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["Patrick B. Hillyard" <phillyar@stanford.edu>]

Matthieu,
Thank you very much for your response.  By "polarization" I meant the 
phonon polarization vector, like you assumed...

I also should have been more clear about the second point.  By saying 
that the polarization vector should be the same for a given mode/point, 
I meant that the atomic motion should be characterized by the same 
polarization vector for each atom in the unit cell (then motion could be 
along this vector or along the negative of the vector, thereby allowing 
for optical modes).

I am still trying to understand how to compare eigendisplacements with 
both real and imaginary components to a physical displacement.  It seems 
to me that the relevant portion is either only the real part or the 
complex magnitude...
Thanks,
Pat


Matthieu Verstraete wrote:
> fun with phonons.....
>
>
> > I am dealing with a multiple atom per unit cell system.  My questions 
> > are with respect to obtaining the polarization vector.  It seems to me 
> > that the polarization vector should be proportional to the 
> > displacement vector.  Is this correct?
> Do you mean the phonon normal mode eigenvector or the electrical 
> polarization? (probably the former, but you say "the polarization") In a 
> multi atom case it's more complicated, as the displacement vector 
> component is renormalized by the mass for each atom, wrt the phonon 
> eigenvector.
>
> > I ask this because I believe the polarization vector should be the 
> > same for each atom for a given mode/q point.
> Not at all: for optical modes and 2 atoms per unit cell the atoms move 
> in opposite directions. For more complex structures like perovskites you 
> have rotational modes of whole blocks (tetrahedra, octahedra) of atoms. 
> The eigenvector of 1 mode at 1 qpoint has 3 components for each atom, 
> and they can be in any direction a priori (constrained by the symmetry 
> irreps of course).
>
> > Also, I observe imaginary displacement components for nonzero q.  What 
> > is the physical meaning of an imaginary displacement component.  Is 
> > the physically observable displacement the complex magnitude or is it 
> > just the real component of the displacement vector?
> For non zero q, the displacements have to be multiplied by a phase 
> factor exp[iq(r+R)], then norm-squared, to get the actual displacements 
> of an atom in any given unit cell R. The complex character of the 
> components of the matrix comes from the generalized way the 
> perturbations are calculated. For all of this, see Xavier and Changyol 
> Lee's 2 prb papers in 1995 I think, or Stefano Baroni's Rev Mod Phys 
> (don't have the refs on hand, but they are cited in the abinit article 
> and on the web site)
>
> Matthieu