Dear Nicki and Sridhar, Thanks a lot for your replies! I think you are right that the imaginary omega leads to the negative lambda.
Best regards, Yours Ding-Fu 2015-02-12 22:23 GMT+08:00 Sridhar Sadasivam <[email protected]>: > 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 <[email protected]> > 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 <[email protected]>: >> >>> 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: [email protected] >>> 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* >>> >>> >>> >>> >>> _______________________________________________ >>> Pw_forum mailing >>> [email protected]http://pwscf.org/mailman/listinfo/pw_forum >>> >>> >>> >> >> >> -- >> >> >> *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: [email protected] <[email protected]>* >> >> _______________________________________________ >> Pw_forum mailing list >> [email protected] >> http://pwscf.org/mailman/listinfo/pw_forum >> > > > _______________________________________________ > Pw_forum mailing list > [email protected] > http://pwscf.org/mailman/listinfo/pw_forum > -- *Dingfu Shao, Ph.D Candidate* *Institute of Solid State Physics* *Chinese Academy of Sciences* *P. O. Box 1129* *Hefei 230031* *Anhui Province* *P. R. China* *Email: [email protected] <[email protected]>*
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