I am trying to plot 3D band structure of my system of interest. I have used Quantum Espresso software for calculating the band structure and plotted 2D band diagram. But from here I am unable to understand how to plot 3D band structure i.e. E vs (kx, ky) plot. Can anyone please suggest me how to do this? Is there any visualizer to do this automatically from quantum espresso output file?
1 Answer
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Usually people just do it by picking a path through the Brillouin zone and then plotting it in one dimension. You can use the seekpath or pymatgen (I think pymatgen has this) tools to generate paths through k space that connect high symmetry points, or you can just look at textbooks or even the Wikipedia page on the Brillouin zone to see what high symmetry points are typically used for different structure types. If you see a band structure of a bulk solid in a textbook or paper, plotting the band energies along high symmetry paths is the most common way to represent it visually. The density of states can also be a useful way to visualize which energy levels are available in your system and how many electrons are in a given energy window.
You can also make it a 3D plot where you have the x and y axes corresponding to slices of the Brillouin zone and the z axis is the energy; this is the sort of plot you might have generated for 2D materials. Such a plot can in principle also be made for 3D materials by just fixing a k point along the third direction. This approach might be useful for layered solids, for example.
