In my phonon calculation utilizing DFPT in VASP for a monolayer material with space group 187, I've noticed that while most of the phonon bands are positive, two of them appear to be straight. What could be the explanation for this observation?
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Such bands are usually called 'flat bands'. The group velocity vanishes, signalling that such an excitation is non-dispersive, i.e. is localized. See here. Think 'molecular modes'. For an isolated molecule, $\omega(k) \equiv \omega$ is independent of $k$, thus is flat. The oscillations are not wave-like but are localized.
In many cases, flat bands in a crystal are interesting. However, rarely is a band in a real crystal truly flat. They are usually 'flattish' at best. Maybe there is something wrong with your calculation?
As a check, I suggest visualizing the displacements of the flat modes. I usually use this online tool.
Since you have used VASP-DFPT, I assume you used the interface to phonopy. Did you use a supercell? Even with DFPT in VASP, you have to use a supercell. If not, you are only sampling the zone-center and the Fourier interpolation of a single point can be anything. See my comment on this wrong answer. The VASP DFPT routines only do $q=\Gamma$ and you must use a supercell. Even the phonopy documentation uses a supercell. $q \neq \Gamma$ is supposed to be added in one of the 6.* versions, but is not working as far as I know.
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$\begingroup$ If something seems wrong in my calculations. How can I figure it out? $\endgroup$ Commented Apr 17 at 17:40
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$\begingroup$ @FarahShehzadi I suggest first to figure out if something is wrong or not before asking for more help. $\endgroup$ Commented Apr 17 at 17:52
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$\begingroup$ my material has space group 187(p6m2),point group as D3h,i expected 9 phonon bands whereas i got 6 bands and two of them as flat.i used dfpt,with 1x1x1 unitcell and phonopy.now i dont know what i am doing wrong. $\endgroup$ Commented Apr 17 at 17:57
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$\begingroup$ @FarahShehzadi Using a 1x1x1 unitcell is wrong for a start. What do the displacements of the flat bands look like? Use the tool I provided. You can update your answer to add pictures and I will look at them. If you expected 9 bands (i.e. 3 atoms per unitcell?), then there are 9 bands. Some of the bands in your plot are just degenerate. Check it. Compare your dispersions to ones in literature. See if they match. $\endgroup$ Commented Apr 17 at 18:00
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1$\begingroup$ Thanks for moving this to the VASP chat room @FarahShehzadi, it is a bit long for a comment chain. $\endgroup$ Commented Apr 18 at 0:50