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

[Thomas Brumme]

Hey Lorenzo,

There are definitely regions in the BZ where the spin is restricted to 
certain directions but away from these high-symmetry points (or lines) 
it is pointing in different directions. For example at the K point it 
needs to point in the z direction. And I see this in the results - 
expectation values of Sx and Sy are zero and Sz is 0.47. But 0.47 for an 
s=1/2 particle? This is what I don't understand but which might be due 
to SOC (I thought)... But then, why it is like this in a TMD 
heterostructure but not in HfNCl (same BZ) where I see 0.499?

Thomas

On 1/23/20 4:25 PM, Lorenzo Paulatto wrote:
>>     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. 
>
> I'm not an expert in this subject, but I see it like this: you want to 
> isolate a quasi-particle band, which is more or less equivalent that 
> getting its Wannier function.  When doing a non-collinear calculation, 
> Wannier functions are spinors.
>
> It could be possible, for your case, to compute this Wannier function 
> and see if its spin angle turns out to be constant, e.g. because of 
> symmetry reason or dimensionality. (See Wannier90 example 17 or 18)
>
> cheers
>
>
>

-- 
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