about the real-space matrices for C2y in the example of kdotp-symmetry

[Heng Gao]

Hi Xiangru,

I have asked the same question to Dominik.  Please see the following reply from him. I hope it will be helpful.

1. The symmetry operations are given with respect to the reduced coordinate system, with the basis being the one described in eq. (2). While C2y is obviously [-1 0 0 ; 0 1 0 ; 0 0 -1 ] in cartesian coordinates, this transforms to [ 0  1 0 ; 1 0 0; 0 0 -1]. The matrix T = [[a, -a, -c], [b, b, 0], [0, 0, d]] transforms from reduced to cartesian coordinates. So to get the C2y matrix in reduced coordinates you need to compute the basis transformation
    
    C_2y_reduced = T^-1 C_2y_cartesian T

The same is also done for the other symmetries, but only mirror and rotation change under the basis transformation.

Best,
Heng



Heng Gao
Ph.D. candidate
Department of Physics, and 
International Centre for Quantum and Molecular Structures, 
Shanghai University,
99 Shangda Road, Shanghai, 200444 China
E-mail: gaoheng1015 at shu.edu.cn
 
From: xiangru kong
Date: 2017-10-19 04:30
To: z2pack
Subject: about the real-space matrices for C2y in the example of kdotp-symmetry
Dear Dominik,

What is the basis for the the real-space matrices for C2y in the example of kdotp-symmetry?

In my opinion,  the real-space matrices for C2y should be reasonable for diag{-1,1,-1}.


Thanks 
Xiangru Kong


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