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

[Hari Paudyal]

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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