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

[nicvok]

Dear Ding-Fu Shao, 

you’re right that the eph-linewidth scales linearly with the ph frequency. But, IMO, there are no negative frequencies; they are imaginary and are displayed as negative numbers for simplicity. So gamma should be positive&real or complex for „negative“ frequencies. Maybe something strange in-routine is happening when one tries to calculate gamma for non-stable modes. Not sure, just guessing.

best regards Nicki

--------------------------------------------------------
Nicki Frank Hinsche, Dr. rer. nat.
Institute of physics - Theoretical physics,
Martin-Luther-University Halle-Wittenberg,
Von-Seckendorff-Platz 1, Room 1.07
D-06120 Halle/Saale, Germany
Tel.: ++49 345 5525460
--------------------------------------------------------

> Message: 9
> Date: Thu, 12 Feb 2015 09:54:38 +0800
> From: Dingfu Shao <dingfu.shao at gmail.com>
> Subject: [Pw_forum] Is the phonon line-width gamma positive for a
> 	instable mode with negative freqency?
> To: PWSCF Forum <pw_forum at pwscf.org>
> Message-ID:
> 	<CAH0vKF03OpU17rBvjJacX11RRzP5FE=sQYAhebsCSi-t7yRBwg at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
> 
> 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*
> 
> 
> * <dingfu.shao at gmail.com>*
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