Dear Ali Sufyan
You can use Mathematica:
https://www.wolframalpha.com/input/?i=plot++x%5E2%2By%5E2%2Bz%5E2%3D1
You can easily plot color map 3D surfaces by using OriginPro 9.0 or later.
Vassilis
I think it is a standard feature of almost any surface plotter. I have used opendx in the past. Other open source options are visit or math packages such as R or octave.
thanks for your answers. but i think i could not write my question properly. if you please see the figure 2 of the paper "Topological nodal-line semimetals in alkaline-earth stan
nides, germanides and silicides " whose link is given below
https://arxiv.org/pdf/1605.04050.pdf
they plot the electronic band structure firstly which is very simple in DFT but then in Fig 2.b, they plot 3D iso-eneryg surface. now question is that can i plot this even if i don't have Hamiltonian of my system and just by some DFT codes? actually i am new in this field and have totally stuck at this point. i will be very thankful to you people if you guide me to understand it.
You just need to run the band structure solution on a 3D grid in momentum space. For good plotting it is easier to use a regular cubic grid in kx, ky, kz although it may be computationally time consuming if your mesh size has to be very fine to resolve features. To make things even easier for setting up the visualization, you can embed your Brillouin zone in a cube and set energy values to zero for points outside the zone (or use symmetry to populate the external points with energy value already calculated on corresponding points inside the zone). You should construct the 3D matrix for each energy eigenvalue of the band structure solution in momentum space, so you may end up with a lot of data. Notice that the band solver will order eigenvalues simply by energy value but when you have band crossings (which always occur in 3D potentials) the solver will not be able to resolve whether the bands actually split or cross because you work with a finite number of points and the model may not have all the physics anyway. Rule of thumb is that bands should physically split at symmetry points and cross elsewhere. Anyway, once you have your 3D grid matrices of energy values, you then have to render isosurfaces with a visualization package. Strangely enough, commercial scientific visualization software was much better 20 years ago because it was profitable to develop for the research communities. Now, the really specialized companies have all disappeared and the best is probably to rely on open source software, but it is a little more daunting to set things up if one does not have experience. If you do not have commercial software that does isosurface rendering already, you could look at the Visualization Toolkit (VTK) library which has been integrated in various open source applications, including Python. Look for information at https://www.vtk.org/Wiki/Main_Page . If you have access to MATLAB, you can do basic isosurfaces there: https://www.mathworks.com/help/matlab/ref/isosurface.html . If you instead need free software, you can use GNU Octave that is an open source alternative to MATLAB: https://www.gnu.org/software/octave/
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