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

Which version of abinit are you using? There are 3 versions of the 
nmsq_gam routine, depending on whether you sum over bands or not and 
whether you do the scalar product with the eigvec or not (one combination 
is missing for the moment: no sum over bands but do the scalar product). 
nmsq_gam.F90 is the case where no summing is done.

http://www.abinit.org/package/robodoc_5.4.4/17ddb/nmsq_gam_F90.html#robo_top_of_doc

In all cases a temporary array, with summed and scalar producted matrix 
elements, is made to output Matteo's QPT averages, which do not have any 
interpolation etc...

> gkk_qpt_tmp and the gkq_1band output, and these two matrix are related with:
>
>              gkk_qpt_tmp = eigvec * gkq_1band * eigvec+
>
>     I got puzzled for this representation. The gkq_1band matrix is already
> multiplied with reduced phonon displacement matrix displ_red,  and  what's
> the meaning of  this multiply-again operation? Is it an unit transform?
Do you mean the second *eigvec? The gkk_qpt_tmp are actually a matrix 
which is closer to the phonon linewidths. These are related to the mat 
elem squared, hence the double "vector matrix vector" product. A second 
reason is just a basis change to cartesian coordinates (see below as 
well), where an interpolation can be done consistently: the phonon 
eigenvectors change from q to q' and can not be used in any simple way to 
interpolate.

>  Also, when I check these two gkk matrix, I found that the gkq_1band
> satisfies the symmetry induced selection rule while gkk_qpt_tmp does not.
> For example, for a (5,5) CNT, phonon mode 60 at Gamma point is with A1g
> representation of D10h group, and related el-ph scattering selection rule is
> that intraband scattering should be allowed and interband scattering should
> be forbbiden. In gkq_1band, this selection rule is well satisfied( means
> that gkq_1band(ib1,ib1,ibranch=60,q=3*0.0) is much larger than
> gkq_1band(ib1,ib2,ibranch=60,q=3*0.0)), while in gkk_qpt_tmp, which is
> multiplied with eigvectors of phonon,  the  result is  just  opposite,
> gkk_qpt_tmp(ib1,ib1,ibranch=60,q=3*0.0) is  much  smaller  than  other

That should be impossible: the whole subroutine is looping over ib1 ib2, 
so if the diagonal elements are large they should stay larger, no? What 
may be confusing the analysis is that the matrix multiplication takes you 
to cartesian coordinates, and not to phonon-eigenmode space, so the 
identification of the irrep is not straightforward. Later in the code 
(mkph_linwid after the Fermi surface averaging in integrate_gamma) the 
gamma matrices (remember ~ phonon linewidths) are diagonalized, which 
should restore the symmetry groups. This would be an interesting test.

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