the high symmetry k-point path. A detailed description of the high symmetry point will be described in the next part.


Check the 'Band Structure' solver tab is existing on the top. The tab is for making a visualization file of the calculated band structure. It means, if you did not add this tab when performing the band structure calculation, you can't see the band structure results as a graph.



2. High symmetry point
To accurately draw a band structure, you need to set a k-point sampling path by passing the high symmetry point of the Brillouin zone. The species of the point depends on the crystal system. There are diverse high symmetry point paths, even if the same crystal system. The high-symmetry points of major crystal systems are described as follows.

Or, you can set the k-point path by referring to the reference paper.


You can change the high symmetry k-point path at the following part:

First, select a crystal system that considers the model. Then, enter the number of sampling cases until the next k-point is on the weight input field, and select the desired high-symmetry k-point. In the meantime, set the weight to 1 as there is no k-point after the last high-symmetry k-point.
The following figure shows the cases in which the k-point was set as automatic (left) or K-Γ-M-K (right) when drawing the band structure for a graphene unit cell.

👉 Check the calculation results


If a k-point is set as automatic, as k-points are uniformly sampled in space, the sampled points are less continuous. So the shape of the band structure is not smooth. However, if a k-point path is set to a high symmetric point, then the shape is smooth. In particular, you can check the Dirac point, which is one of the characteristics of graphene.



3. Density of states (nscf calculation)
Weekly tip #12 described that the x-axis of DOS and the y-axis of the band structure can be combined. Adding a band structure displays DOS and the band structure together. However, if you calculate only the band structure, it is observed that the DOS graph is not good. For a proper display of the DOS graph, the calculation needs one more step.

In weekly tip #8, DOS requires very dense k-points. However, as the energy/structure is converged faster than DOS, it is not necessary to increase k-points only for DOS data when performing the Self-Consistent Field (SCF) calculation. Consequently, the calculation is done only by increasing k-points through non-scf (nscf) calculation results in obtaining better DOS data and decreasing consumption in computing resources.


The calculation of 'calculation type: nscf / bands' can be performed only in the restart Quantum Espresso module. So, add a new Quantum Espresso module and connect that to the existing Quantum Espresso module. You can check the 'restart' word on the solver tab of the top. Or, you can check the added 'restart_mode=”restart”' keyword to the input script textarea of the left-bottom. 

If you want to make the DOS calculation converged, you should increase sufficiently the number of k-points. It can be done by selecting the 'Data to get: Density of states'. Change the option as 'calculation type: nscf' under the '&CONTROL' namelist.
Therefore, for graphene, we can obtain the band structure like the following graph by applying the following workflow to calculate the band structure and DOS calculation:


👉 Check the calculation results



For now, we have learned the necessary information to get a band structure. It requires calculations with several steps. Because of several steps required for its calculation, it can get complex and confusing. However, its usefulness cannot be denied. For example, a graphene band structure calculation takes approximately 30 min through Materials Square. 
Use Materials Square to obtain a band structure in an interesting structure!