[Pw_forum] Eigenvectors

[Stefano Baroni]

On Aug 10, 2004, at 3:35 PM, Michael Malorny wrote:

> Dear pwscf users,
>
> I am currently trying to calculate the scattering cross sections of
> wurtzite CdS and CdSe semiconductors.

Raman cross section, I guess ???
First or second order? Second, I guess (see below)

> As I am planning to investigate
> mixed crystals formed by these two systems in the future I also take
> supercells of the pure materials into account.
>
> For the calculation of the scattering cross section the eigenvectors of
> the dynamical matrix are needed which I extract amongst other things 
> from
> the program matdyn of the pwscf-2.0-package.
>
> I calculated the cross section of CdS with wurtzite structure and of 
> CdS
> supercells generated by expanding the wurtzite cell by the factors 
> 2x2x2
> and 4x4x4, respectively. As expected, the cross sections of the three
> systems are identical at the Gamma and the A point of the first BZ. 
> But at
> all other points in between the cross sections differ more or less.

what do you mean by "cross section at other points"? To first order, 
light is only scattered by zone-center phonons.
Or you rather mean "contribution of other points to the *second-order* 
Raman cross section"???

> Has anybody an explanation for this strange behaviour or can even help 
> me
> solving my problem? I found out that the eigenvectors possess imaginary
> parts even at the Gamma point which shouldn't occur in my 
> understanding.

Your understanding may be partial. Have you checked if the phase of all 
the components of the eigenvectors is the same? If so (as I suspect) 
there is nothing wrong. Phonon eigenvectors at Gamma need not be real, 
because the overall phase is arbitrary. Time-reversal invariance 
imposes that this arbitrary phase *can* be chosen in such a way as to 
make all the components real (i.e. the phase of all the components has 
to be the same). Whether or not a given computer routine choses the 
arbitrary phase in such a way as to make eigenvectors real whenever 
possible is a matter of programming, not of physics ...

> Could this be an explanation and if so, is there a possibility to
> circumvent this problem?

In order to (try to) provide any explanation I am afraid we will need 
to know more about what you are doing ...

Take care,
Stefano Baroni

---
Stefano Baroni    ---  SISSA  &  DEMOCRITOS National Simulation Center
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