[Pw_forum] Eigenvectors

[Michael Malorny]

Dear pwscf users,
dear Mr. Baroni,

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

Thanks for your prompt reply and sorry for my brief first message but I
wanted to await *some* answer before I start posting tons of megs of
output data to this forum... :)  But, nevertheless, you are right: I
should have been more precise in some points.

I try to accompany an inelastic X-ray scattering experiment on a CdS/CdSe
mixed crystal by calculating the double differential X-ray scattering
cross section (coherent part only). As a reminder, this cross section is
mainly governed by two factors:

1) Q*w where Q=q+G (q wave vector in the 1st BZ and G some reciprocal
lattice vector) and w is an eigenvector of the dynamical matrix.

2) exp(-i*G*tau) where tau are the atomic positions of the (extended) unit
cell.

> 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"???

By "other points" I meant q-points of the reciprocal space in the
Gamma-A-direction differnt to the (high symmteric) points Gamma and A
themselves.

At these high symmetric points the cross section of the wurtzite system
and of the two extended systems (by 2x2x2 and 4x4x4) is identical. At all
other q-points in this direction the results differ (and which shouldn't
happen in my understanding).

I made the same calculation some time before for zincblende CdS/CdSe. For
this purpose I used a very old version of pwscf (I received from Pasquale
Pavone). I had no problems with these calculations then but it turned out
that this old version of pwscf is only capable of calcualting systems with
cubic structure (it uses only one effective charge Z=Zeff/sqrt(epsilon)
per atom and therefore neglects the matrix shape of epsilon and Z). This
forced me to use a more recent version of pwscf.

> 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 ...

Though these information might help I doubt that the phase of all the
components of the eigenvectors are the same. But please take a look at
some arbitrary chosen eigenvectors of wurtzite CdS at Gamma I calculated.
I am quite confused by now and needed some confirmation on that... :/

( 0.000004029391, 0.000000263701)
( 0.001946182788,-0.000035622049)
( 0.000087470906, 0.000000000000)

(-0.000059417376, 0.000001103247)
(-0.000087293368, 0.000001587443)
( 0.001945612898, 0.000000000000)

(-0.001947221674, 0.000036655808)
( 0.000006678272,-0.000000461971)
(-0.000059187286, 0.000000000000)

Many thanks for your help in advance and best regards


Michael