[Pw_forum] problem of Bi2Se3 with spin orbit coupling parity analysis at TRIM points

[Andrea Dal Corso]

On Mon, 2017-05-29 at 19:31 +0800, balabi wrote:
> Thank you so much for reply.
> 
> 
> I thought nosym is just used for preventing additional k points to be
> generated. The documentation doesn't say that  nosym will make
> symmetry analysis fail.
> 
> 
> Besides, I rerun the calculation, turning off nosym. But There comes
> another problem.
> 
> 
> A partial output of bands.x now for gamma point is below
> 
> 
> Band symmetry, D_3d (-3m)  double point group:
> 
> 
>      e(  1 -  4) =    -16.63750  eV     4   --> G_5+  L_4+     
>      e(  1 -  4) =    -16.63750  eV     4   --> G_6+  L_5+     
>      e(  1 -  4) =    -16.63750  eV     4   --> G_5-  L_4-     
>      e(  1 -  4) =    -16.63750  eV     4   --> G_6-  L_5-     
>      e(  5 -  6) =    -16.62527  eV     2   --> G_4+  L_6+     
>      e(  7 -  8) =    -16.62265  eV     2   --> G_4-  L_6-     
>      e(  9 - 10) =    -13.66107  eV     2   --> G_4-  L_6-     
>      e( 11 - 12) =    -13.65905  eV     2   --> G_4+  L_6+     
>      e( 13 - 14) =    -13.64175  eV     2   --> G_4+  L_6+     
>      e( 15 - 16) =    -13.63940  eV     2   --> G_5+  L_4+
> 
> 
The number is the degeneracy of the band. In this case there are four
degenerate bands and their symmetry is G_5+ + G_6+ + G_5- + G_6-. 
Sometimes the bands are more degenerate than predicted by group theory
due to time reversal (the additional degeneracy due to time reversal is
not analyzed by the routine). In other cases there might also be some
accidental degeneracy.
In any case the reducible representation is correctly decomposed in
terms of its irreducible representations. 

HTH,

Andrea

> Previously I thought the number right before the arrow means
> duplication of the same symmetry. But the above output make this
> assumption false. What does number 4 mean in " e(  1 -  4) =
>  -16.63750  eV     4   --> G_5+  L_4+"??
> And since the e(1-4) four bands each has different symmetry, why don't
> they write like this
> 
> 
> e(  1 -  1) =    -16.63750  eV     1   --> G_5+  L_4+     
> e(  2 -  2) =    -16.63750  eV     1   --> G_6+  L_5+     
> e(  3 -  3) =    -16.63750  eV     1   --> G_5-  L_4-     
> e(  4 -  4) =    -16.63750  eV     1   --> G_6-  L_5-  
> 
> 
> Thank you for helping
> 
> 
> 
> 
> 
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-- 
Andrea Dal Corso                    Tel. 0039-040-3787428
SISSA, Via Bonomea 265              Fax. 0039-040-3787249
I-34136 Trieste (Italy)             e-mail: dalcorso at sissa.it