[QE-users] [External Email] Re: orbital character order with spin-orbit coupling

[Hari Paudyal]

Dear  Thomas Brumme,

Thank you for the explanation, I really appreciate it.

Sincerely,
Hari Paudyal
Binghamton University, SUNY

On Wed, Nov 10, 2021 at 3:59 AM Thomas Brumme <tbrumme at msx.tu-dresden.de>
wrote:

> 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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