[Pw_forum] LO-TO splitting in dynmat.x

[xirainbow]

Dear Professor Stefano:
Thanks very much for your patient instruction.
I will read your mentioned paper carefully.
And now, I imagine that the phonon dispersion near Gamma point may look
like:

                                ^ Frequency
                                 |
                                 |
            *@@@@@* |*@@@@@**    **LO*
                                 |
                                 |
*           **$$$$$$$$$**@$$$$$$$$$   TO*
                                 |
  <-----------------------|------------------------->
                          Gamma         wavevector near Gamma

When q->0, there is  LO-TO splitting.
When q=0,  q has no direction. Therefore, optical modes can not be
classified into longitude or transverse ones. As a result, at q=0,  *$*=*@.*
However, there is not infinite crystal; and electric-static interaction
always occurs for finite crystal.
Therefore, in experiment, LO-TO splitting exists at the q=0.

On Fri, Apr 29, 2011 at 3:16 PM, Stefano de Gironcoli <degironc at sissa.it>wrote:

>  the electristatic interaction at the origin of LO-TO splitting is always
> present...
>
> for any q<>0 (even very small) it is included in the calculation.
>
> in the limit of q->0 in non-metallic systems it gives origin to a non
> analytic behavior that must be calculate separately.
>
> If you want to Fourier interpolate the phonon dispersions calculated on a
> regular grid of q-points
> you are in trouble because non analyticity of the phonon dispersion implyes
> long-range (1/R^3) interatomic force constants and so you need to
>
> 1) evaluate Z* and epsilon_infty in the limit of q->0 that determine the
> non-analyticity
> 2) remove from dynamical matrix in every q point in you grid an
> electrostatic model that gives the correct non-analyticity for q->0 and is
> smooth elsewhere
> 3) Fourier interpolate  the modified (hopefully short-range) dynamical
> matrices
> 4) add back the model in any q-point you want to study.
>
> This is what the sequence ph.x -> q2r.x -> matdyn.x does (in example06 for
> instance)
>
> thete is some discussion of these issues in Review of Modern Physics 73,
> 515 (2001) and in Phys Rev 43, 7231 (1991)
>
> stefano
>
> On 04/29/2011 05:05 AM, xirainbow wrote:
>
> Dear Eyvaz:
> Thank you very much;)
>
>
>  Is there LO-TO splitting far away from Gamma point?
> No.
>
>
>  Does LO-TO splitting must disappear at the boundary of Brillouin zone?
>
>
>
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-- 
____________________________________
Hui Wang
School of physics, Fudan University, Shanghai, China
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