[Pw_forum] Off diagonal elements of the dielectric function using turboEELS

[Timrov Iurii]

Dear Dr. Gunnar Palsson,

> I was wondering if turboEELS or some other aspect of TDDFT generalised to extended systems can calculate the off-diagonal elements of the dielectric tensor, for instance epsilon_xy?

The turboEELS code allows one to compute the loss function -Im[1/eps(q,w)], where q is the transferred momentum, and w is the frequency. Depending on the direction of the transferred momentum q in the Brillouin zone and depending on its modulus |q|, the value of the loss function changes. The code works with finite values of q (q=0 is not allowed, but only small values of q can be considered, q->0). From the knowledge of 1/eps(q,w) it is possible to compute eps(q,w).

Conversely, the epsilon.x code works for q=0, and it allows one to compute the dielectric matrix/tensor eps_ij(q=0,w), where i and j are the Cartesian indices X,Y,Z (see notes espresso/PP/Doc/eps_man.tex).  In particular, see equation after Eq.(10), and also see Eq.(11) [in order to understand why it is a matrix and not a function]. Moreover, epsilon.x is based on the independent particle approximation, while turboEELS is based on TDDFPT which includes Hartree and exchange-correlation interactions.

Concerning your question: I am not sure, but it seems to me that if one considers the TDDFPT formalism of  turboEELS exactly at q=0 (this limit must be implemented) one should obtain the inverse and direct dielectric *matrices*. I have to admit I have never thought in detail about this. 

HTH

Regards,
Iurii

--
Dr. Iurii Timrov
Postdoctoral Researcher
Swiss Federal Institute of Technology Lausanne (EPFL)
Laboratory of Theory and Simulation of Materials (THEOS)
CH-1015 Lausanne, Switzerland
+41 21 69 34 881
http://people.epfl.ch/265334

________________________________________
From: pw_forum-bounces at pwscf.org <pw_forum-bounces at pwscf.org> on behalf of Gunnar Karl Pálsson <gunnar.karl at gmail.com>
Sent: Saturday, August 26, 2017 7:07 PM
To: PWSCF Forum
Subject: [Pw_forum] Off diagonal elements of the dielectric function using      turboEELS

Hi all,

I was wondering if turboEELS or some other aspect of TDDFT generalised to extended systems can calculate the off-diagonal elements of the dielectric tensor, for instance epsilon_xy? The reason I am interested in the off-diagonal components is for the calculation of the
Magneto-Optical Kerr rotation angle which is proportional to this quantity. If it does not, is this a straight forward extension that could be done or is
there some inherent limitation? I see that it is possible to calculate these components with epsilon.x using the 'offdiag'
flag. For cubic systems the off-diagonal elements are probably zero but in the presence of spin-orbit coupling for a magnetic
material like bcc iron it could be possible to calculate given that turboEELS has nicely been extended to metals and
can deal with spin-orbit coupling?

Best regards,

Dr. Gunnar Palsson
Researcher
Department of Physics and Astronomy
Uppsala University
Sweden
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