How to distinguish different phonon branches?

qiub

Hi, I'm trying to distinguish phonon branches in the case of branch crossings in some complex phonon dispersions, like in the below example:

http://cmt.dur.ac.uk/sjc/thesis/thesis/img354.gif

My question is, how can I know which portions near the crossing belong to the same branch? I've this question because when I want to calculate group velocity, it becomes quite confusing, please help me, thanks!

genneth

Quite often, there are distinguishing features between the branches near a crossing point, so it is not really possible to say which line belongs to which. One general method is to postulate a phonon-phonon interaction (say, universal repulsion), which will cause the crossing points to be teased apart, and thus reveal some underlying differences (maybe, depends on the interaction).

qiub

Thanks for the reply! I also got another reply from other sources. He suggested that the way to determine which frequencies belong to the same branch, a dot product of eigenvectors from neighboring k points can be carried out, the ones with most overlap should be belong to the same branch.

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genneth	Quite often, there are distinguishing features between the branches near a crossing point, so it is not really possible to say which line belongs to which. One general method is to postulate a phonon-phonon interaction (say, universal repulsion), which will cause the crossing points to be teased apart, and thus reveal some underlying differences (maybe, depends on the interaction).

qiub	Thanks for the reply! I also got another reply from other sources. He suggested that the way to determine which frequencies belong to the same branch, a dot product of eigenvectors from neighboring k points can be carried out, the ones with most overlap should be belong to the same branch.