[Pw_forum] Is the phonon line-width gamma positive for a instable mode with negative freqency?

[Sridhar Sadasivam]

Dear Ding-Fu,
As Nicki pointed out, omega(q,v) is imaginary for unstable modes. So
omega^2 is negative and hence lambda is negative.

If you look at the definition of electron-phonon matrix element g, it
contains a sqrt(omega(q,v)) in the denominator. Thus |g|^2 contains
omega(q,v) in the denominator. And this omega(q,v) cancels with the other
omega(q,v) in the formula for gamma. I think this is the reason, that gamma
is still positive for unstable modes.

Sridhar
Graduate Student
Purdue University

On Thu, Feb 12, 2015 at 8:46 AM, Dingfu Shao <dingfu.shao at gmail.com> wrote:

> Dear Ion,
>
>       Thanks for your reply.  Now I understand it.
>
> Best regards,
>
> Yours Ding-Fu Shao
>
>
> 2015-02-12 15:44 GMT+08:00 Ion Errea <ion.errea at ehu.eus>:
>
>>  Dear Ding-Fu,
>>
>> Considering that the g contains a omega(q,v)^-1/2, gamma(q,v) is
>> independent of the phonon frequency and, thus, always positive.
>>
>> On the contrary, calculating lambda for a mode with imaginary frequencies
>> makes no sense, as the crystal is unstable in the harmonic approximation.
>>
>> Bests,
>>
>> Ion Errea
>>
>> Donostia International Physics Center (DIPC),
>> Manuel de Lardizabal Pasealekua 4,
>> 20018 Donostia-San Sebastián, Basque Country, Spain
>>
>> Email:  ion.errea at ehu.eus
>> Tel:    +34 943 01 54 23
>> Fax:    +34 943 01 56 00
>> Web:    http://ionerrea.wordpress.com/
>>
>> 12/02/15 02:54(e)an, Dingfu Shao igorleak idatzi zuen:
>>
>>  Dear QE developers and users,
>>
>>        When calculating the electron-phonon coupling, the phonon
>> line-width gamma is defined as
>> gamma(q,v) = 2 * pi * omega(q,v) * sum( |g|^2) * delta(E_q) *
>> delta(E_(k+q)).  (1)
>>
>>  And the electron-phonon coupling strength for mode v at q is
>>
>>  lambda(q,v) = gamma(q,v) / (pi * h * N(E_F) * (omega(q,v))^2)
>> (2).
>>
>>  (See
>> http://www.quantum-espresso.org/wp-content/uploads/Doc/ph_user_guide/node12.html
>> )
>>
>>  Accoding to these definitions, it seems that the  phonon line-width
>> gamma(q,v), electron-phonon coupling strength  lambda(q,v) must be BOTH
>> negative when a instable mode with negetive frequency omega(q,v) is
>> calculated.
>>
>>  However, I checked the electron phonon coupling I calculated before, I
>> found with a  negetive omega(q,v), there are negative lambda(q,v) and
>> positive gamma(q,v). I found some similar report, for example, PHYSICAL
>> REVIEW B 86, 155125 (2012), in which the positive gammas were calculated
>> for the instable mode.
>>
>>  That  realy puzzles me. Can anybody explain it?
>>
>>  Thanks a lot!
>>
>>  Best regards,
>>  yours
>>  Ding-Fu Shao
>>
>>
>>
>>
>>
>>
>> --
>>
>>
>> *Ding-Fu Shao, Ph.D *
>>
>> *Institute of Solid State Physics*
>>
>> *Chinese Academy of Sciences*
>>
>> *P. O. Box 1129*
>>
>> *Hefei 230031*
>>
>> *Anhui Province*
>>
>> *P. R. China*
>>
>>
>>
>>
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>>
>>
>
>
> --
>
>
> *Ding-Fu Shao, Ph.D *
>
> *Institute of Solid State Physics*
>
> *Chinese Academy of Sciences*
>
> *P. O. Box 1129*
>
> *Hefei 230031*
>
> *Anhui Province*
>
> *P. R. China*
>
> *Email: dingfu.shao at gmail.com <dingfu.shao at gmail.com>*
>
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