Symmetry in dielectric tensor

[mingjian]

Hello,

I've followed the `Dielectric properties of SiC` tutorial to compute both the IPA and RPA dielectric functions. In the OUTCAR of the IPA calculation, six components (xx, yy, zz, yz, zx, and xy) are provided for both the real and imaginary parts, respectively. In the OUTCAR of the RPA calculation, a generic 3x3 matrix is printed (with both real and imaginary parts). I've a couple of questions:

1. In the IPA calculation, we should treat the tensor as a symmetric (not Hermitian) matrix, right? Also, are the off-diagonal components symmetrized , e.g. yz := (yz + zy)/2 ?
2. In the RPA calculation, since the full matrix is given, can I expect it to be a generic complex matrix? I mean non-symmetric or non-Hermitian?

I am asking these questions because I am interested in magneto-optic properties (e.g. https://en.wikipedia.org/wiki/Magneto-optic_effect). In this case, the dielectric tensor can be a generic matrix due to the internal magnetic field (which breaks time-reversal symmetry), without the need of an external magnetic field.

3. If the IPA and RPA calculations are impossible to explore such effects, any other suggestions?

Thanks!

[merzuk.kaltak]

Dear mingjian,

regarding your first and second questions:

The implemented formula for the imaginary part of the dielectric function when using LOPTICS is a hermitian matrix in the spatial indices α and β. Due to the connection with the Kramers-Kroenig transformation, the real part of the dielectric function is also hermitian in α, β.
The same holds true for the dielectric function in the RPA. Here the function is again symmetric in α, β. To see this you have to take the G=0=G' component of χ and write the limit q->0 limit as qe_α, where e_α indicates the spatial unit vector in α direction. This essentially gives you again a hermitian matrix in α, β.

[merzuk.kaltak]

Concerning your third question,

Indeed you can calculate this effect using VASP. You have to calculate the current-current response function using spin-orbit coupling, essentially setting LOPTICS=T and LSORBIT=T. The main theory is explained in this paper.
In the attachment you find Nikolaus Kandolf's master thesis, who reproduced the results from figure 3 of the paper.