# How to differentiate longitudinal and transverse phonons from the phonon dispersion curve?

I know that there are two kinds of phonons: acoustic and optical. Acoustic phonons have zero frequency at the $$\Gamma$$ point, whereas optical phonons have a non-zero frequency at the $$\Gamma$$ point.

I also know that either type of phonon can be longitudinal or transverse depending on how the atoms vibrate relative to the axis of vibrations.

My question is: Given a phonon dispersion curve, how can one tell if a phonon branch is longitudinal or transverse, especially for optical phonons?

• are you not able to see them when you pick points on the phonon curve and plot the displacement vectors (and an extra vector for the direction of propagation to compare)? Commented May 14, 2023 at 5:10
• I don't totally get you. The displacement curve is not present on the phonon band structure. Commented May 14, 2023 at 5:29
• If they have different dispersion relation, they are marked accordingly. Otherwise, we usually have two transverse modes per every longitudinal one. An example of figure which poses difficulty could help Commented May 14, 2023 at 7:07
• I am saying that you cannot only look at the phonon band structure alone. But when calculating the phonon band structure, there will be eigenvectors of the oscillation matrix, and if you inspect them, you will be able to find out. Commented May 14, 2023 at 11:31
• @naturallyInconsistent, that was my first guess, too. That the band structure alone is not sufficient to tell. Seeing a non-annotated phonon band structure in a journal paper, you cannot tell which is LO and which is TO. Commented May 16, 2023 at 5:14