[QE-users] orbital character order with spin-orbit coupling

[Thomas Brumme]

Dear Hari Paudyal,

in case of SOC, the orbital quantum number is not a good quantum number 
anymore and you
have to use the total angular momentum. Thus, strictly speaking there is 
no pz-state anymore.
Yet, if you work through the details of spin-orbit coupling and the 
details given in this
publication which - I think - describes the implementation in QE:

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.71.115106

you will understand that the pz mixes with other states and that the SOC 
states with a large
contribution of pz-character are those with m_j = +- 1/2 for both j = 
5/2 and j = 3/2

Cheerio

Thomas Brumme


P.S.: Signing your email with your affiliation is highly recommended.


On 11/9/21 10:01 PM, Hari Paudyal via users wrote:
> Hi experts,
>
> Can anyone help me to identify pz, px, py characters in the spin-orbit 
> coupling (SOC) band projection?
>
> It is well explained without SOC, the order will be pz, px, py as 
> follows (in my calculation for Se atom)
> ......
>      state #  12: atom   2 (Se ), wfc  2 (l=1 m= 1)
>      state #  13: atom   2 (Se ), wfc  2 (l=1 m= 2)
>      state #  14: atom   2 (Se ), wfc  2 (l=1 m= 3)
> .....
>
> However, with SOC, it shows as follows based on j = l+s, and j = l-s, 
> where s = 0.5
> ....
>      state #  23: atom   2 (Se ), wfc  2 (l=1 j=1.5 m_j=-1.5)
>      state #  24: atom   2 (Se ), wfc  2 (l=1 j=1.5 m_j=-0.5)
>      state #  25: atom   2 (Se ), wfc  2 (l=1 j=1.5 m_j= 0.5)
>      state #  26: atom   2 (Se ), wfc  2 (l=1 j=1.5 m_j= 1.5)
>      state #  27: atom   2 (Se ), wfc  3 (l=1 j=0.5 m_j=-0.5)
>      state #  28: atom   2 (Se ), wfc  3 (l=1 j=0.5 m_j= 0.5)
>
> for l = 1 (p orbital), and s =  0.5 j = 1.5, and mj = -1.5, -0.5, 0.5, 1.5
> for l = 1 (p orbital), and s = -0.5 j = 0.5, and mj = -0.5, 0.5
> This makes sense, but which one are pz, px, and py?
>
> Sincerely,
> Hari Paudyal
>
>
>
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-- 
Dr. rer. nat. Thomas Brumme
Theoretical chemistry
TU Dresden - BAR / II49
Helmholtzstr. 18
01069 Dresden

Tel:  +49 (0)351 463 40844

email: thomas.brumme at tu-dresden.de

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