The change of sign might simply be a phase change. Since wave functions can change by a phase (exp(i phi)) and are still the same wave functions, also the corresponding momentum matrix elements might show this.

About the abrupt change of the matrix elements I can only speculate: There are 2 bands crossing (either in VB or CB) and the wave function changes character .... ???

Did you check your band structure ?

Am 29.11.2016 um 17:16 schrieb Yong Woo Kim:
Dear Wien2k users,

Hello, I am running wien version 14.2 on linux compiled with gfortran.

Right now I am trying to calculate the momentum matrix elements of Al2O3 
sapphire.
I have managed to get some results but some part of the results worry me that I 
may have done it wrong.
I am particularly interested in the matrix elements between the highest valence 
and the lowest conduction band.

The following is part of the results that I have obtained along the Gamma-A 
direction that I want to obtain the results for.

36      37      -0.475170000000000      2.31369000000000e-11    
0.464830760000000
36      37      -0.475054000000000      2.33653000000000e-11    
0.464900790000000
36      37      -0.474937000000000      2.35933000000000e-11    
0.464971500000000
36      37      0.474819000000000       -2.38216000000000e-11   
0.465042880000000
36      37      0.474699000000000       -2.40493000000000e-11   
0.465114930000000
36      37      0.474579000000000       -2.42775000000000e-11   
0.465187660000000
36      37      -0.474457000000000      2.45054000000000e-11    
0.465261060000000
36      37      0.474334000000000       -2.47330000000000e-11   
0.465335140000000
36      37      -0.474210000000000      2.49604000000000e-11    
0.465409880000000
36      37      0.474085000000000       -2.51880000000000e-11   
0.465485300000000
36      37      0.473959000000000       -2.54153000000000e-11   
0.465561390000000
36      37      0.473832000000000       -2.56427000000000e-11   
0.465638150000000
36      37      -0.473704000000000      2.58700000000000e-11    
0.465715590000000
36      37      -7.66604000000000e-13   -8.84059000000000e-18   
0.465756180000000
36      37      1.32939000000000e-11    -3.78270000000000e-19   
0.465793770000000
36      37      -6.20312000000000e-13   -1.29951000000000e-17   
0.465831680000000
36      37      -6.78245000000000e-12   -2.77438000000000e-17   
0.465869910000000
36      37      1.13307000000000e-11    -2.48713000000000e-17   
0.465908460000000
36      37      -2.17293000000000e-12   5.12272000000000e-17    
0.465947330000000
36      37      7.86763000000000e-12    -1.91488000000000e-17   
0.465986520000000

36 and 37 are the band index for my valence and conduction band. Each row 
refers to a k point along the G-A path and I have 501 rows in total.

I also eliminated the x,y components and leaved only the z component plus the 
energy difference.

One minor concern is that the signs of the values change and this doesn't seem 
to be right.

Another concern is that as can be seen from the real part of z above, the value 
suddenly drops to less than 1e-10 order.

Although not shown here, at the same k point, the real part of the x component 
showed the opposite behaviour,

increasing from less that 1e-10 to about 0.4. This abrupt change doesn't seem 
to be right either.

The procedure went like this.

run_lapw

create case.klist_band

x lapw2 -fermi

x lapw1 -band

x optic

I have tried this for different k mesh by using x kgen and run_lapw repeatedly 
from 1000 to 15000 and the results only had minor differences.

Any help would be really appreciated.

Thank you very much in advance.

Yong Woo Kim



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