Phonon dispersion relation : meaning of mode crossings

[dmit11]

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!

 

[Pete99]

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...