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How to distinguish different phonon branches?

  1. Jul 8, 2009 #1
    Hi, I'm trying to distinguish phonon branches in the case of branch crossings in some complex phonon dispersions, like in the below example:


    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!
  2. jcsd
  3. Jul 10, 2009 #2
    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).
  4. Jul 10, 2009 #3
    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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