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Dear Guido,<br>
<br>
no problem! Input is welcome and I also wanted to know if my
reasoning is wrong and in this case more people can help better -
it's like the "Ask the Audience" joker in "Who wants to be a
millionaire" :D<br>
<br>
The spin expectation values can be calculated for each k point like
in a text book. The expectation value of the Pauli matrices with the
spinor wave functions.<br>
And I use this to get a Hamiltonian consisting of the Pauli matrices
and with k-dependent prefactors. But the length of the spin vector
(i.e., the vector with the 3 expectation values Sx, Sy, Sz) is not
1/2 but 0.468 in the TMD heterostructure at and close to the
conduction-band minimum. I expected 1/2 like in the first system I
calculated.<br>
<br>
That's why I was thinking if only the length of the spin vector for
the whole band is 1/2... How to do the averaging in this case? Or is
it due to SOC and only the total angular momentum makes sense? How
to define this for a band and not an atom?<br>
<br>
Concerning the actual calculation: this is done in
PP/src/compute_sigma_avg.f90 and seems to be correct... Or is there
something missing in the PAW case which is not important for US-PP?<br>
<br>
Thomas<br>
<br>
<div class="moz-cite-prefix">On 1/23/20 3:37 PM, Guido Menichetti
wrote:<br>
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<div>Dear Thomas,</div>
<div><br>
</div>
<div><span lang="en"><span title="">sorry if I intrude on the
conversation.</span></span></div>
<div><span lang="en"><span title=""><br>
</span></span></div>
<div><span lang="en"><span title="">How do you evaluate the DFT
expectation values for Sx, Sy, Sz from QE?</span></span></div>
<div><span lang="en"><span title="">Could the discrepancy arise
from the way it is calculated?<br>
</span></span></div>
<div><span lang="en"><span title=""><br>
</span></span></div>
<div><span lang="en"><span title="">Regards,</span></span></div>
<div><span lang="en"><span title="">G.</span></span></div>
</div>
<br>
<div class="gmail_quote">
<div dir="ltr" class="gmail_attr">Il giorno gio 23 gen 2020 alle
ore 15:22 Thomas Brumme <<a
href="mailto:thomas.brumme@uni-leipzig.de"
moz-do-not-send="true">thomas.brumme@uni-leipzig.de</a>>
ha scritto:<br>
</div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Hey
Lorenzo,<br>
<br>
the "problem" is actually more complex and it is not a real
problem but <br>
something I thought about and maybe I'm just missing
something.<br>
<br>
I calculate the band structure for some 2D systems including
SOC and <br>
want to fit a model to the spin state such that I can extract
SOC <br>
parameters. First order would be Rashba-type SOC but 2nd and
3rd order <br>
is something else which also depends on the local symmetry.
For one <br>
system this works without problems. Then I wanted to transfer
the ideas <br>
and my "code" to a heterobilayer of TMDs and there it sort of
works but <br>
there is one problem:<br>
<br>
In order to fit the model, I first fit a generic Pauli
Hamiltonian (to <br>
which the model is fitted) - in this way the code can be
easily adapted <br>
to other local symmetries because only the 2nd stage needs to
be <br>
changed. Anyways, in the Pauli Hamiltonian I assume that the
spin is 1/2 <br>
- an electron or hole. Yet, the DFT expectation values for Sx,
Sy, Sz do <br>
not result in a spin of 1/2 (for the TMD heterostructure) but
a little <br>
bit less, 0.468, and this value is too different from 1/2 to
say it is <br>
numerical noise. And then I thought that, well, spin is not a
good <br>
quantum number and I would need the total angular momentum. Or
do I need <br>
to calculate the spin expectation values for the whole BZ and
then a <br>
single band would add up to 1/2? Is it OK to just, lets say,
use S^2 = <br>
0.468 instead of 1/2 and say that this is due to SOC?<br>
<br>
Regards<br>
<br>
Thomas<br>
<br>
On 1/23/20 12:36 PM, Lorenzo Paulatto wrote:<br>
> Hello Thomas,<br>
> if I remember correctly, the fact that the spin does not
commute with <br>
> the Hamiltonian mean that the spin can be:<br>
> 1. k-point dependent, you do not have spin-up and
spin-down bands <br>
> which can be separated<br>
> 2. aligned along any direction, instead of just Z<br>
><br>
> I think, but am not 100% sure, that if J is a good
quantum number for <br>
> isolated atoms with mean-field interacting electrons,
this is not true <br>
> for bulk crystals (what is L in the bulk?)<br>
><br>
> With the options of bands.x setting lsigma=.true. you can
plot the <br>
> spin projected over x y and z and do some kind of
color-codes plot of <br>
> the bands<br>
><br>
> cheers<br>
><br>
><br>
><br>
> On 22/01/2020 16:57, Thomas Brumme wrote:<br>
>> Dear all,<br>
>><br>
>> I tried to find something in the archive but was not
successful.<br>
>><br>
>> In noncollinear calculations I can plot the spin
expectation values <br>
>> using bands.x.<br>
>> Those are calculated using the standard Pauli
matrices. Yet, spin is <br>
>> not a good<br>
>> quantum number anymore once I have SOC. Thus, I
actually have to look <br>
>> at the<br>
>> total angular momentum, J. Is it possible to get the
expectation <br>
>> values of J?<br>
>> Does it make sense at all to think about implementing
it?<br>
>><br>
>> Regards<br>
>><br>
>> Thomas<br>
>><br>
><br>
<br>
-- <br>
Dr. rer. nat. Thomas Brumme<br>
Wilhelm-Ostwald-Institute for Physical and Theoretical
Chemistry<br>
Leipzig University<br>
Phillipp-Rosenthal-Strasse 31<br>
04103 Leipzig<br>
<br>
Tel: +49 (0)341 97 36456<br>
<br>
email: <a href="mailto:thomas.brumme@uni-leipzig.de"
target="_blank" moz-do-not-send="true">thomas.brumme@uni-leipzig.de</a><br>
<br>
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<div>***************************************<br>
<div><br>
Guido Menichetti<br>
Post-Doc researcher in
Condensed matter physics<br>
Istituto Italiano di
Tecnologia<br>
Theory and technology of 2D
materials<br>
Address: Via Morego, 30, 16163
Genova<br>
Email: <span><a
href="mailto:guido.menichetti@iit.it"
target="_blank"
moz-do-not-send="true">guido.menichetti@iit.it</a></span></div>
<div> <a
href="mailto:guido.menichetti@df.unipi.it"
target="_blank"
moz-do-not-send="true">guido.menichetti@df.unipi.it</a>
<br>
<a
href="mailto:menichetti.guido@gmail.com"
target="_blank"
moz-do-not-send="true">menichetti.guido@gmail.com</a></div>
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<pre class="moz-signature" cols="72">--
Dr. rer. nat. Thomas Brumme
Wilhelm-Ostwald-Institute for Physical and Theoretical Chemistry
Leipzig University
Phillipp-Rosenthal-Strasse 31
04103 Leipzig
Tel: +49 (0)341 97 36456
email: <a class="moz-txt-link-abbreviated" href="mailto:thomas.brumme@uni-leipzig.de">thomas.brumme@uni-leipzig.de</a>
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