[Pw_forum] non-cubic dielectric tensor in a cubic crystal.

[Eduardo Menendez]

 Thanks for your response Paolo.  I did exactly as you said, I used
dynmat.x . I think the asymetry comes from Eq. (2)  of Fennie&Rabe due to
having a different  frequency, or from eq (3) due to having a different
eigenvector. In fact, when I specify no direction with the vector q(i), I
get three equal frecuencies and equal components for the dielectric tensor.
Looking at the eigenvectors, I think the asymetry comes from Eq. 2. I made
a simple calculation with the following data


# mode   [cm-1]    [THz]      IR
    1     -0.00   -0.0000    0.0000
    2      0.00    0.0000    0.0000
    3      0.00    0.0000    0.0000
    4    133.01    3.9875    2.3657
    5    133.01    3.9875    2.3657
    6    154.23    4.6238    2.3657

Electronic dielectric permittivity tensor (F/m units)
        11.387818    0.000000   -0.000000
         0.000000   11.387818   -0.000000
         0.000000    0.000000   11.387818

 ... with zone-center polar mode contributions
        14.306543    0.000000    0.000000
         0.000000   15.312431   -0.000000
         0.000000   -0.000000   15.312431

     freq (    6) =       4.623845 [THz] =     154.234861 [cm-1]
 ( -0.750355   0.000000     0.000000   0.000000    -0.000000   0.000000   )
 (  0.661035  -0.000000    -0.000000   0.000000     0.000000  -0.000000   )

Only the 6th  eigenvector has component in axis 1. A very simple
calculation shows that you are right, regarding Eq (2) I just need to
correct the omega_m from 154 to 133 cm^-1

[emenendez at leftraru2 VC-relax]$ echo '11.387818+(15.312431-11.387818)'|bc -l
15.312431
[emenendez at leftraru2 VC-relax]$ echo
'11.387818+(15.312431-11.387818)*(133.01/154.23)^2'|bc -l
14.30677507068329634588

So, is this an error ?

Thank you again
Eduardo






---------- Mensaje reenviado ----------
> From: Paolo Giannozzi <p.giannozzi at gmail.com>
> To: PWSCF Forum <pw_forum at pwscf.org>
> Cc:
> Date: Mon, 11 Jan 2016 21:51:24 +0100
> Subject: Re: [Pw_forum] non-cubic dielectric tensor in a cubic crystal.
> Hi Eduardo
>
> you used dynmat.x, didn't you? the \epsilon_0 tensor is computed is
> subroutine polar_mode_permittivity of PHonon/PH/dynmat.f90. The header
> mentions a nonexistent reference (the correct page number should be 184111):
>   ! Algorithm from Fennie and Rabe, Phys. Rev. B 68, 18411 (2003)
> My guess is that the algorithm assumes TO frequencies only, but LO
> frequencies are used instead since you specified a direction for q=>0.
>
> Paolo
>
> On Mon, Jan 11, 2016 at 8:10 PM, Eduardo Menendez <eariel99 at gmail.com>
> wrote:
>
>> Hi,
>>
>> I am computing the dielectric funciton of a cubic material (CdTe).
>> I am surprised that the to see a result like this the dielectric tensor
>> below:
>>
>> # mode   [cm-1]    [THz]      IR
>>     1      0.00    0.0000    0.0000
>>     2      0.00    0.0000    0.0000
>>     3      0.00    0.0000    0.0000
>>     4    133.01    3.9875    2.3657
>>     5    133.01    3.9875    2.3657
>>     6    154.23    4.6238    2.3657
>>
>> Electronic dielectric permittivity tensor (F/m units)
>>         11.387818    0.000000   -0.000000
>>          0.000000   11.387818   -0.000000
>>          0.000000    0.000000   11.387818
>>
>>  ... with zone-center polar mode contributions
>>         14.306543    0.000000   -0.000000   (HERE IS ACKWARD)
>>          0.000000   15.312431   -0.000000
>>         -0.000000   -0.000000   15.312431
>>
>> I (guess that) undertand the first tensor above as \epsilon_{\infty}, and
>> the second tensor as \epsilon_0. Why is the first component 14.3 different
>> from the others 15.31, shouldn't it be a diagonal tensor ? 15.31 is
>> consistent with epsilon_infty and the Lyddane-Sachs-Teller formula.
>>
>> Well, I set q(1)=1, q(2)=0,q(3)=0, so I guess the component 11 is a
>> longitudinal dielectric constant. I see that changing the vector q also
>> change the tensor However, I think that for an LO phonon the electric
>> displacement is 0, so is null the longitudinal dielectric constant.
>>
>> Sorry, I did never see this in textbooks. Finally, and practically,  if
>> 14.3 is a longitudinal dielectric constant, is this the dielectric constant
>> that screens a static constant electric field ?
>>
>> Thank you,
>>
>> Eduardo Menendez Proupin
>> Departamento de Fisica, Facultad de Ciencias, Universidad de Chile
>> URL: http://www.gnm.cl/emenendez
>>
>>
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