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

Dingfu Shao dingfu.shao at gmail.com
Thu Feb 12 02:54:38 CET 2015

```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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