The ABINIT Users Mailing List ( CLOSED )

[Matthieu Verstraete <mjv500@york.ac.uk>]

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


--
================================================================
Dr. Matthieu Verstraete                 mailto:mjv500@york.ac.uk
Dept. of Physics, University of York,     tel: +44 1904 43 22 08
Heslington, YO10 5DD York, United Kingdom fax: +44 1904 43 22 14