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Dear Thomas,</div>
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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.</div>
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Regards<br>
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<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Thomas Brumme <tbrumme@msx.tu-dresden.de><br>
<b>Sent:</b> Sunday, July 4, 2021 10:24 AM<br>
<b>To:</b> Quantum ESPRESSO users Forum <users@lists.quantum-espresso.org>; Elio Physics <Elio-Physics@live.com><br>
<b>Subject:</b> Re: [QE-users] How to extract the px, py, pz, dz2, ....contributions with SOC from projdos out</font>
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<p style="margin-top: 0px; margin-bottom: 0px;"><font size="+1">Dear Elie,</font></p>
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<p style="margin-top: 0px; margin-bottom: 0px;"><font size="+1">The short answer is: You can't!</font></p>
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</font></p>
<p style="margin-top: 0px; margin-bottom: 0px;"><font size="+1">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 dzē 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) (<a class="x_moz-txt-link-freetext" href="https://link.aps.org/doi/10.1103/PhysRevB.71.115106">https://link.aps.org/doi/10.1103/PhysRevB.71.115106</a>) 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</font><font size="+1"><font size="+1"> for both j=3/5 and j=5/2</font> (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.</font></p>
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</font></p>
<p style="margin-top: 0px; margin-bottom: 0px;"><font size="+1">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., dzē like. OR you plot the corresponding wave function in real space and decide by "looking" at the form of |psi|ē.</font></p>
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<p style="margin-top: 0px; margin-bottom: 0px;"><font size="+1">Regards</font></p>
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<p style="margin-top: 0px; margin-bottom: 0px;"><font size="+1">Thomas</font></p>
<p style="margin-top: 0px; margin-bottom: 0px;"><font size="+1"><br>
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</font></p>
<p style="margin-top: 0px; margin-bottom: 0px;"><font size="+1">P.S.: another detail concerning, e.g., the states at K in a WS2 monolayer - is this your system? :)</font></p>
<p style="margin-top: 0px; margin-bottom: 0px;"><font size="+1">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:
<a class="x_moz-txt-link-freetext" href="https://link.aps.org/doi/10.1103/PhysRevB.101.235408">
https://link.aps.org/doi/10.1103/PhysRevB.101.235408</a><br>
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<div class="x_moz-cite-prefix">On 7/4/21 6:52 AM, Elio Physics wrote:<br>
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<span style="font-family:Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">Dear all,</span>
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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:</div>
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state # 1: atom 1 (S ), wfc 1 (l=0 j=0.5 m_j=-0.5)
<div> state # 2: atom 1 (S ), wfc 1 (l=0 j=0.5 m_j= 0.5)</div>
<div> state # 3: atom 1 (S ), wfc 2 (l=1 j=0.5 m_j=-0.5)</div>
<div> state # 4: atom 1 (S ), wfc 2 (l=1 j=0.5 m_j= 0.5)</div>
<div> state # 5: atom 1 (S ), wfc 3 (l=1 j=1.5 m_j=-1.5)</div>
<div> state # 6: atom 1 (S ), wfc 3 (l=1 j=1.5 m_j=-0.5)</div>
<div> state # 7: atom 1 (S ), wfc 3 (l=1 j=1.5 m_j= 0.5)</div>
<span> state # 8: atom 1 (S ), wfc 3 (l=1 j=1.5 m_j= 1.5)</span></div>
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<span>.</span></div>
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<span>.</span></div>
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<span> state # 39: atom 5 (W ), wfc 3 (l=2 j=1.5 m_j=-1.5)
<div> state # 40: atom 5 (W), wfc 3 (l=2 j=1.5 m_j=-0.5)</div>
<div> state # 41: atom 5 (W), wfc 3 (l=2 j=1.5 m_j= 0.5)</div>
<div> state # 42: atom 5 (W), wfc 3 (l=2 j=1.5 m_j= 1.5)</div>
<div> state # 43: atom 5 (W ), wfc 4 (l=2 j=2.5 m_j=-2.5)</div>
<div> state # 44: atom 5 (W ), wfc 4 (l=2 j=2.5 m_j=-1.5)</div>
<div> state # 45: atom 5 (W), wfc 4 (l=2 j=2.5 m_j=-0.5)</div>
<div> state # 46: atom 5 (W), wfc 4 (l=2 j=2.5 m_j= 0.5)</div>
<span> state # 47: atom 5 (W), wfc 4 (l=2 j=2.5 m_j= 1.5)</span></span></div>
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The l=1 wavefunctions are the p contributions. But How can we specifically identify which one is px, py and pz?
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Similary, how to identify which ones of the 10 d orbitals are the dz^2 for example</div>
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regards<br>
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Elie</div>
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Federal Universiy of Rondonia<br>
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<span style="font-family:Calibri,Helvetica,sans-serif; font-size:12pt; color:rgb(0,0,0)">Brazil</span><br>
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<pre class="x_moz-signature" cols="72">--
Dr. rer. nat. Thomas Brumme
Theoretical chemistry
TU Dresden - BAR / II49
Helmholtzstr. 18
01069 Dresden
Tel: +49 (0)351 463 40844
email: <a class="x_moz-txt-link-abbreviated" href="mailto:thomas.brumme@tu-dresden.de">thomas.brumme@tu-dresden.de</a></pre>
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