[Wien] parity using x irrep

[Jan Richter]

Dear Wien2K users,


I am calculating the band structure of a Bi2Te3 slab.  The structure is inversion symmetric and I have spin-orbit coupling on.  I would like to calculate the parity of each of the band up to Fermi level for a collection of eight different K-points (the Time Reversal Invariant Momentum or TRIM points).  While I have successfully set and run a calculation for the TRIM points, I am confused by the output.

The overall symmetry of the lattice as determined by Wien2K is

> Supercell                               
>  H    lattice
>  Symmorphic crystal with inversion symmetry
>  Complex eigenfunctions
>  Spin-orbit eigenfunctions (->time inversion)
>  No spin-polarization
> 
> 
>  Transformations:
>  From k-list in lapw1 to Cartesian coord. system (BR1)
>  1.1547 0.5774 0.0000
>  0.0000 1.0000 0.0000
>  0.0000 0.0000 1.0000
> 
>  From k-list in lapw1 to prim. reciprocal space  (DB1)
>  1.0000 0.0000 0.0000
>  0.0000 1.0000 0.0000
>  0.0000 0.0000 1.0000


The irrep program produces the following output for the gamma point .  I have a few questions.

1.  First I would like to know the parity of the band.  I see that for example, the first band is a combination of two irreps G5+ and G6+ from which I assume the parity is 1 (correct) based upon the product of the characters of the "I" class.  Is this correct?

2.  For band 3, the irreps are given as "??" .  What happened?  Is there something I can do to find the correct character?

3. For band 5, I can see an apparently error message STOP: X= .....   I am going out on a limb here, but I suspect that something went wrong.  Any ideas of what -- and even better how to fix it.

4. I have spin-orbit coupling on so I thought the bands would become non-degenerate, but the degeneracy is still listed (ndg) as two.  Why is this?



I have included a struct file for those interested.  Thanks for any help in advance.

> knum =  1    kname= GAMMA     
> k = 0.000000 0.000000 0.000000
> 
>        The point group is D3d
>        12 symmetry operations in  6 classes
>        Table 55   on page  58 in Koster  et al [7]
>        Table 42.4 on page 371 in Altmann et al [8]
> 
>                    E   2C3   3C2     I  2IC3  3IC2                                      
>        G1+   A1g   1     1     1     1     1     1  
>        G2+   A2g   1     1    -1     1     1    -1  
>        G3+   Eg    2    -1     0     2    -1     0  
>        G1-   A1u   1     1     1    -1    -1    -1  
>        G2-   A2u   1     1    -1    -1    -1     1  
>        G3-   Eu    2    -1     0    -2     1     0  
>        --------------------------------------------
>        G4+   E1/2g 2     1     0     2     1     0  
>        G5+  1E3/2g 1    -1     i     1    -1     i  
>        G6+  2E3/2g 1    -1    -i     1    -1    -i  
>        G4-   E1/2u 2     1     0    -2    -1     0  
>        G5-  1E3/2u 1    -1     i    -1     1    -i  
>        G6-  2E3/2u 1    -1    -i    -1     1     i  
> 
> 
> bnd ndg  eigval     E         2C3         3C2           I        2IC3        3IC2   
>   1  2 -2.435193 2.00+0.00i -2.00+0.00i  0.00+0.00i  2.00+0.00i -2.00+0.00i  0.00+0.00i =G5+ + G6+ 
>   3  2 -2.434907 1.99+0.00i -1.99+0.00i  0.00+0.00i -1.99+0.00i  1.99+0.00i  0.00+0.00i ??
>   5  2 -2.431910 1.98+0.00i  0.99+0.00i -0.01+0.00i  STOP: X=( 0.01176 0.00000) Xold=(-0.00515 0.00000)



---------------------------------------------------------------------------------------------------
Dr. Jan Richter

Functional Nano-Phase-Change (FUNPC) Research
Nanoelectronics Research Institute (NRI) 
National Institute for Advanced Industrial Science and Technology (AIST)
AIST Central 4, Higashi 1-1-1
Tsukuba, Ibaraki, Japan 305-8562

tel: +81-298-61-2221
fax: +81-298-51-2902
email: jan.richter at aist.go.jp
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