Phonon dispersion relation : meaning of mode crossings

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SUMMARY

The discussion centers on the interpretation of mode crossings in phonon dispersion relations, specifically in the context of solid state physics as outlined in Ashcroft & Mermin's work. It is established that when two phonon branches cross, they are uncoupled, indicating no interaction between them. Additionally, the presence of a single transverse branch in certain high symmetry directions suggests degeneracy, while other directions may reveal two distinct branches due to differing phonon behaviors.

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  • Understanding of phonon dispersion relations
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  • Knowledge of Bravais lattices, particularly face-centered cubic (FCC) structures
  • Ability to interpret graphical representations of phonon branches
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dmit11
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Hello all,


What does it mean when two phonon branches get crossed in phonon dispersion relation ? Also, in certain high symmetry direction, one can find only one transverse branch and other direction two separate branches, what do these response mean?

(Ref. Solid state physics by Ashcrof & Mermin, Fig 22.13: Typical dispersion curves in monoatomic Bravais lattice. FCC (lead))

Thank you!
 
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Hi!

I would say that if two branches cross each other they are uncoupled, since if there were some coupling between them they would mix and avoid crossing.

Regarding the number of branches in different directions it might be that in some directions the two branches are degenerate and then you only see one single line in the plot, while in other directions both branches show up.

However I do not have Ashcrof & Mermin to see if this is what you are asking for...
 

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