[Pw_forum] Identifying the phonon mode from eigen vector

Stefano Baroni baroni at sissa.it
Wed Feb 8 11:21:45 CET 2012

On Feb 8, 2012, at 4:00 AM, Ajit Vallabhaneni wrote:

> Dear users and developers,
>           I am trying to understand how the atoms will be displaced for each of the six phonon modes in graphene at various q's from the eigen vectors. At gamma point (0,0,0), the eigen vectors are symmetric with the real part being of the same sign for acoustic modes and of opposite signs for optical modes with zero imaginary part for all of them. But for a different q like the one showed below, I can tell which are long, transv and out of plane (z) modes, but i want to know if it is possible to distinguish optical and acoustic modes  (assuming frequencies and dispersion curves are not known).

Dear Ajit,

In general, the distinction between acoustic and optical modes is conventional. "acoustic modes" are all those whose frequency is continuously connected with the three zone-center zero modes whose eigen-displacements correspond to a rigid translation of the entire crystal. All the others are, by convention, "optic modes". There is no rigorous way of telling which is which in the most general crystal structure at the most general q-point in the Brillouin zone. If asked to bet, I would say that modes whose displacements in the unit cell are "more parallel" would have a more "optic character" than those whose displacements are "anti-parallel", but again this statement is not rigorous, nor entirely meaningful either ...

> On a relevant note, i read some previous archives of 2009 discussing the possibility of identifying the frequencies by it's branch, not just from lowest to highest, i was wondering if that is possible at all without looking at the eigen vectors at each q.

As said, the only meaningful statement can be made on the branch to which a mode belongs. If the frequency of the branch vanishes at q=0, then the entore branch is (conventionally) acoustic, otherwise it is deemed to be optic ...

Hope this helps ...

Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center - Trieste
http://stefano.baroni.me [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

La morale est une logique de l'action comme la logique est une morale de la pensée - Jean Piaget

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