Re: [Phonopy-users] Whether the eigenvector in the band.yaml is equal to the eα?

[<ji...@ma...>]

Thank you, Huang.







-----原始邮件-----
发件人:"Zhishuo Huang" <zhi...@gm...>
发送时间:2024-09-05 21:18:40 (星期四)
收件人: "pho...@li..." <pho...@li...>
主题: Re: [Phonopy-users] Whether the eigenvector in the band.yaml is equal to the eα?


Dear Jiang, 


I can make a commit about the eigenvectors. 


The dynamic matrix in your email is define with the mass-weighted coordinates, which is for the convenience of the derivation.
The diagonalization of these dynamic matrice gives the phonon frequencies, of which the eigenvector should be mass weighted. 
In phonopy, the yaml file contains mass-weighted one, which is the product of 1/M1/2 and the polarization vector (real displacement the atoms moves). 


You can check the orthonormal of these eigenvectors at each q (or for one supercell in phonopy).
Mass-weighted eigenvectors should be orthonormal, while for the polarization vectors (non-mass-weighted), they are not orthogonal to each other. 


Hope it is clear. 


Best regards
Zhishuo Huang 


From: jiangb--- via Phonopy-users <pho...@li...>
Sent: 05 September 2024 16:54
To: pho...@li... <pho...@li...>
Cc: ji...@ma... <ji...@ma...>
Subject: [Phonopy-users] Whether the eigenvector in the band.yaml is equal to the eα?
 

Dear Prof. Atsushi Togo,

 

I am writing this email to ask for your help. 

 

I use the phonopy to calculate the phonon and its eigenvector. However, I don't know whether the eigenvector in the band.yaml is equal to the eα (eβ) denoted as below .  Some tutorials treat the eα as the product of the eigenvector in the band.yaml and the 1/M1/2.  Which one is right? 

 

And the axis of the eigenvector in the band.yaml confused me as well. The eigenvector in the band.yaml is along the xyz axis or along the a,b,c axis?




Jiang