<div dir="ltr"><div><div><div><div>Dear Nicki and Sridhar,<br><br></div> Thanks a lot for your replies! I think you are right that the imaginary omega leads to the negative lambda.<br><br></div>Best regards,<br><br></div>Yours<br></div>Ding-Fu<br> </div><div class="gmail_extra"><br><div class="gmail_quote">2015-02-12 22:23 GMT+08:00 Sridhar Sadasivam <span dir="ltr"><<a href="mailto:sridhu88@gmail.com" target="_blank">sridhu88@gmail.com</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr">Dear Ding-Fu,<div>As Nicki pointed out, omega(q,v) is imaginary for unstable modes. So omega^2 is negative and hence lambda is negative.</div><div><br></div><div>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. </div><div><br></div><div>Sridhar</div><div>Graduate Student</div><div>Purdue University</div></div><div class="HOEnZb"><div class="h5"><div class="gmail_extra"><br><div class="gmail_quote">On Thu, Feb 12, 2015 at 8:46 AM, Dingfu Shao <span dir="ltr"><<a href="mailto:dingfu.shao@gmail.com" target="_blank">dingfu.shao@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir="ltr"><div>Dear Ion, </div>
<div> </div>
<div> Thanks for your reply. Now I understand it.</div>
<div> </div>
<div>Best regards,</div>
<div> </div>
<div>Yours Ding-Fu Shao</div>
<div> </div><div class="gmail_extra"><br><div class="gmail_quote">2015-02-12 15:44 GMT+08:00 Ion Errea <span dir="ltr"><<a href="mailto:ion.errea@ehu.eus" target="_blank">ion.errea@ehu.eus</a>></span>:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div>
<div>Dear Ding-Fu,<br>
<br>
Considering that the g contains a omega(q,v)^-1/2, gamma(q,v) is
independent of the phonon frequency and, thus, always positive. <br>
<br>
On the contrary, calculating lambda for a mode with imaginary
frequencies makes no sense, as the crystal is unstable in the
harmonic approximation.<br>
<br>
Bests,<br>
<pre cols="72">Ion Errea
Donostia International Physics Center (DIPC),
Manuel de Lardizabal Pasealekua 4,
20018 Donostia-San Sebastián, Basque Country, Spain
Email: <a href="mailto:ion.errea@ehu.eus" target="_blank">ion.errea@ehu.eus</a>
Tel: <a href="tel:%2B34%20943%2001%2054%2023" value="+34943015423" target="_blank">+34 943 01 54 23</a>
Fax: <a href="tel:%2B34%20943%2001%2056%2000" value="+34943015600" target="_blank">+34 943 01 56 00</a>
Web: <a href="http://ionerrea.wordpress.com/" target="_blank">http://ionerrea.wordpress.com/</a> </pre>
12/02/15 02:54(e)an, Dingfu Shao igorleak idatzi zuen:<br>
</div>
<blockquote type="cite"><div><div><div><div>
<div dir="ltr">
<div>
<div>Dear QE developers and users,<br>
<br>
</div>
When calculating the electron-phonon coupling, the
phonon line-width gamma is defined as <br>
gamma(q,v) = 2 * pi * omega(q,v) * sum( |g|^2) * delta(E_q) *
delta(E_(k+q)). (1)<br>
<br>
</div>
<div>And the electron-phonon coupling strength for mode v at q
is<br>
<br>
</div>
<div>lambda(q,v) = gamma(q,v) / (pi * h * N(E_F) *
(omega(q,v))^2) (2).<br>
</div>
<div><br>
</div>
<div>(See <a href="http://www.quantum-espresso.org/wp-content/uploads/Doc/ph_user_guide/node12.html" target="_blank">http://www.quantum-espresso.org/wp-content/uploads/Doc/ph_user_guide/node12.html</a>)<br>
<br>
</div>
<div>Accoding to these<span style="color:rgb(67,67,67);font-family:Tahoma,Arial;font-size:12px;font-style:normal;font-variant:normal;font-weight:normal;letter-spacing:normal;line-height:24px;text-align:left;text-indent:0px;text-transform:none;white-space:normal;word-spacing:0px;background-color:rgb(242,242,242);display:inline!important;float:none"><span> </span></span>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.<br>
<br>
</div>
<div>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.<br>
<br>
</div>
<div>That realy puzzles me. Can anybody explain it? <br>
<br>
</div>
<div>Thanks a lot!<br>
<br>
</div>
<div>Best regards,<br>
</div>
<div>yours<br>
</div>
<div>Ding-Fu Shao<br>
</div>
<div><br>
</div>
<div> <br>
<br>
</div>
<div>
<div>
<div>
<div>
<div>
<div>
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<div>
<div>
<div><br>
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