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]
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