[QE-users] How to extract the px, py, pz, dz2, ....contributions with SOC from projdos out

[Elio Physics]

Dear Thomas,

Thank you for the generous and detailed answer. Indeed, what made me confused is that some papers still use the terminology "dz2' ,for example, even in the presence of the SOC. I will definitely be looking at the papers you suggested to decide which option I will adopt for the discussion I need.

Regards

________________________________
From: Thomas Brumme <tbrumme at msx.tu-dresden.de>
Sent: Sunday, July 4, 2021 10:24 AM
To: Quantum ESPRESSO users Forum <users at lists.quantum-espresso.org>; Elio Physics <Elio-Physics at live.com>
Subject: Re: [QE-users] How to extract the px, py, pz, dz2, ....contributions with SOC from projdos out


Dear Elie,


The short answer is: You can't!


Spin-orbit interaction couples the orbital angular momentum with the spin momentum and thus neither l or s are good quantum number anymore. You now have to use the total angular momentum J. Sure, a lot of people still use the nomenclature from the non-SOC calculations, such as speaking in the case of 2D TMDCs of dz² states at the K point, but strictly speaking this is not correct. If you really want to understand the relation between J and L in detail, I can recommend the paper by Andrea Dal Corso and Adriano Mosca Conte, Phys. Rev. B 71, 115106 (2005) (https://link.aps.org/doi/10.1103/PhysRevB.71.115106) which nicely shows which spherical harmonics are included in which spin-angle functions for which total angular momentum j. If I remember this correctly (some time ago that I did this and I can't find the table anymore) the states with higher mj (+-3/2 and +- 5/2) have more in-plane character for both j=3/5 and j=5/2 (i.e., the contain terms with spherical harmonics which are usually combined such that the result is in the xy-plane) while the states with mj=+-1/2 have more out-of-plane character (z direction). But I could be wrong here since I don't have the details anymore.


The only option for you - if you don't want to check the paper or if this is too much and if nobody else comments here - is to do a non-SOC calculation and then hope that SOC is not mixing states too much and you can still call the result, e.g., dz² like. OR you plot the corresponding wave function in real space and decide by "looking" at the form of |psi|².


Regards


Thomas



P.S.: another detail concerning, e.g., the states at K in a WS2 monolayer - is this your system? :)

The states are not simple split into spin up and spin down even if a lot of people use this nomenclature. For the valence band the two SOC-split bands are to nearly 100% spin up or down but not for the conduction band where you won't have states which are 100% up or down, even if there is no in-plane contribution... Some details can also be found here: https://link.aps.org/doi/10.1103/PhysRevB.101.235408


On 7/4/21 6:52 AM, Elio Physics wrote:
Dear all,

I am studying the contribution of the orbitals to the bands of a structure, in the presence of spin orbit coupling. At the beginning of the projwfc.x output file, I got:

     state #   1: atom   1 (S  ), wfc  1 (l=0 j=0.5 m_j=-0.5)
     state #   2: atom   1 (S  ), wfc  1 (l=0 j=0.5 m_j= 0.5)
     state #   3: atom   1 (S  ), wfc  2 (l=1 j=0.5 m_j=-0.5)
     state #   4: atom   1 (S  ), wfc  2 (l=1 j=0.5 m_j= 0.5)
     state #   5: atom   1 (S  ), wfc  3 (l=1 j=1.5 m_j=-1.5)
     state #   6: atom   1 (S  ), wfc  3 (l=1 j=1.5 m_j=-0.5)
     state #   7: atom   1 (S  ), wfc  3 (l=1 j=1.5 m_j= 0.5)
     state #   8: atom   1 (S  ), wfc  3 (l=1 j=1.5 m_j= 1.5)
.
.
.
      state #  39: atom   5 (W ), wfc  3 (l=2 j=1.5 m_j=-1.5)
     state #  40: atom   5 (W), wfc  3 (l=2 j=1.5 m_j=-0.5)
     state #  41: atom   5 (W), wfc  3 (l=2 j=1.5 m_j= 0.5)
     state #  42: atom   5 (W), wfc  3 (l=2 j=1.5 m_j= 1.5)
     state #  43: atom   5 (W ), wfc  4 (l=2 j=2.5 m_j=-2.5)
     state #  44: atom   5 (W ), wfc  4 (l=2 j=2.5 m_j=-1.5)
     state #  45: atom   5 (W), wfc  4 (l=2 j=2.5 m_j=-0.5)
     state #  46: atom   5 (W), wfc  4 (l=2 j=2.5 m_j= 0.5)
     state #  47: atom   5 (W), wfc  4 (l=2 j=2.5 m_j= 1.5)

The l=1 wavefunctions are the p contributions. But How can we specifically identify which one is px, py and pz?
Similary, how to identify which ones of the 10 d orbitals are the dz^2 for example

regards

Elie
Federal Universiy of Rondonia
Brazil



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