[Wien] Differences in band character plotting using two methods under rotated local basis

[Peter Blaha]

Hi,

First of all, the method using   x qtl   is the method of choice, 
although I admit that I would have thought that   x lapw2 with modified 
rot.loc. should give identical results. I would need to test myself.

Second: Are you using the latest version ?

Your sequence :
 > x lapw1 -p -band
 > x lapwso -p
 > x lapw2 -p -so -band -qtl (on the unmodified highest symmetry loc rot
 > matrix)
 > x qtl -p -so -band (which rewrites case.qtl based on the axes in 
case.inq)

is correct and also the   x qtl step has the proper   -band switch.
This should direct the "hidden"  x lapw2 -fermi step also to have -band 
included and thus it should not produce an error.

Could you please check   :log

You should see the sequence of these calculations including the relevant 
switches.  Please check if your   lapw2  -fermi  step has the -band 
option propagated.

Best regards
Peter Blaha

Am 14.10.2024 um 07:46 schrieb Yichen Zhang:
> Dear WIEN2k developers and users,
> 
> Recently, I'm trying to plot the band characters in a 45 deg locally 
> rotated xy basis. I'm using WIEN2k 23.2. Following previous mails, there 
> are two ways of doing that.
> 1) Directly modifying the local rotation matrix in case.struct, right 
> before x lapw2 -band -qtl.
> 2) Using the qtl programme.
> 
> I attempted both ways, but noticed that the results are different.
> 
> Firstly, for method 1), the local rotation matrix for all atoms 
> corresponding to the local point group symmetry was
> 0.0000000 1.0000000 0.0000000
> 0.0000000 0.0000000 1.0000000
> 1.0000000 0.0000000 0.0000000
> Essentially, it swapped xyz a bit. (The system is orthorhombic, so this 
> default loc rot matrix has changed the y to z, which happens to be the z 
> direction I wanted for consistency with experimental definition of out- 
> of-plane in ARPES.) In order to project px and py orbitals on 45 deg 
> rotated xy axes. I changed the loc rot matrix to
> 0.7071068 0.7071068 0.0000000
> 0.0000000 0.0000000 1.0000000
> 0.7071068 - .7071068 0.0000000
> (Notice that this 45 deg basis is an arbitrary basis for the space 
> group, as a and b are inequivalent in the orthorhombic structure.)
> 
> Then for method 2), I changed the case.inq file (originally with loro=0) 
> to the following:
> -9.0      3.0       Emin  Emax
>      4                  number of atoms
>      1 -2 0 2        iatom, qsplit, symmetrize, locrot
> 4      0 1 2 3     nL, l-values
> 0. 1. 0.
> 1. 0. 1.
>      2 -2 0 2        iatom, qsplit, symmetrize, locrot
> 3      0 1 2        nL, l-values
> 0. 1. 0.
> 1. 0. 1.
>      3 -2 0 2        iatom, qsplit, symmetrize, locrot
> 3      0 1 2        nL, l-values
> 0. 1. 0.
> 1. 0. 1.
>      3 -2 0 2        iatom, qsplit, symmetrize, locrot
> 3      0 1 2        nL, l-values
> 0. 1. 0.
> 1. 0. 1.
> My ISPLIT in case.struct is 8 for QSPLIT=-2 to refer to.
> To get the band character plot from this case.inq file, I couldn't find 
> very detailed documentation. The way I attempted was after SOC converged 
> SCF, I ran
> x lapw1 -p -band
> x lapwso -p
> x lapw2 -p -so -band -qtl (on the unmodified highest symmetry loc rot 
> matrix)
> x qtl -p -so -band (which rewrites case.qtl based on the axes in case.inq)
> Due to running band structure after SCF and the lapw2 -fermi included in 
> x qtl, it would report a FERMI error saying number of k points 
> inconsistent when reading kgen and asking to check IN1 and KGEN files. 
> This issue has been discussed before in the mailing list due to running 
> band structure before x qtl. Despite the error in lapw2, qtl finished 
> successfully and provided an updated qtl file from the qtl programme.
> 
> Therefore, my first question is: is there a way to avoid this error in 
> using qtl for band character calculation? If I hadn't done lapw1 for 
> band structure, qtl would tend to use the SCF klist which is not the 
> band structure path I wanted from klist_band. However, to have qtl 
> running along klist_band, the lapw2 -fermi error becomes inevitable due 
> to getting eigenenergies and eigenvectors of the band structure klist 
> first? For now, I cannot find a way to avoid this error under the 
> current implemented workflow of  "x qtl". Is there a better way to do this?
> 
> My second question is: when I compare the results from the two methods, 
> they are different. The qtl results seem to be more consistent with 
> ARPES observation of px and py orbitals under different light 
> polarization. In this qtl with symmetrization=0 (as used above), one 
> diagonal is pure px and the other diagonal is pure py. This is what we 
> expected from the isolated local layer. (Certainly, symmetrization=1 in 
> the case.inq would destroy this result). While for the method 1) of 
> directly modifying the loc rot matrix in case.struct, the results still 
> show certain px and py imbalances between two diagonals, but with much 
> mixing. So why are they different? Does x lapw2 -band -qtl have some 
> sort of symmetrization that mixes the 45 deg rotated x and y axes? I 
> briefly looked into the code but only found symmetrization programme 
> used in lapw2 for spin-polarized calculation, which is irrelevant here.
> 
> Just for clarity, considering the whole crystal, the two diagonals are 
> equivalent. I projected the orbitals to a 45 deg off basis just to see 
> the local orbital texture as the local layer is rotated 45 deg. 
> Therefore, when one goes from one diagonal to the other, px naturally 
> becomes py in the 45 rotated xy basis. That's why x qtl results with 
> clean-cut px py projections seem more natural to me, but results from x 
> lapw2 under modified loc rot matrix in the case.struct file seem a bit 
> confusing to me.
> 
> Looking forward to hearing comments and to finding out if I have done 
> something wrong here.
> 
> Best regards
> Yichen
> 
> -- 
> Yichen Zhang
> Department of Physics and Astronomy
> Rice University
> 6100 Main St., Houston, TX 77005-1892
> Email: zycforphysics at gmail.com <mailto:zycforphysics at gmail.com>
> 
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-- 
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Peter Blaha,  Inst. f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-158801165300
Email: peter.blaha at tuwien.ac.at
WWW:   http://www.imc.tuwien.ac.at      WIEN2k: http://www.wien2k.at
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