[Wannier] Wannier Digest, Vol 148, Issue 6

[Stepan Tsirkin]

Dear Sayantika,

Regarding your questions I can comment the following:

(1)It is true that a quasi-2D material can have non-zero in-plane orbital moment. It strictly vanishes only for completely materials that are delta-localized in the plane. The confusion probably comes from the fact that the equation for m_x involves derivative over kz, and there is no actually k_z in the quasi-2D material.
However, for a (quasi)2D material this derivative should be understood as the position operator: \hat{z}=i\partial_{k_z}. Note that in the lab calculation, if your slab is thick enough and the the energies E_k and wavefunctions \Psi_k do not depend on kz, the Bloch waves |u>=\Psi*exp(-ik*r) do depend on kz, and hence \partial_{kz}|u>=-i*z*|u> . So it is not that trivial that you were missing. The gyrotropic_box parameter defines a box in k-space, and may be used to calculate a contribution of a specific part of the BZ, e.g. a specific Fermi pocket. But it is not related to the question that you raised.

(2) Yes,  gyrotropic-K_spin.dat contains the contribution  of spin only. That should be added to the orbital part. The spin part may (but does to have to) have the opposite sign to the orbital contribution. That was the case for the valence band of tellurium, as we showed in our paper. Also I now noticed that the typos in the user manual: The chapter 13, describing gyrotropic module, refers to "berry_task". That's wrong, it should be "gyrotropic_task" . I will fix this soon on github.

Also in case if you are not very happy with the speed of the calculation, you might have a look at wannier-berri project:https://github.com/stepan-tsirkin/wannier-berri  which has that functionality and improved performance. For any questions about it please contact me directly.

If you have any further questions, feel free to ask.

Stepan Tsirkin
University of Zurich
stepan.tsirkin at uzh.ch

On 14.05.20 12:00, wannier-request at lists.quantum-espresso.org wrote:
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>     1. Queries regarding gyrotropic module (Sayantika Bhowal)
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> ----------------------------------------------------------------------
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> Message: 1
> Date: Wed, 13 May 2020 11:34:22 -0500
> From: Sayantika Bhowal <sayantika.bhowal31j at gmail.com>
> To: wannier at lists.quantum-espresso.org
> Subject: [Wannier] Queries regarding gyrotropic module
> Message-ID:
> 	<CA+C9_dAdnM=SzcWGofpH5bSeVfTvQ3KwEX1QzBWXffMx2+7SyQ at mail.gmail.com>
> Content-Type: text/plain; charset="utf-8"
>
> Hi All,
>
> I am using the gyrotropic module in wannier90 to compute the response K of
> the kinetic magnetoelectric effect. I have the following questions:
>
> (1) For 2D material, the orbital moment is expected to be along the
> z-direction, so it is expected that components such as Kxy would be zero.
> But in the calculation, I find that it has some small but non-zero value.
> Is it due to the fact that the materials are not strictly 2D (but
> quasi-2D)? Is it possible to avoid this problem with a suitable choice of
> gyrotropic_box? Sorry if I am missing something trivial.
>
> (2) For the spin part, I just want to be sure if case-gyrotropic-K_spin.dat
> file contains only the spin contribution (not the spin+orb contribution) to
> K when the berry_task = -spin. Is this correct? Also, why the spin part
> appears with a -ve sign?
> Any comments or suggestions would be helpful.
> Thank you in advance,
>
> Sincerely,
> Sayantika  Bhowal