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Phonon-photon interactions are related, but by no means necessary to understand the origin of the LO-TO splitting, which is exclusively due to the long range nature of the Coulomb interaction. SB<br id="lineBreakAtBeginningOfMessage">
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<div>On 17 Jun 2024, at 14:31, EDUARDO ARIEL MENENDEZ PROUPIN <emenendez@us.es> wrote:</div>
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Rijan, </div>
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You may find discontinuities in the phonon dispersion when approaching the Gamma point from different directions in non-cubic systems. I would be surprised if your system has cubic symmetry. The discontinuities and the LO-TO splitting are due to the non-analytic
term as Lorenzo has already explained.</div>
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I just want to add that the non-analytic term appears because, for low wavevector, the phonon dispersion law crosses, in fact avoids crossing, with the dispersion law of light. The excitations that propagate in a crystal for a wavevector near Gamma are polaritons
(phonons coupled with light or excitons coupled with light). </div>
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The dispersion law of polaritons does not have discontinuities. The phonon dispersion law computed by Quantum ESPRESSO for small wavevector is valid for as long as the wavevector q is much larger than the wavector of light with the same frequency as the phonon,
i.e. q>>n\omega/c, n being the index of refraction. </div>
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A basic theory of polaritons in cubic crystals is found in solid-state physics books like the great one from Grosso and Pastori-Parravicini, and also the classic from Ashcroft&Mermin if I remember well. The theory of phonon-polaritons in anisotropic crystals
is well explained in this article by Ruppin and Englman and references therein</div>
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1970 Rep. Prog. Phys. 33 149<br>
(<a href="http://iopscience.iop.org/0034-4885/33/1/304">http://iopscience.iop.org/0034-4885/33/1/304</a>)</div>
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Hope it helps,</div>
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Eduardo A. Menéndez Proupin</div>
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Message: 4<br>
Date: Mon, 17 Jun 2024 11:22:37 +0200<br>
From: Lorenzo Paulatto <<a href="mailto:lorenzo.paulatto@cnrs.fr">lorenzo.paulatto@cnrs.fr</a>><br>
To: <<a href="mailto:users@lists.quantum-espresso.org">users@lists.quantum-espresso.org</a>><br>
Subject: Re: [QE-users] discontinuities in phonon band and 2D phonon<br>
bandstructure<br>
Message-ID: <<a href="mailto:1794c32e-54ae-49b5-9590-e7890a70ceaf@cnrs.fr">1794c32e-54ae-49b5-9590-e7890a70ceaf@cnrs.fr</a>><br>
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Hello,<br>
<br>
that is the non-analytical contribution to the LO-TO split. You have to<br>
keep in mind that Gamma is actually infinity, and you can go to infinity<br>
in many different ways. The theory is in X. Gonze, J.-C. Charlier, D.C.<br>
Allan, and M.P. Teter Phys. Rev. B 50, 13035 (1994)<br>
<br>
<br>
kind regards<br>
<br>
<br>
On 13/06/2024 21:57, Karkee, Rijan via users wrote:<br>
> Dear QE users,<br>
><br>
> I am seeing discontinuity in phonon bandstructure at Gamma. Is there a<br>
> way to get rid of this or is this trying to tell something?<br>
><br>
> Also, like for electronic band calculation in pw.x? (using crystal_c<br>
> or tpiba_c) is there a way to have 2D plot of phonon dispersion?<br>
><br>
> Thanks for your suggestions.<br>
><br>
><br>
> Best<br>
> Rijan<br>
><br>
> LANL<br>
><br>
<br>
**************************************</div>
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<div style="margin: 0px;"><font class="Apple-style-span"><span style="font-size: 12px;">Stefano Baroni - Trieste — </span><a href="http://stefano.baroni.me" style="color: rgb(0, 0, 0); font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-decorations-in-effect: none; -webkit-text-stroke-width: 0px;">http://stefano.baroni.me</a><span style="font-size: 12px;"> </span></font></div>
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