Dear Guido,
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
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.
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.
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?
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?
Thomas
On 1/23/20 3:37 PM, Guido Menichetti wrote:
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
<[email protected] <mailto:[email protected]>>
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: [email protected]
<mailto:[email protected]>
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Quantum ESPRESSO is supported by MaX
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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: [email protected] <mailto:[email protected]>
[email protected] <mailto:[email protected]>
[email protected] <mailto:[email protected]>
****************************************
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu/quantum-espresso)
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--
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: [email protected]
_______________________________________________
Quantum ESPRESSO is supported by MaX (www.max-centre.eu/quantum-espresso)
users mailing list [email protected]
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