[QE-users] discontinuities in phonon band and 2D phonon bandstructure

[Stefano Baroni]

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

On 17 Jun 2024, at 14:31, EDUARDO ARIEL MENENDEZ PROUPIN <emenendez at us.es> wrote:

Rijan,
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.

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).
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.

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

1970 Rep. Prog. Phys. 33 149
(http://iopscience.iop.org/0034-4885/33/1/304)

Hope it helps,

Eduardo A. Menéndez Proupin
Departamento de Física Aplicada I
Universidad de Sevilla
Teléfono: +34 9554 20231
https://personal.us.es/emenendez/
https://personal.us.es/emenendez/docencia/

________________________________




Message: 4
Date: Mon, 17 Jun 2024 11:22:37 +0200
From: Lorenzo Paulatto <lorenzo.paulatto at cnrs.fr<mailto:lorenzo.paulatto at cnrs.fr>>
To: <users at lists.quantum-espresso.org<mailto:users at lists.quantum-espresso.org>>
Subject: Re: [QE-users] discontinuities in phonon band and 2D phonon
        bandstructure
Message-ID: <1794c32e-54ae-49b5-9590-e7890a70ceaf at cnrs.fr<mailto:1794c32e-54ae-49b5-9590-e7890a70ceaf at cnrs.fr>>
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Hello,

that is the non-analytical contribution to the LO-TO split. You have to
keep in mind that Gamma is actually infinity, and you can go to infinity
in many different ways. The theory is in X. Gonze, J.-C. Charlier, D.C.
Allan, and M.P. Teter Phys. Rev. B 50, 13035 (1994)


kind regards


On 13/06/2024 21:57, Karkee, Rijan via users wrote:
> Dear QE users,
>
> I am seeing discontinuity in phonon bandstructure at Gamma. Is there a
> way to get rid of this or is this trying to tell something?
>
> Also, like for electronic band calculation in pw.x? (using crystal_c
> or tpiba_c) is there a way to have 2D plot of phonon dispersion?
>
> Thanks for your suggestions.
>
>
> Best
> Rijan
>
> LANL
>

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