<div dir="ltr"><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">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">thomas.brumme@uni-leipzig.de</a><br>
<br>
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</blockquote></div><br clear="all"><br>-- <br><div dir="ltr" class="gmail_signature"><div dir="ltr"><div><div dir="ltr"><span><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr"><div><div dir="ltr">
<div dir="ltr" style="font-size:12pt;color:rgb(0,0,0);font-family:Calibri,Arial,Helvetica,sans-serif">
<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">guido.menichetti@iit.it</a></span></div><div> <a href="mailto:guido.menichetti@df.unipi.it" target="_blank">guido.menichetti@df.unipi.it</a> <br> <a href="mailto:menichetti.guido@gmail.com" target="_blank">menichetti.guido@gmail.com</a></div><div><br></div>****************************************</div>
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