[QE-users] Expectation values of total angular momentum in SOC case

[Guido Menichetti]

Dear Thomas,

sorry if I intrude on the conversation.

How do you evaluate the DFT expectation values for Sx, Sy, Sz from QE?
Could the discrepancy arise from the way it is calculated?

Regards,
G.

Il giorno gio 23 gen 2020 alle ore 15:22 Thomas Brumme <
thomas.brumme at uni-leipzig.de> ha scritto:

> Hey Lorenzo,
>
> the "problem" is actually more complex and it is not a real problem but
> something I thought about and maybe I'm just missing something.
>
> I calculate the band structure for some 2D systems including SOC and
> want to fit a model to the spin state such that I can extract SOC
> parameters. First order would be Rashba-type SOC but 2nd and 3rd order
> is something else which also depends on the local symmetry. For one
> system this works without problems. Then I wanted to transfer the ideas
> and my "code" to a heterobilayer of TMDs and there it sort of works but
> there is one problem:
>
> In order to fit the model, I first fit a generic Pauli Hamiltonian (to
> which the model is fitted) - in this way the code can be easily adapted
> to other local symmetries because only the 2nd stage needs to be
> changed. Anyways, in the Pauli Hamiltonian I assume that the spin is 1/2
> - an electron or hole. Yet, the DFT expectation values for Sx, Sy, Sz do
> not result in a spin of 1/2 (for the TMD heterostructure) but a little
> bit less, 0.468, and this value is too different from 1/2 to say it is
> numerical noise. And then I thought that, well, spin is not a good
> quantum number and I would need the total angular momentum. Or do I need
> to calculate the spin expectation values for the whole BZ and then a
> single band would add up to 1/2? Is it OK to just, lets say, use S^2 =
> 0.468 instead of 1/2 and say that this is due to SOC?
>
> Regards
>
> Thomas
>
> On 1/23/20 12:36 PM, Lorenzo Paulatto wrote:
> > Hello Thomas,
> > if I remember correctly, the fact that the spin does not commute with
> > the Hamiltonian mean that the spin can be:
> > 1. k-point dependent, you do not have spin-up and spin-down bands
> > which can be separated
> > 2. aligned along any direction, instead of just Z
> >
> > I think, but am not 100% sure, that if J is a good quantum number for
> > isolated atoms with mean-field interacting electrons, this is not true
> > for bulk crystals (what is L in the bulk?)
> >
> > With the options of bands.x setting lsigma=.true. you can plot the
> > spin projected over x y and z and do some kind of color-codes plot of
> > the bands
> >
> > cheers
> >
> >
> >
> > On 22/01/2020 16:57, Thomas Brumme wrote:
> >> Dear all,
> >>
> >> I tried to find something in the archive but was not successful.
> >>
> >> In noncollinear calculations I can plot the spin expectation values
> >> using bands.x.
> >> Those are calculated using the standard Pauli matrices. Yet, spin is
> >> not a good
> >> quantum number anymore once I have SOC. Thus, I actually have to look
> >> at the
> >> total angular momentum, J. Is it possible to get the expectation
> >> values of J?
> >> Does it make sense at all to think about implementing it?
> >>
> >> Regards
> >>
> >> Thomas
> >>
> >
>
> --
> 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: thomas.brumme at uni-leipzig.de
>
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-- 
***************************************

Guido Menichetti
Post-Doc researcher in Condensed matter physics
Istituto Italiano di Tecnologia
Theory and technology of 2D materials
Address: Via Morego, 30, 16163 Genova
Email:  guido.menichetti at iit.it
             guido.menichetti at df.unipi.it
             menichetti.guido at gmail.com

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