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 >
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