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

[Yichen Zhang]

Dear Lukasz and Gavin,

Thank you very much for directing me to a previous discussion on QTL quantization axis for Y_lm orbitals. I learned more about how to possibly get the complex coefficient from there.

For my case regarding band character plot in x qtl, it is very clear to check if px py and pz are along the right directions. Since two are similar in plane p orbitals, one is out-of-plane for this layered case. In-plane px and py will also have very distinct diagonal dependence if the basis is correctly rotated by 45 deg due to the local layer structure. So I get the results that we expected and are reasonable from x qtl.

I was aware of the QTL technical report. I have read it again to improve my basic understandings, especially regarding the improvement on the cross terms < L | X | L’>. 

My main problem is related with lapw2, since it doesn’t give what was expected. I learned that it averages within the MULT loop, but I’m not sure if it also rotates the local rotation matrix of equivalent atoms according to the symmetry operation that connects the equivalent atoms. If this is true, that could explain why there is px-py mixing in lapw2 under 45 rotated xy basis. But I cannot find the corresponding code that does this for now due to my limited understanding. For isolated atom without symmetrization (as done in the previous x qtl results), one should expect only px for one diagonal and only py for the other 90 deg off diagonal under the 45 rotated xy basis, even though the two diagonals are equivalent in the whole crystal structure BZ. This is what I obtained in x qtl, but not in lapw2 (due to the MULT loop averaging I currently don’t understand very well).

I have also sent the corresponding files to Peter for checking potential user errors.

It would be nice for me to find out if the 45 rotated xy local basis (x’y’) is rotated again when evaluating the other equivalent atom within the MULT loop, which is connected by a 2 fold axis along x. Then the x’y’ would be averaged with y’x'. (I could still be wrong here)

Thank you so much for all these comments and suggestions.

Best regards
Yichen